Question 1

A put option with 60 days to maturity,exercise price of $12.00 and the risk-free rate is 5% p.a.If a call option is trading at $2.30 and a put option with $0.06 and the current share price is $14.00,what is the arbitrage possible per contract according to put-call parity?

Accepted Answer

Using equation 16.5,put-call parity can be written as c - g = P - PV(X).We can solve for what the call price (c)should be if there is no arbitrage possible;that is: c = 0.10 + 14.00 - 11.86 = $2.24.Hence,the call option value according to put-call parity is $2.24.Therefore,the call is mispriced by $2.30 - $2.24 = $0.06,and hence the arbitrage profit per contract is $0.06.

Question 2

The premium of an American put option is generally greater than that of the European put option because:

Accepted Answer

The option premium of an American option is greater than or equal to the option premium of an otherwise identical European option.The American option can be exercised at any time up to expiration,while the European option cannot be exercised until the expiration date.This right is valuable.

Question 3

Assume a one-period world with current share price of $5.00,interest rate of 8% over the period and a price increase factor of 1.25.Given this information,the current premium on a call option with an exercise price of $4.50 using the binomial model is:

Accepted Answer

If the asset price increases,it will increase to 5 F1F1F1S1F1F1F10 1.25 = 6.25.If the asset price decreases,it will go to 5 F1F1F1S1F1F1F10 (1/1.25)= 4.80.At the up price,the option can be exercised for a profit of $6.25 - 4.50 = $1.75.At the down price,the option will be exercised for a gain of $0.30.Given the values of u = 1.25,d = 0.80 and (1 + R)= 1.08,this gives values of alpha and (1 - alpha)of 0.6222 and 0.3778 respectively.The current option premium is therefore calculated as [(0.6222 F1F1F1S1F1F1F10 1.75)+ (0.3778 F1F1F1S1F1F1F10 0.30)]/1.08 = [1.0889 + 0.1133]/1.08 = 1.1131.

Question 4

A compound option is:

Accepted Answer

A compound option is basically an option written on an option that captures the ex-dividend day effect,where a sudden large fall in price may result in optimal early exercise.Early exercise prior to the ex-dividend date will not always be optimal,and so it is the option to exercise at this time that is valuable.

Question 5

Using the Black-Scholes model,the delta of a call option is:

Accepted Answer

Looking at equation 16.26,we can see that the delta of a call option is N(d1).

Question 6

is created by combining a call option and a put option with the same time to maturity,but with the call strike price being greater than the put strike price.

Accepted Answer

This strategy tends to use out-of-the-money options,and so is somewhat cheaper to set up,though prices need to move further before either the call or the put is in-the-money.

Question 7

Assume a two-period world with a current share price of $21.00,an interest rate of 6.5% over the period,a price increase factor of 1.43 and a price decrease factor of 0.55.What are the possible end-of-period prices?

Accepted Answer

Following example 16.1,we can compute the possible end-of-period prices as follows:

Question 8

A call option with 60 days to maturity,exercise price of $12.00,underlying spot price of 14.00 p.a.is valued at $2.24.If the put option with these characteristics is trading at $0.06,at what risk-free rate will put-call parity hold? (Assume the call option premium is correctly priced and there are no dividends. )

Accepted Answer

Using equation 16.5,put-call parity can be written as c - g = P - PV(X).In this example,we can write this as 2.24 - 0.06 = 14.00 - 12/(1 + r F1F1F1S1F1F1F10 60/365).Solving for r gives 7%.

Question 9

For a call option,the rate of increase in the share price is 2%,while the rate of decrease in the share price is 1%.If the share price increases,the call price is $10.10,while the call price will be $9.95 if the share price decreases.Given this information,and that the asset price is currently $10.00 and the risk-free rate is 5% p.a. ,calculate the risk-free hedge ratio.

Accepted Answer

Using equation 16.18,we can calculate the risk-free hedge ratio as follows: hedge ratio = (10.10 - 9.95)/[(0.02 - 0.01)10] = (0.15)/1 = 0.15.

