Question

(Please do it on paper)

Suppose you are given the following data:

2-month option on XYZ stock:

Underlying S = 48.1

Strike X = 50

Put price = $2.2

1. What should be the price of call to prevent arbitrage if 2-month interest rate is 6% p.a.?

2. If the actual call price was $1.3 how would you implement an arbitrage opportunity?

3. Compute your payoff at maturity.

Answer 1

From the put call parity equation  

c+ K/(1+r) = p+S

where c and p are call and put option premiums respectively

K is the strike price of the options =50

, r is the interest rate for 2 months = 6% per annum =1% for 2 months

and t is the time period = 2 months = 1 period

S is the spot price = 48.1

So the price of call option should be

c= 2.2+48.1-50/1.01 = 0.795

Price of call option should be $0.795 or $0.80

b) If actual call price is $1.3 , steps of arbitrage are as follows

1. Today, Buy the put option and stock for $2.2 and $48.1 , Simultaneously sell the call option for $1.3. Fund the net amount of (2.2+48.1-1.3) = $49 by borrowing the same at 6% p.a. or 1% or 2 months

2. After 2months, if Stock price> 50, put option becomes worthless, short call option will be exercised , so sell the stock at exercise price of $50, repay the loan amount of $49*1.01 = $49.49 and take the remaining amount as arbitrage profit

3.After 2months, if Stock price< 50, Call option becomes worthless, long put option will be exercised , so sell the stock at exercise price of $50, repay the loan amount of $49*1.01 = $49.49 and take the remaining amount as arbitrage profit

c) The payoff at maturity in both cases will be $0.51 for $49 borrowed and one put option purchased and one calll option shorted.