Using the continuous-dividend-adjusted option model, calculate the dividend-adjusted stock price, dividend-adjusted call price, and dividend-adjusted put price for the XYZ stock and options described in Problem 1. In your calculations, assume an annual dividend yield of \(8 \%\).

Problem 1.

Suppose XYZ stock currently is trading at \(\$ 100\) per share, has an annualized standard deviation of 0.50 , will not pay any dividends over the next three months, and the continuously compounded annual risk-free rate is \(3 \%\).

a. Using the Black-Scholes OPM, calculate the equilibrium price for a three-month XYX 100 European call option.

b. Using the Black-Scholes OPM, calculate the equilibrium price for a three-month XYZ 100 European put option.

c. Show the Black-Scholes put price is the same price obtained using the put-call parity model.

d. Describe the arbitrage strategy one would pursue if the XYZ 100 call was overpriced and if it was underpriced.

e. Describe the arbitrage strategy one would pursue if the XYZ 100 put was overpriced and if it was underpriced.