Requirement 1 To determine: To determine the implied standard deviation of the call at price of $8. Introduction: Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date. Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 16, Problem 30PS

Summary Introduction

Requirement 1

To determine:

To determine the implied standard deviation of the call at price of $8.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

The Standard deviation is 0.3213

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $8.

Performing the what-if analysis by setting the call option value to $8, and changing the standard deviation accordingly, we get the following data:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3213	d1	0.0089
Expiration (in years)	0.5	d2	-0.2183
Risk-free rate (annual)	0.05	N(d1)	0.5036
Stock Price	100	N(d2)	0.4136
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	10.4076

The Standard deviation for call price of $8 is 0.3213

Summary Introduction

Requirement 2

To determine:

To determine the impact on the volatility when the option sells at $9

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the option sells at $9

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $9.

Using the spreadsheet and setting the value to $9, we get

INPUTS		OUTPUTS
Standard deviation (annual)	0.3568	d1	0.0318
Expiration (in years)	0.5	d2	-0.2204
Risk-free rate (annual)	0.05	N(d1)	0.5127
Stock Price	100	N(d2)	0.4128
Exercise price	105	B/S call value	9.0000
Dividend yield (annual)	0	B/S put value	11.4075

This shows an increase in the standard deviation which is now 0.3568

With increase in the value of the option, the volatility increases. So there is an increase in the implied volatility

Summary Introduction

Requirement 3

To determine:

To determine the effect on implied volatility when the option price is $8 but expiration time is only four months

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the expiration time is reduced while keeping the option price same.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the expiration time is set to 4 months, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.4087	d1	-0.0182
Expiration (in years)	0.33333	d2	-0.2541
Risk-free rate (annual)	0.05	N(d1)	0.4927
Stock Price	100	N(d2)	0.3997
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	11.2645

This shows that implied volatility rises to 0.4087 when the option price is kept at $8 and maturity time is lowered to 4 months.

With shorter maturity, the value of the option generally decreases. To keep the value of the option the same, then the implied volatility has to increase in this scenario.

Summary Introduction

Requirement 4

To determine:

To determine the effect on implied volatility when the option price is $8 but exercise price is lowered to $100.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility decreases.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the exercise price is lowered to $100, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.2406	d1	0.2320
Expiration (in years)	0.5	d2	0.0619
Risk-free rate (annual)	0.05	N(d1)	0.5917
Stock Price	100	N(d2)	0.5247
Exercise price	100	B/S call value	8.0010
Dividend yield (annual)	0	B/S put value	5.5320

This shows that implied volatility reduces to 0.2406 when the option price is kept at $8 and exercise price is lowered to $100.

With lower exercise price, the value of call increases. But here to keep the value of the option the same, then the implied volatility has to decrease in this scenario.

Summary Introduction

Requirement 5

To determine:

To determine the effect on implied volatility when the option price is $8 but stock price is lowered to $98.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the stock price is decreased.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the stock price is lowered to $98, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3566	d1	-0.0484
Expiration (in years)	0.5	d2	-0.3006
Risk-free rate (annual)	0.05	N(d1)	0.4807
Stock Price	98	N(d2)	0.3819
Exercise price	105	B/S call value	8.0001
Dividend yield (annual)	0	B/S put value	12.4077

This shows that implied volatility increases to 0.35666 when the option price is kept at $8 and stock price is lowered to $98.

With lower stock price, the value of call decreases. But here to keep the value of the option the same, then the implied volatility has to increase in this scenario.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Write as like research paper: abstrac,litut review,model.current problem questionire,table,graph, charts, image, analysis, result,conclusion, referencce15-20 1. Provide literature as research paper" liturature review" content as journal 2. article,textbooks.current newspaper article.organizational doccument and website **citation as liturature citation reference 15-20 in liturature review content paragraph. 2. Show latest problem of current knowledge ang give a **model immage, and display show awareness of that problem and questionire. 3. Current that research methodology.show graph.table.chrts.assesment task 4. Design and Result,5. Conclution, 6. Referance 15-20 TASK DESCRIPTION Children educatio Spouse's willingn allowanc travel Spouseoverseas job assistanc Host country housing assistanc Income tax equalisati on policy Overseas health care plan Length of the foreign assignme dareer and repatriati Cross- Personali cultural compete Prior ncies internati Receptivity to Internation al…

