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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

In the Black-Scholes-Merton formula for a European call option on a non-dividend-paying stock, N(d2) is best interpreted as which of the following?

N(d2) is the risk-neutral probability that the European call expires in the money. It multiplies the discounted strike in the formula. It is not the real-world probability, because the stock's actual drift does not enter the model, and the delta of the call is N(d1).

  1. AThe risk-neutral probability that the call finishes in the money at expiryCorrect
  2. BThe real-world probability that the stock price rises over the option's life
  3. CThe hedge ratio of the call with respect to the stock price
  4. DThe present value of the strike price per unit of option value

Explanation

The term K e^(-rT) N(d2) is the discounted expected strike payment, so N(d2) is the probability, under the risk-neutral measure, that S_T exceeds K. N(d1) is the call delta, which is the hedge ratio and is therefore not the answer. The real-world probability would use the stock's actual drift, which does not appear in the formula.

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