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

In the Black-Scholes-Merton model for a non-dividend-paying stock, N(d2) has which interpretation?

N(d2) is the risk-neutral probability that the European call finishes in the money, meaning the terminal stock price exceeds the strike. It is not the delta, which is N(d1), and it is not a real-world probability because BSM values options under the risk-neutral measure.

  1. AThe delta of the European call option
  2. BThe risk-neutral probability that the European call finishes in the moneyCorrect
  3. CThe real-world probability that the stock price rises over the option's life
  4. DThe hedge ratio of the European put option

Explanation

N(d2) is the risk-neutral probability that S_T exceeds K, so the call expires in the money. N(d1) is the call delta, which is why the first option is wrong. The model prices under the risk-neutral measure, so it does not give a real-world probability.

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