EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 21, Problem 2CP
Summary Introduction
To select:
A correct option for the open interest on a futures contract
Introduction:
Maintenance margin is the minimum amount of equity that a future margin account may have and usually set at 75% to 85% of the initial margin.
When a futures contract is purchased, a minimum deposit is required known as Initial margin.
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Explain in detail with an example how the change of the variables (like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration) of Black-Scholes-Merton Formula affect the price of the option.
Both call and put options are affected by the following five factors: the exercise price, the underlying stock price, the time to expiration, the stock’s standard deviation, and the risk-free rate. However, the direction of the effects on call and put options could be different.
Use the following table to identify whether each statement describes put options or call options.
Statement
Put Option
Call Option
1. When the exercise price increases, option prices increase.
2. An option is more valuable the longer the maturity.
3. The effect of the time to maturity on the option prices is indeterminate.
4. As the risk-free rate increases, the value of the option increases.
Both call and put options are affected by the following five factors: the exercise price, the underlying stock price, the time to expiration, the stock’s standard deviation, and the risk-free rate. However, the direction of the effects on call and put options could be different.
Use the following table to identify whether each statement describes put options or call options.
Statement
Put Option
Call Option
1. An option is more valuable the longer the maturity.
2. A longer maturity in-the-money option on a risky stock is more valuable than the same shorter maturity option.
3. When the exercise price increases, option prices increase.
4. As the risk-free rate increases, the value of the option increases.
Chapter 21 Solutions
EBK INVESTMENTS
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- In the Black-Scholes option pricing model, the value of a call is inversely related to: a. the risk-free interest stock b. the volatility of the stock c. its time to expiration date d. its stock price e. its strike pricearrow_forwardWhat impact does each of the followingparameters have on the value of a call option?(5) Variability of the stock pricearrow_forwardExplain in your own words what dynamic hedging is, and how a trader could profit by dynamically hedging an option if they have a forecast of volatility that is different to implied volatility.arrow_forward
- Select all that are true with respect to the Black Scholes Option Pricing Model (BSOPM) Group of answer choices When using BSOPM to value a stock option, the BSOPM assumes that stock prices follow a normal distribution. When using BSOPM to value a stock option, the BSOPM assumes that stock returns follow a normal distribution. Half of the observations in a normal distribution are above the mean and half are below the mean. Fisher Black and Myron Scholes were awarded the Nobel Prize in 1997 for their work in Option Pricing.arrow_forwardSelect all that are true with respect to the Black Scholes Option Pricing Model (OPM) in practice): Group of answer choices BSOPM assumes that the volatility of the underlying stock returns is constant over time. BSOPM assumes that the underlying stock can be traded continuously. BSOPM assumes that there are no transaction costs. There is only one input to the BSOPM that is not observable at the time you are valuing a stock option, and that input is volatility. Implied volatility is estimated by calculating the daily volatility of the underlying stock’s return that occurred over the prior six months.arrow_forwardThe below question is related to the "Financial Derivatives and Risk Management". Describe the five variables like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration that the Black-Scholes-Merton Formula uses to calculate the price of call and put options. Provide an adequate assumptions to support your explanations.arrow_forward
- We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity theorem as well as a numerical example to prove your answer.arrow_forwardWhat impact does each of the followingparameters have on the value of a call option?(1) Current stock pricearrow_forwardEquating theoretical option price and the market option price, we can solve for implied indicators. Which is appropriate to be used as a quote for option? a) Implied strike price b) Implied volatility c) Implied risk-free rate d) None of the abovearrow_forward
- My question is for a synthetic call option why do we need to borrow the present value of the strike price and what does it mean in a simple language explanation. Similarly why do we need to lend the present value of the stock at risk-free rate and what does it mean in simple language explanation? Please also clarify the significance of risk free rate? Why is it used in put call parity. Synthetic Call Option: If an investor believes that a call option is over-priced, then he/she can sell the call on the market and replicate a synthetic call. Borrow the present value of the strike price at the risk free rate and purchase the underlying stock and a put. Synthetic Put Option: Similar to the synthetic call option. A synthetic put can be created by re-arranging the put-call parity relationship, if the trader believes the put is overvalued. Synthetic Stock: A synthetic stock can also be created by rearranging the put-call parity identity. In this case, the investor will buy the…arrow_forwardVolatility smile” is referred to as evidence against the Black-Scholes model. Why is that? A) Black-Scholes model assumes that different options on a given stock have different values for implied volatility b.) Volatility of returns on one and the same stock, over one and the same future period of time, can only take one value C) Black-Scholes model generates option premium close to the observed premium if the observed stock volatility is usedarrow_forwardDescribe the five variables (Assets price, Strick price or Exercise Price, Risk- Free- Rate, Time to Expiration, Volatility) that Black-Scholes-Merton Formula uses to calculate the price of call and put options. Explain how the change in these variables (Assets price, Strick price or Exercise Price, Risk- Free- Rate, Time to Expiration, Volatility) affects the price of the option.arrow_forward
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