Question 10

A call option with 60 days to maturity,exercise price of $12.00,underlying spot price of $14.00 and risk-free rate of 7% p.a.is valued at $2.20.What is the value of a put option with the same characteristics? (Assume the call option premium is correctly priced and there are no dividends. )

Accepted Answer

Using equation 16.5,a put-call parity can be written as c - g = P - PV(X).In this example,we can write this as 2.20 - g = 14.00 - 12/(1+0.07 F1F1F1S1F1F1F10 60/365);that is: g = 2.20 - 14.00 + 11.86 = 0.06.Hence,the put option value due to put-call parity is $0.06.

Question 11

A combination of purchasing a call and put option with the same exercise price and time to expiry is called:

Accepted Answer

A bought straddle is formed by buying a call option and a put option,both with the same exercise price and time to expiry.

Question 12

A call option has a price of $2.50 with exercise price of $14.00 and underlying asset price of $15.00.If the time to maturity is 60 days and the risk-free return is 7% p.a. ,what is the pricing bounds error?

Accepted Answer

The lower pricing bounds for the European call option have not been breached because 2.50 > 15 - 13.84.The error is therefore 0,meaning there is no pricing bounds error.

Question 13

A put option with 60 days to maturity,exercise price of $12.00,underlying spot price of 14.00 and risk-free rate of 7% p.a.is valued at $0.10.What is the value of a call option with the same characteristics? (Assume the put option premium is correctly priced and there are no dividends. )

Accepted Answer

Using equation 16.5,put-call parity can be written as c - g = P - PV(X).In this example,we can write this as c - 0.10 = 14.00 - 12/(1+0.07 F1F1F1S1F1F1F10 60/365).That is c = 0.10 + 14.00 - 11.86 = $2.24.Hence,the call option value according to put-call parity is $2.24.

Question 14

A put option has a price of $2.50 with exercise price of $14.00 and underlying asset price of $12.00.If the time to maturity is 30 days and the risk-free return is 7% p.a. ,what is the pricing bounds error?

Accepted Answer

The lower pricing bounds for the European put option have not been breached because 2.50 > 13.92 - 12.The error is therefore 0,meaning there is no pricing bounds error.

Question 15

A call option has a price of $0.50 with exercise price of $14.00 and underlying asset price of $15.00.If the time to maturity is 60 days and the risk-free return is 7% p.a. ,what is the pricing bound error?

Accepted Answer

The lower pricing bounds for the European call option have been breached: 0.50 < 15 - 13.84.The error is therefore 1.16 - 0.50 = 0.66.

Question 16

A call option has a price of $4.50 with exercise price of $14.00 and underlying asset price of $15.00.If the time to maturity is 60 days and the risk-free return is 7% p.a. ,what is the pricing bounds error?

Accepted Answer

The lower pricing bounds for the European call option have not been breached because 4.50 > 15 - 13.84.The error is therefore 0,meaning there is no pricing bounds error.

Question 17

The most difficult parameter to estimate in the Black-Scholes model is the:

Accepted Answer

Although the Black-Scholes model requires five parameters,the most difficult parameter to estimate is the standard deviation of the underlying asset price.Asset price,exercise price,risk-free rate of return and time to expiry are observable,but standard deviation is not observable in the same way.

Question 18

Using the Black-Scholes model,the delta of a put option is:

Accepted Answer

Looking at equation 16.26,we can see that the delta of a put option is N(-d1).

Question 19

A put option with 60 days to maturity,exercise price of $12.00,and the risk-free rate is 7% p.a.If a call option is trading at $2.24 and a put option with $0.06,what is the share price that will result in put-call parity holding?

Accepted Answer

Using equation 16.5,put-call parity can be written as c - g = P - PV(X).In this example,we can write as 2.24 - 0.06 = 14.00 - P/(1+0.07 F1F1F1S1F1F1F10 60/365).Solving for P gives a spot price of $14.00.

Question 20

A put option has a price of $1.50,with exercise price of $14.00 and underlying asset price of $12.00.If the time to maturity is 30 days and the risk-free return is 7% p.a. ,what is the pricing bounds error?

Accepted Answer

The lower pricing bounds for the European put option have been breached because 1.50 < 13.92 - 12.The error is therefore 0.42.

Quiz 16: Option Contracts