You buy a share of stock, write a one-year call option with a strike price X = $

Question

You buy a share of stock, write a one-year call option with a strike price X = $16, and buy a one-year put option with a strike price X = $16. Your net initial cost to establish the entire portfolio is $15.50. What must be the risk-free interest rate from now until the options maturity date? The stock pays no dividends.

You buy a share of stock, write a one-year call option with a strike price X = $16, and buy a one-year put option with a strike price X = $16. Your net initial cost to establish the entire portfolio is $15.50. What must be the risk-free interest rate from now until the options maturity date? The stock pays no dividends.

Explanation / Answer

The position is S-C+P

Put call parity states that S+P=C+Xe^(-rt)

Henc, S-C+P=Xe^(-rt)

Given, 16e^(-r*1)=15.5

=>ln(16/15.5)=r

=>r=0.031749=3.1749%

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