The current price of a stock is $100.Consider the Black-Scholes model price of a six-month call option at strike $101,given an interest rate of 2% and a dividend rate of 1%? The volatility is 25%.What is the real-world (physical)probability of the option ending up in the money if the growth rate of the stock is expected to be 5% per year?
A)0.45
B)0.48
C)0.49
D)0.50

Question

Quizplus · Accepted Answer

The real-world probability of the option ending up in the money can be estimated using the risk-neutral probability adjusted for the expected growth rate of the stock. The Black-Scholes model provides a framework for pricing options but does not directly give the real-world probability. However, by adjusting the drift term in the Black-Scholes formula to account for the expected growth rate instead of the risk-free rate, we can estimate the real-world probability. Given the parameters, the calculation involves using the cumulative distribution function of the standard normal distribution, adjusted for the expected growth rate. The correct answer, in this case, is closest to 0.49, reflecting the complex calculations behind option pricing and the adjustment for the real-world growth rate of the stock.

The Current Price of a Stock Is $100