Chartered Financial Analyst (CFA) Practice Exam Level 2

In the Black-Scholes-Merton model, what does N(d2) represent?

1. The probability a call option will expire worthless

2. The risk neutral probability a call option will expire in the money

3. The pricing model for bond options

4. The actual market probability of a stock price increase

The correct answer is: The risk neutral probability a call option will expire in the money

In the Black-Scholes-Merton model, N(d2) specifically represents the risk-neutral probability that a call option will expire in the money. This interpretation arises from the mathematical properties of the model, which operates under the assumption that markets are efficient and investors are risk-neutral. When calculating N(d2), we refer to the cumulative distribution function of the standard normal distribution, which yields a value between 0 and 1. This value reflects the evaluation of the underlying asset's price at expiration—specifically, its likelihood of being above the strike price for the call option, assuming the world operates under risk-neutral dynamics. This is a fundamental aspect of option pricing, as it allows traders and investors to estimate the fair value of options by incorporating probabilities derived from the modeled random walk of the underlying asset’s price. The other concepts, while relevant to finance, do not accurately capture the meaning of N(d2) within the context of the Black-Scholes-Merton framework.