Write in memo format a response to your Manager, based on the information presented below for the Duncan Company and also based on your additional research. Your Manager has advised you to make any assumptions where necessary. Duncan Company is a large manufacturer and distributor of cake supplies. It is based in United Kingdon (Headquarters) It sends supplies to firms throughout the United States and the Caribbean . It markets its supplies through periodic mass mailings of catalogues to those firms. Its clients can make orders over the phone and Duncan ships the supplies upon demand. The main competition for Duncan’s comes from one U.S. firm and one Canadian firm. Another British firm has a small share of the U.S. market but is at a disadvantage because of its distance. The British firm’s marketing and transportation costs in the U.S. market are relatively high. a) Duncan Company plans to penetrate either the Canadian market or two other Caribbean Countries (Jamaica and Haiti). What…

Answer of the question in the picture

Answer 2

Question

Chapter 16, Problem 30PS

Summary Introduction

Requirement 1

To determine:

To determine the implied standard deviation of the call at price of $8.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

The Standard deviation is 0.3213

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $8.

Performing the what-if analysis by setting the call option value to $8, and changing the standard deviation accordingly, we get the following data:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3213	d1	0.0089
Expiration (in years)	0.5	d2	-0.2183
Risk-free rate (annual)	0.05	N(d1)	0.5036
Stock Price	100	N(d2)	0.4136
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	10.4076

The Standard deviation for call price of $8 is 0.3213

Summary Introduction

Requirement 2

To determine:

To determine the impact on the volatility when the option sells at $9

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the option sells at $9

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $9.

Using the spreadsheet and setting the value to $9, we get

INPUTS		OUTPUTS
Standard deviation (annual)	0.3568	d1	0.0318
Expiration (in years)	0.5	d2	-0.2204
Risk-free rate (annual)	0.05	N(d1)	0.5127
Stock Price	100	N(d2)	0.4128
Exercise price	105	B/S call value	9.0000
Dividend yield (annual)	0	B/S put value	11.4075

This shows an increase in the standard deviation which is now 0.3568

With increase in the value of the option, the volatility increases. So there is an increase in the implied volatility

Summary Introduction

Requirement 3

To determine:

To determine the effect on implied volatility when the option price is $8 but expiration time is only four months

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the expiration time is reduced while keeping the option price same.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the expiration time is set to 4 months, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.4087	d1	-0.0182
Expiration (in years)	0.33333	d2	-0.2541
Risk-free rate (annual)	0.05	N(d1)	0.4927
Stock Price	100	N(d2)	0.3997
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	11.2645

This shows that implied volatility rises to 0.4087 when the option price is kept at $8 and maturity time is lowered to 4 months.

With shorter maturity, the value of the option generally decreases. To keep the value of the option the same, then the implied volatility has to increase in this scenario.

Summary Introduction

Requirement 4

To determine:

To determine the effect on implied volatility when the option price is $8 but exercise price is lowered to $100.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility decreases.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the exercise price is lowered to $100, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.2406	d1	0.2320
Expiration (in years)	0.5	d2	0.0619
Risk-free rate (annual)	0.05	N(d1)	0.5917
Stock Price	100	N(d2)	0.5247
Exercise price	100	B/S call value	8.0010
Dividend yield (annual)	0	B/S put value	5.5320

This shows that implied volatility reduces to 0.2406 when the option price is kept at $8 and exercise price is lowered to $100.

With lower exercise price, the value of call increases. But here to keep the value of the option the same, then the implied volatility has to decrease in this scenario.

Summary Introduction

Requirement 5

To determine:

To determine the effect on implied volatility when the option price is $8 but stock price is lowered to $98.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the stock price is decreased.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the stock price is lowered to $98, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3566	d1	-0.0484
Expiration (in years)	0.5	d2	-0.3006
Risk-free rate (annual)	0.05	N(d1)	0.4807
Stock Price	98	N(d2)	0.3819
Exercise price	105	B/S call value	8.0001
Dividend yield (annual)	0	B/S put value	12.4077

This shows that implied volatility increases to 0.35666 when the option price is kept at $8 and stock price is lowered to $98.

With lower stock price, the value of call decreases. But here to keep the value of the option the same, then the implied volatility has to increase in this scenario.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 16, Problem 30PS

Summary Introduction

Requirement 1

To determine:

To determine the implied standard deviation of the call at price of $8.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

The Standard deviation is 0.3213

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $8.

