"You buy a share of stock, write a 1-year call option with X = $15, and buy a 1-year put option with X = $15. Your net outlay to establish the entire portfolio is $13.9. The stock pays no dividends"What is the risk-free interest rate?

The risk-free interest rate is 7.53%.

Explanation:

We use the Put-Call Parity relationship.

C + D(t)*K = P + S

Where:

C = Call price

D(1) = Discount factor for one year maturity/risk –free rate of return

K = Strike Price ($15)

P = Put Price

S = Current stock price.

Our portfolio consists of an algebraic rearrangement of the above expression. Portfolio = S - C + P = 13.9.

Substituting from above we find that S - C + P = D(1)*K

Therefore D(1)*K = D(1)*15 = 13.9

D(1) = 0.926667

Therefore our 1 year risk free rate is 7.53% under simple annual compounding (1/0.926667)

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