Question

You buy a share of stock, write a one-year call option with X = $10, and buy a one-year put option with X = $10. Your net outlay to establish the entire portfolio is $9.50. What is the payoff of your portfolio? What must be the risk-free interest rate? The stock pays no dividends. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

The payoff of your portfolio shows a risk-less with time-T and stock value equal to $10.

The risk-free interest rate must be 5.26%

Explanation:

position                 Sr<10       Sr>10

buy stock               Sr              Sr

short call                  0             -(Sr - 10)

long call                   10 - Sr       0

total                           10              10

Therefore, The payoff of your portfolio shows a risk-less with time-T and stock value equal to $10.

risk - free interest rate = [[strike price/expected value]/net cost] - 1

                                      = [10/9.5] - 1

                                      = 5.26%

Therefore, The risk-free interest rate must be 5.26%