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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 on a non-dividend-paying stock, the term N(d2) is best interpreted as:

N(d2) is the risk-neutral probability that the call expires in the money, meaning the stock finishes above the strike. It is not a real-world probability because the model uses the risk-free rate as drift, and the call's delta is N(d1) instead.

  1. AThe risk-neutral probability that the call finishes in the moneyCorrect
  2. BThe real-world probability that the stock price rises over the option's life
  3. CThe hedge ratio of the call, which is the change in call price per unit change in stock price
  4. DThe present value of the strike price in the formula

Explanation

In BSM the call value is S0 N(d1) - K e^{-rT} N(d2). N(d2) is the risk-neutral probability that S_T exceeds K. The real-world probability would use the true drift, not r. The hedge ratio (delta) is N(d1), not N(d2).

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