讲解

问题如下：

Question An analyst gathers the following Black–Scholes–Merton option valuation model outputs for a call option on a non-dividend-paying stock:

The probability that the call option expires in the money is:

选项：

A.A.40.6%. B.B.48.8%. C.C.59.4%.

解释：

A Incorrect because N(−d₂), or 40.6%, is the probability that the put option expires in the money, not the call option.

B Incorrect because N(d₂) is the probability that the call option expires in the money, not d₁. N(x) denotes the standard normal cumulative distribution function, which is the probability of obtaining a value of less than x based on a standard normal distribution. Also, x will have the value of d₁ or d₂. N(x) reflects the likelihood of observing values less than x from a random sample of observations taken from the standard normal distribution.

C Correct because the N(d₂) term (being 59.4%) has an additional important interpretation. It is a unique measure of the probability that the call option expires in the money, and correspondingly, 1 – N(d₂) = N(−d₂) is the probability that the put option expires in the money. Specifically, the probability based on the RN probability of being in the money, not one’s own estimate of the probability of being in the money nor the market’s estimate. That is, N(d₂) = Prob(S_T > X) based on the unique RN probability.