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ACCA Strategic Professional · Advanced Financial Management · Application of option pricing theory in investment decisions

In the Black-Scholes call valuation formula, what does the term N(d2) represent?

N(d2) is the risk-neutral probability that the call ends in the money, so that the share price at expiry exceeds the exercise price. It weights the present value of the exercise price in the formula. N(d1) is the call's delta, not N(d2).

  1. AThe risk-neutral probability that the call will finish in the money and be exercisedCorrect
  2. BThe delta of the call, being the change in option value per unit change in share price
  3. CThe probability that the share price will rise above its current level, using real-world returns
  4. DThe proportion of the option's value that is time value rather than intrinsic value

Explanation

N(d2) is the risk-neutral probability that the share price at expiry exceeds the exercise price. It multiplies the discounted exercise price in the formula. The delta of the call is N(d1), which is the other term in the formula. N(d2) is not a real-world probability because the model values the option under risk-neutral drift.

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