Question

1. Tucker Inc. common stock currently trades for $90/share. 6-month European put options on the stock have an exercise price and premium of $93 and $4, respectively. The annual risk free rate is 2%. What should be the value of a 6-month European call option on the stock with an exercise price of $93 according to put-call parity? Round intermediate steps to four decimals and your final answer to two decimals.

a. 7.90

b. 0.065

c. 1.93

d. 2.84

e. 2.15

2. Suppose 6-month European call options with an exercise price of $93 actually have a market price of $2.15. Which of the following strategies could you employ to earn an arbitrage return?

a. Short the market call, buy the stock, buy the put and short the present value of the exercise price at the risk-free rate.

b. Buy the market call, short the stock, short the put and invest the present value of the exercise price at the risk-free rate.

c. Short the market call, buy the stock, buy the put and invest the present value of the exercise price at the risk-free rate.

d. Arbitrage is not possible.

e. None of the above.

3. Find the arbitrage profit you could earn per call option.

a. 575

b. 209

c. 69

d. 22

e. 0

I have bolded the answers I got. I just want to double check my work. If one of the answers is wrong, please let me know why. Thank you!

Answer 1

1. your first answer is correct i.e. c. 1.93.

Formula for call option premium is below:

C₀ = P₀+S₀-X*e^-r*t

C₀ = Call premium; P₀ = put premium; S₀ = underlying price; X =strike price of call option; r = risk-free rate; t = time period

C₀ = $4 + $90 - $93*e^-0.02*0.5 = $94 - $93*e^-0.01 = $94 - $93*0.9900 = $94 - $92.07 = $1.93

2. Your answer is correct i.e. e. None of the above.

Formula is as below:

C₀+X*e^-r*t = P₀+S₀

$2.15 + $93*e^-0.02*.05 = $4 + $90

$2.15 + $93*e^-0.01 = $94

$2.15 + $93*0.9900 = $94

$2.15 + 92.07 = $94

$94.22 = $94

From above calculations, we can see that Call portfolio is over priced compared to put+underlying portfolio, so to earn arbitrage profit, we need to short the call option, buy the put option, buy the stock and borrow the $4+$90-$2.15 = $91.85 at risk-free rate to execute these transactions.

3. The answer is d.22.

We borrowed $91.85 and will need to pay after 6-months $91.85*e^0.02*0.5 = $91.85*1.0101 = $92.78

At the expiration of option share price will be either greater than strike price of $93 or less than this. If it's greater than then call option will be exercised and we'll get $93. If it's less than then put option will be exercised and we'll get $93 by selling the stock.

Arbitrage profit = $93 - $92.78 = $0.22 or one option contract is for 100 shares. so per call option profit $0.22*100 = $22.