Performing the what-if analysis by setting the call option value to $8, and changing the standard deviation accordingly, we get the following data:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3213	d1	0.0089
Expiration (in years)	0.5	d2	-0.2183
Risk-free rate (annual)	0.05	N(d1)	0.5036
Stock Price	100	N(d2)	0.4136
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	10.4076

The Standard deviation for call price of $8 is 0.3213

Summary Introduction

Requirement 2

To determine:

To determine the impact on the volatility when the option sells at $9

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the option sells at $9

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $9.

Using the spreadsheet and setting the value to $9, we get

INPUTS		OUTPUTS
Standard deviation (annual)	0.3568	d1	0.0318
Expiration (in years)	0.5	d2	-0.2204
Risk-free rate (annual)	0.05	N(d1)	0.5127
Stock Price	100	N(d2)	0.4128
Exercise price	105	B/S call value	9.0000
Dividend yield (annual)	0	B/S put value	11.4075

This shows an increase in the standard deviation which is now 0.3568

With increase in the value of the option, the volatility increases. So there is an increase in the implied volatility

Summary Introduction

Requirement 3

To determine:

To determine the effect on implied volatility when the option price is $8 but expiration time is only four months

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the expiration time is reduced while keeping the option price same.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the expiration time is set to 4 months, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.4087	d1	-0.0182
Expiration (in years)	0.33333	d2	-0.2541
Risk-free rate (annual)	0.05	N(d1)	0.4927
Stock Price	100	N(d2)	0.3997
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	11.2645

This shows that implied volatility rises to 0.4087 when the option price is kept at $8 and maturity time is lowered to 4 months.

With shorter maturity, the value of the option generally decreases. To keep the value of the option the same, then the implied volatility has to increase in this scenario.

Summary Introduction

Requirement 4

To determine:

To determine the effect on implied volatility when the option price is $8 but exercise price is lowered to $100.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility decreases.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the exercise price is lowered to $100, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.2406	d1	0.2320
Expiration (in years)	0.5	d2	0.0619
Risk-free rate (annual)	0.05	N(d1)	0.5917
Stock Price	100	N(d2)	0.5247
Exercise price	100	B/S call value	8.0010
Dividend yield (annual)	0	B/S put value	5.5320

This shows that implied volatility reduces to 0.2406 when the option price is kept at $8 and exercise price is lowered to $100.

With lower exercise price, the value of call increases. But here to keep the value of the option the same, then the implied volatility has to decrease in this scenario.

Summary Introduction

Requirement 5

To determine:

To determine the effect on implied volatility when the option price is $8 but stock price is lowered to $98.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the stock price is decreased.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the stock price is lowered to $98, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3566	d1	-0.0484
Expiration (in years)	0.5	d2	-0.3006
Risk-free rate (annual)	0.05	N(d1)	0.4807
Stock Price	98	N(d2)	0.3819
Exercise price	105	B/S call value	8.0001
Dividend yield (annual)	0	B/S put value	12.4077

This shows that implied volatility increases to 0.35666 when the option price is kept at $8 and stock price is lowered to $98.

With lower stock price, the value of call decreases. But here to keep the value of the option the same, then the implied volatility has to increase in this scenario.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 16, Problem 30PS

Summary Introduction

Requirement 1

To determine:

To determine the implied standard deviation of the call at price of $8.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

The Standard deviation is 0.3213

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $8.

Performing the what-if analysis by setting the call option value to $8, and changing the standard deviation accordingly, we get the following data:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3213	d1	0.0089
Expiration (in years)	0.5	d2	-0.2183
Risk-free rate (annual)	0.05	N(d1)	0.5036
Stock Price	100	N(d2)	0.4136
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	10.4076

The Standard deviation for call price of $8 is 0.3213

Summary Introduction

Requirement 2

To determine:

To determine the impact on the volatility when the option sells at $9

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the option sells at $9

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $9.

Using the spreadsheet and setting the value to $9, we get

INPUTS		OUTPUTS
Standard deviation (annual)	0.3568	d1	0.0318
Expiration (in years)	0.5	d2	-0.2204
Risk-free rate (annual)	0.05	N(d1)	0.5127
Stock Price	100	N(d2)	0.4128
Exercise price	105	B/S call value	9.0000
Dividend yield (annual)	0	B/S put value	11.4075

This shows an increase in the standard deviation which is now 0.3568

With increase in the value of the option, the volatility increases. So there is an increase in the implied volatility

Summary Introduction

Requirement 3

To determine:

To determine the effect on implied volatility when the option price is $8 but expiration time is only four months

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the expiration time is reduced while keeping the option price same.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the expiration time is set to 4 months, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.4087	d1	-0.0182
Expiration (in years)	0.33333	d2	-0.2541
Risk-free rate (annual)	0.05	N(d1)	0.4927
Stock Price	100	N(d2)	0.3997
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	11.2645

This shows that implied volatility rises to 0.4087 when the option price is kept at $8 and maturity time is lowered to 4 months.

