Question

The price of a European call that expires in six months and has a strike price of $28 is $2. The underlying stock price is $27, and a dividend of $0.50 is expected in two months and again in five months. The continuously compounded interest rate is 10%. What is the price of a European put option that expires in six months and has a strike price of $28?  Explain the arbitrage opportunities in the earlier problem if the European put price is $3.25.

Answer 1

Value of europian call option = $2

Strike price = $28

Underlying stock price = $27

Dividend = $0.50

Compound interest rate = 10%

Maturity period = six months

Value of put option = price of europian call option - underlying stock price + (strike price*e^-rt) + dividend

= $2-$27+($28*e^-10*6/12)+($0.50^-10*2/12)+($0.50*^-10*5/12)

= -$25+($28*0.951229)+[($0.50*0.983471)+($0.50*0.959189)]

=-$25+$26.634412+$0.4917+$0.4796

= $2.606

Thus value of put option will be $2.606

Arbitrage opportunity =

Under Call Put Parity theory,

Call value - Put value = Current stock price - excercise price*e^rt

If above relationship gets violated then there is a an arbitage opportunity.

In the given case,

Call - put = $2 - $3.25 = $1.25

Current price - excercise price*e^rt = $27 - $28*0.951229 = $0.36558

Here, call - put > current price - excercise price*e^rt

So, Dealer would sell the call, buy the put and buy the stock. He would earn more than the riskless rate on a riskless investment.