Question

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.

• 7.90
• .065
• 1.93
• 2.84
• 2.15

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?

• Short the market call, buy the stock, buy the put and short the present value of the exercise price at the risk-free rate.
• Buy the market call, short the stock, short the put and invest the present value of the exercise price at the risk-free rate.
• Short the market call, buy the stock, buy the put and invest the present value of the exercise price at the risk-free rate.
• Arbitrage is not possible.
• None of the above.

Find the arbitrage profit you could earn per call option.

• 575
• 209
• 69
• 22
• 0

Answer 1

Call-put parity equation can be used in following manner

C + K* e^ (-r*t) = P + S0 ……………………………. (1)

Where,

C = price of the call option =?

P= price of the put option =$4

S0 = spot price = $90

Strike price K = $93

The risk-free rate r= 2%

Time period t= 6 months or 0.5 year

Now putting all the values in the put-call parity equation

C + $93 * e^ (-0.02*0.5) = $4 + $90

C = $94 – $92.0746 = $1.9254 or $1.93

Therefore correct answer is option: 1.93

If the call price is 2.15 not the 1.93, then the put–call parity does not hold and there is an arbitrage opportunity

We can see that left side of equation (1) is underpriced therefore it should be brought and right side of equation is overpriced therefore it should be sold. Therefore, buy the market call, short the stock, short the put and invest the present value of the exercise price at the risk-free rate.

Therefore correct answer is option: Buy the market call, short the stock, short the put and invest the present value of the exercise price at the risk-free rate.

This arbitrage opportunity involves

Buying a call option = -$2.15

Selling a put option = +$4

Selling a share = +$90

Net amount received = -$2.15+ $4 +$90 = $91.85

And invests the proceeds at the risk-free rate = $91.85 *(1+2%)

= $93.69

Net profit = proceeds - exercise price

= $93.69 -$93

= $0.69

Therefore correct answer is option: 0.69