Chapter 15, Problem 4PS

Summary Introduction

(A)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Pay off from a call option:

The payoff from a call contract for its holder is the current price of the underlying asset less the strike price. So, lower the strike price compared to the current price of the underlying asset, higher is the value of the call option. In other words, the worth of call options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is more than the strike price. And the worth of a call option dictates the purchase price of a call option. More worthy the call option, higher will be its purchase price.

When the strike price is more than the stock price, the exercise of call option will cause negative cash flow. So, in that case, call option is not exercised and causes zero payoff.

Profit from a call option:

The profit from a call contract for its holder is the payoff from a call option less its purchase price, paid earlier.

To compute:

1. The payoff and profits for call option when strike price is $70.

Answer to Problem 4PS

The payoff and profits are $1 and -$1.02 respectively.

Explanation of Solution

Call option

Given:

Stock price (S) = $71

Strike price (X) = $70

Purchase price or premium (as given in 15.1 example) = $2.02

Calculation:

  $\begin{array}{c}Payofffrominvestment=S-X\\ =\$71-\$70\\ =\$1\\ \mathrm{Pr}ofitfrominvestment=Payofffrominvestment-Purchasepriceofoption\\ =\$1-\$2.02\\ =-\$1.02\end{array}$

Summary Introduction

(B)

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Pay off from a put option:

The payoff from a put option contract for its holder is the strike price less the current price of the underlying asset. So, higher the strike price compared to the current price of the underlying asset, higher is the value of the put option. In other words, the worth of put options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is less than the strike price. And the worth of a put option dictates the purchase price of a put option. More worthy the put option, higher will be its purchase price.

When the strike price is less than the stock price, the exercise of put option will cause negative cash flow. So, in that case, put option is not exercised and causes zero payoff.

Profit from a put option:

The profit from a put contract for its holder is the payoff from a put option less its purchase price, paid earlier.

To compute:

The payoff and profits for put option when strike price is $70.

Answer to Problem 4PS

The payoff and profits are $0 and -$0.24 respectively.

Explanation of Solution

b. Put option

Given:

Stock price (S) = $71

Strike price (X) = $70

Purchase price or premium (as given in 15.1 example) = $0.24

Calculation:

  $\begin{array}{c}Payofffrominvestment=X-S\\ =\$70-\$71\\ =0(ifS>X)\\ \mathrm{Pr}ofitfrominvestment=Payofffrominvestment-Purchasepriceofoption\\ =0-\$0.24\\ =-\$0.24\end{array}$

Summary Introduction

(C)

Call option:

A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.

Pay off from a call option:

The payoff from a call contract for its holder is the current price of the underlying asset less the strike price. So, lower the strike price compared to the current price of the underlying asset, higher is the value of the call option. In other words, the worth of call options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is more than the strike price. And the worth of a call option dictates the purchase price of a call option. More worthy the call option, higher will be its purchase price.

When the strike price is more than the stock price, the exercise of call option will cause negative cash flow. So, in that case, call option is not exercised and causes zero payoff.

Profit from a call option:

The profit from a call contract for its holder is the payoff from a call option less its purchase price, paid earlier.

To compute:

The payoff and profits for call option when strike price is $72.

Answer to Problem 4PS

The payoff and profits are $0 and -$0.67 respectively.

Explanation of Solution

c. Call option

Given:

Stock price (S) = $71

Strike price (X) = $72

Purchase price or premium (as given in 15.1 example) = $0.67

Calculation:

  $\begin{array}{c}Payofffrominvestment=S-X\\ =\$71-\$72\\ =0(ifX>S)\\ \mathrm{Pr}ofitfrominvestment=Payofffrominvestment-Purchasepriceofoption\\ =\$0-\$0.67\\ =-\$0.67\end{array}$

Summary Introduction

(D)

Put option:

A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.

Pay off from a put option:

The payoff from a put option contract for its holder is the strike price less the current price of the underlying asset. So, higher the strike price compared to the current price of the underlying asset, higher is the value of the put option. In other words, the worth of put options increases with the difference between the price of underlying asset and the strike price where the stock price of underlying asset is less than the strike price. And the worth of a put option dictates the purchase price of a put option. More worthy the put option, higher will be its purchase price.

When the strike price is less than the stock price, the exercise of put option will cause negative cash flow. So, in that case, put option is not exercised and causes zero payoff.

Profit from a put option:

The profit from a put contract for its holder is the payoff from a put option less its purchase price, paid earlier.

To compute:

The payoff and profits for put option when strike price is $72.

Answer to Problem 4PS

The payoff and profits are $1 and $0.1 respectively.

Explanation of Solution

d. Put option

Given:

Stock price (S) = $71

Strike price (X) = $72

Purchase price or premium (as given in 15.1 example) = $0.90

Calculation:

  $\begin{array}{c}\text{Payoff}\text{from}\text{investment=X-S}\\ \text{=\$72-\$71}\\ \text{=\$1}\\ \text{Profit}\text{from}\text{investment=Payoff}\text{from}\text{investment-Purchase}\text{price}\text{of}\text{option}\\ \text{=\$1-\$0}\text{.9}\\ \text{=\$0}\text{.1}\end{array}$