Consider pricing an exchange option on two stocks. Assume the usual lognormal returns distributions on the stock prices as in Magrabe's formula. Which of the following input variables does NOT affect the probability of the option being in-the-money at maturity?
A) The volatility of the assets' returns.
B) The risk-free rate.
C) The correlation between the two assets' returns.
D) The time to maturity of the option.

Question

Quizplus · Accepted Answer

The risk-free rate does not directly affect the probability of the exchange option being in-the-money at maturity because the option's payoff depends on the relative performance of the two stocks, not on the absolute level of interest rates. Magrabe's formula, which is used for pricing exchange options, focuses on the volatilities of the assets, their correlation, and the time to maturity, but not directly on the risk-free rate.

Consider Pricing an Exchange Option on Two Stocks