Question

suppose that the stock price $32, the risk-free interest rate is 10% per year the price of a 4 month european call option is $2.85, and the price of a 4 month european put option is $2.65. both options have the strike price $35. describe an arbitrage strategy and justify it with appropriate calculations.

Answer 1

We can identify the existence of arbitrage opportunity in given case with PUT-CALL Parity Theorem:

where,

C = Call price

X = Strike price

r = risk free rate

t = maturity of options

S = Current price of stock

P = Put Price

There is arbitrage opportunity.

We can see in above equation that Call and risk free bond is overvalued than Stock and Put. Thus, Arbitrage strategy would be:

Sell Call and Borrow money; Buy Stock and Buy Put

Money required to Buy Stock and Put = $34.65

Amount received from sell from Call = $2.85

Amount Borrowed = 34.65-2.85 = $31.80

On expiration:

If stock price is more than $35, then

Sale the stock to Call buyer and receive = $35

Pay the borrowed amount = 31.80*e^(0.1*0.33) = $32.88

Your arbitrage profit would be = 35 - 32.88 = $2.12

If stock price is less than $35, then

Exercise the Put option and sell the Stock to put writer and receive = $35

Pay the borrowed amount = 31.80*e^(0.1*0.33) = $32.88

Your arbitrage profit would be = 35 - 32.88 = $2.12