With shorter maturity, the value of the option generally decreases. To keep the value of the option the same, then the implied volatility has to increase in this scenario.

Summary Introduction

Requirement 4

To determine:

To determine the effect on implied volatility when the option price is $8 but exercise price is lowered to $100.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility decreases.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the exercise price is lowered to $100, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.2406	d1	0.2320
Expiration (in years)	0.5	d2	0.0619
Risk-free rate (annual)	0.05	N(d1)	0.5917
Stock Price	100	N(d2)	0.5247
Exercise price	100	B/S call value	8.0010
Dividend yield (annual)	0	B/S put value	5.5320

This shows that implied volatility reduces to 0.2406 when the option price is kept at $8 and exercise price is lowered to $100.

With lower exercise price, the value of call increases. But here to keep the value of the option the same, then the implied volatility has to decrease in this scenario.

Summary Introduction

Requirement 5

To determine:

To determine the effect on implied volatility when the option price is $8 but stock price is lowered to $98.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the stock price is decreased.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the stock price is lowered to $98, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3566	d1	-0.0484
Expiration (in years)	0.5	d2	-0.3006
Risk-free rate (annual)	0.05	N(d1)	0.4807
Stock Price	98	N(d2)	0.3819
Exercise price	105	B/S call value	8.0001
Dividend yield (annual)	0	B/S put value	12.4077

This shows that implied volatility increases to 0.35666 when the option price is kept at $8 and stock price is lowered to $98.

With lower stock price, the value of call decreases. But here to keep the value of the option the same, then the implied volatility has to increase in this scenario.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 16, Problem 30PS

Summary Introduction

Requirement 1

To determine:

To determine the implied standard deviation of the call at price of $8.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

The Standard deviation is 0.3213

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $8.

Performing the what-if analysis by setting the call option value to $8, and changing the standard deviation accordingly, we get the following data:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3213	d1	0.0089
Expiration (in years)	0.5	d2	-0.2183
Risk-free rate (annual)	0.05	N(d1)	0.5036
Stock Price	100	N(d2)	0.4136
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	10.4076

The Standard deviation for call price of $8 is 0.3213

Summary Introduction

Requirement 2

To determine:

To determine the impact on the volatility when the option sells at $9

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the option sells at $9

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $9.

Using the spreadsheet and setting the value to $9, we get

INPUTS		OUTPUTS
Standard deviation (annual)	0.3568	d1	0.0318
Expiration (in years)	0.5	d2	-0.2204
Risk-free rate (annual)	0.05	N(d1)	0.5127
Stock Price	100	N(d2)	0.4128
Exercise price	105	B/S call value	9.0000
Dividend yield (annual)	0	B/S put value	11.4075

This shows an increase in the standard deviation which is now 0.3568

With increase in the value of the option, the volatility increases. So there is an increase in the implied volatility

Summary Introduction

Requirement 3

To determine:

To determine the effect on implied volatility when the option price is $8 but expiration time is only four months

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the expiration time is reduced while keeping the option price same.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the expiration time is set to 4 months, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.4087	d1	-0.0182
Expiration (in years)	0.33333	d2	-0.2541
Risk-free rate (annual)	0.05	N(d1)	0.4927
Stock Price	100	N(d2)	0.3997
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	11.2645

This shows that implied volatility rises to 0.4087 when the option price is kept at $8 and maturity time is lowered to 4 months.

With shorter maturity, the value of the option generally decreases. To keep the value of the option the same, then the implied volatility has to increase in this scenario.

Summary Introduction

Requirement 4

To determine:

To determine the effect on implied volatility when the option price is $8 but exercise price is lowered to $100.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility decreases.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the exercise price is lowered to $100, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.2406	d1	0.2320
Expiration (in years)	0.5	d2	0.0619
Risk-free rate (annual)	0.05	N(d1)	0.5917
Stock Price	100	N(d2)	0.5247
Exercise price	100	B/S call value	8.0010
Dividend yield (annual)	0	B/S put value	5.5320

This shows that implied volatility reduces to 0.2406 when the option price is kept at $8 and exercise price is lowered to $100.

