Question

PROBLEM 2. 14 pointsl European call and put options with exercise price $22.5 and expiration time in six months are trading at $4.12 and $7.42. The price of the underlying stock is $19.32 and the interest rate is 4.15%. Find an arbitrage opportunity, describe the arbitrage strategy, calculate the arbitrage profit. Provide the details.

financial

Answer 1

Verify that put–call parity holds

Call-put parity equation can be used in following manner

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

Where,

C = Call premium =$4.12

K = exercise price of the call/put option =$22.5

P = Put premium =$7.42

S0 = Current price of underlying stock =$19.32

e^ (-r*t) = the present value of the exercise price discounted from the expiration date at risk-free rate

And r =Risk-free interest rate per year = 4.15% and t= time period =0.5 years (6 months)

Therefore,

$4.12 + $22.5 *e^ (-4.15%*0.5) = $7.42 + $19.32

$4.12 + $22.04 = $7.42 + $19.32

$26.16 ≠ $26.74

As the value of both sides of equation is not same therefore the put–call parity does not hold and there is an arbitrage opportunity

We can see that left side of equation is under-priced therefore it should be brought and right side of equation is over-priced therefore it should be sold.

This arbitrage opportunity involves buying a call option and selling a put option and a share of the company.

-$4.12 + $7.42 +$19.32 = + $22.62

After six months, if share price is more than the strike price, call option will be exercised and if it is below the strike price then put option will be exercised

Therefore, Net profit = + $22.62 - $22.50 = + $0.12