Question

A put option and a call option with an exercise price of $70 expire in four months and sell for $.94 and $5.70, respectively.

If the stock is currently priced at $73.20, what is the annual continuously compounded rate of interest? (Do not round intermediate calculations. Enter your answer as a percent rounded 2 decimal places, e.g., 32.16.)

Answer 1

Using put–call parity, we can solve for the risk-free rate as follows:

S + P = Ee^–Rt + C

$73.20 + $.94 = $70e^–R(4/12) + $5.70

$68.44 = $70e^–R(4/12)

.9777 = e^–R(4/12)

ln(.9777) = ln(e^–R(4/12))

–.0225 = –R(4/12)

R = .0676, or 6.76%