With lower exercise price, the value of call increases. But here to keep the value of the option the same, then the implied volatility has to decrease in this scenario.

Summary Introduction

Requirement 5

To determine:

To determine the effect on implied volatility when the option price is $8 but stock price is lowered to $98.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the stock price is decreased.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the stock price is lowered to $98, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3566	d1	-0.0484
Expiration (in years)	0.5	d2	-0.3006
Risk-free rate (annual)	0.05	N(d1)	0.4807
Stock Price	98	N(d2)	0.3819
Exercise price	105	B/S call value	8.0001
Dividend yield (annual)	0	B/S put value	12.4077

This shows that implied volatility increases to 0.35666 when the option price is kept at $8 and stock price is lowered to $98.

With lower stock price, the value of call decreases. But here to keep the value of the option the same, then the implied volatility has to increase in this scenario.

Answer 6

Chapter 16, Problem 30PS

Summary Introduction

Requirement 1

To determine:

To determine the implied standard deviation of the call at price of $8.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

The Standard deviation is 0.3213

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $8.

Performing the what-if analysis by setting the call option value to $8, and changing the standard deviation accordingly, we get the following data:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3213	d1	0.0089
Expiration (in years)	0.5	d2	-0.2183
Risk-free rate (annual)	0.05	N(d1)	0.5036
Stock Price	100	N(d2)	0.4136
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	10.4076

The Standard deviation for call price of $8 is 0.3213

Answer 7

Chapter 16, Problem 30PS

Summary Introduction

Requirement 1

To determine:

To determine the implied standard deviation of the call at price of $8.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Answer 8

Expert Solution

Answer to Problem 30PS

The Standard deviation is 0.3213

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $8.

Performing the what-if analysis by setting the call option value to $8, and changing the standard deviation accordingly, we get the following data:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3213	d1	0.0089
Expiration (in years)	0.5	d2	-0.2183
Risk-free rate (annual)	0.05	N(d1)	0.5036
Stock Price	100	N(d2)	0.4136
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	10.4076

The Standard deviation for call price of $8 is 0.3213

Answer 13

Summary Introduction

Requirement 2

To determine:

To determine the impact on the volatility when the option sells at $9

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the option sells at $9

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $9.

Using the spreadsheet and setting the value to $9, we get

INPUTS		OUTPUTS
Standard deviation (annual)	0.3568	d1	0.0318
Expiration (in years)	0.5	d2	-0.2204
Risk-free rate (annual)	0.05	N(d1)	0.5127
Stock Price	100	N(d2)	0.4128
Exercise price	105	B/S call value	9.0000
Dividend yield (annual)	0	B/S put value	11.4075

This shows an increase in the standard deviation which is now 0.3568

With increase in the value of the option, the volatility increases. So there is an increase in the implied volatility

Answer 14

Summary Introduction

Requirement 2

To determine:

To determine the impact on the volatility when the option sells at $9

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Answer 15

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the option sells at $9

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

Value of call option is $9.

Using the spreadsheet and setting the value to $9, we get

INPUTS		OUTPUTS
Standard deviation (annual)	0.3568	d1	0.0318
Expiration (in years)	0.5	d2	-0.2204
Risk-free rate (annual)	0.05	N(d1)	0.5127
Stock Price	100	N(d2)	0.4128
Exercise price	105	B/S call value	9.0000
Dividend yield (annual)	0	B/S put value	11.4075

This shows an increase in the standard deviation which is now 0.3568

With increase in the value of the option, the volatility increases. So there is an increase in the implied volatility

Answer 20

Summary Introduction

Requirement 3

To determine:

To determine the effect on implied volatility when the option price is $8 but expiration time is only four months

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the expiration time is reduced while keeping the option price same.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the expiration time is set to 4 months, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.4087	d1	-0.0182
Expiration (in years)	0.33333	d2	-0.2541
Risk-free rate (annual)	0.05	N(d1)	0.4927
Stock Price	100	N(d2)	0.3997
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	11.2645

This shows that implied volatility rises to 0.4087 when the option price is kept at $8 and maturity time is lowered to 4 months.

With shorter maturity, the value of the option generally decreases. To keep the value of the option the same, then the implied volatility has to increase in this scenario.

Answer 21

Summary Introduction

Requirement 3

To determine:

To determine the effect on implied volatility when the option price is $8 but expiration time is only four months

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Answer 22

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the expiration time is reduced while keeping the option price same.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the expiration time is set to 4 months, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.4087	d1	-0.0182
Expiration (in years)	0.33333	d2	-0.2541
Risk-free rate (annual)	0.05	N(d1)	0.4927
Stock Price	100	N(d2)	0.3997
Exercise price	105	B/S call value	8.0000
Dividend yield (annual)	0	B/S put value	11.2645

This shows that implied volatility rises to 0.4087 when the option price is kept at $8 and maturity time is lowered to 4 months.

With shorter maturity, the value of the option generally decreases. To keep the value of the option the same, then the implied volatility has to increase in this scenario.

Answer 27

Summary Introduction

Requirement 4

To determine:

To determine the effect on implied volatility when the option price is $8 but exercise price is lowered to $100.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility decreases.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the exercise price is lowered to $100, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.2406	d1	0.2320
Expiration (in years)	0.5	d2	0.0619
Risk-free rate (annual)	0.05	N(d1)	0.5917
Stock Price	100	N(d2)	0.5247
Exercise price	100	B/S call value	8.0010
Dividend yield (annual)	0	B/S put value	5.5320

This shows that implied volatility reduces to 0.2406 when the option price is kept at $8 and exercise price is lowered to $100.

With lower exercise price, the value of call increases. But here to keep the value of the option the same, then the implied volatility has to decrease in this scenario.

Answer 28

Summary Introduction

Requirement 4

To determine:

To determine the effect on implied volatility when the option price is $8 but exercise price is lowered to $100.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Answer 29

Expert Solution

Answer to Problem 30PS

Implied volatility decreases.

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the exercise price is lowered to $100, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.2406	d1	0.2320
Expiration (in years)	0.5	d2	0.0619
Risk-free rate (annual)	0.05	N(d1)	0.5917
Stock Price	100	N(d2)	0.5247
Exercise price	100	B/S call value	8.0010
Dividend yield (annual)	0	B/S put value	5.5320

This shows that implied volatility reduces to 0.2406 when the option price is kept at $8 and exercise price is lowered to $100.

With lower exercise price, the value of call increases. But here to keep the value of the option the same, then the implied volatility has to decrease in this scenario.

Answer 34

Summary Introduction

Requirement 5

To determine:

To determine the effect on implied volatility when the option price is $8 but stock price is lowered to $98.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the stock price is decreased.

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the stock price is lowered to $98, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3566	d1	-0.0484
Expiration (in years)	0.5	d2	-0.3006
Risk-free rate (annual)	0.05	N(d1)	0.4807
Stock Price	98	N(d2)	0.3819
Exercise price	105	B/S call value	8.0001
Dividend yield (annual)	0	B/S put value	12.4077

This shows that implied volatility increases to 0.35666 when the option price is kept at $8 and stock price is lowered to $98.

With lower stock price, the value of call decreases. But here to keep the value of the option the same, then the implied volatility has to increase in this scenario.

Answer 35

Summary Introduction

Requirement 5

To determine:

To determine the effect on implied volatility when the option price is $8 but stock price is lowered to $98.

Introduction:

Put option is the option which provides the option holder with the right to sell the assets or to exercise the contract but it does not give any obligation. The put option is exercised at a price which is specific or predetermined price before or on the expiration date.

Call option is the option which provides the right to the option holder to purchase the assets or right to exercise the contract. However it does not give the obligation. This option is exercised at a specific or predetermined price on the expiration date or before it.

Answer 36

Expert Solution

Answer to Problem 30PS

Implied volatility increases when the stock price is decreased.

Answer 37

Expert Solution

Answer 38

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given Information:

The spreadsheet containing the data is available in the given website.

Underlying stock sells for $100 a share and no dividend is paid. 5% is Risk free rate.

When the stock price is lowered to $98, while option price is at $8, the values are as below:

INPUTS		OUTPUTS
Standard deviation (annual)	0.3566	d1	-0.0484
Expiration (in years)	0.5	d2	-0.3006
Risk-free rate (annual)	0.05	N(d1)	0.4807
Stock Price	98	N(d2)	0.3819
Exercise price	105	B/S call value	8.0001
Dividend yield (annual)	0	B/S put value	12.4077

This shows that implied volatility increases to 0.35666 when the option price is kept at $8 and stock price is lowered to $98.

With lower stock price, the value of call decreases. But here to keep the value of the option the same, then the implied volatility has to increase in this scenario.