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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

Under the Black-Scholes model for a European option on a non-dividend-paying share, which statement about delta is correct?

The delta of a long European call on a non-dividend-paying share is N(d1), so it lies between 0 and 1. Put delta is N(d1) minus 1, lying between -1 and 0. N(d2) is the exercise probability, not the call delta.

  1. AThe delta of a long European call lies between -1 and 0
  2. BThe delta of a long European put lies between 0 and 1
  3. CThe delta of a long European call lies between 0 and 1Correct
  4. DThe delta of a long European put equals N(d1)
  5. The delta of a long European call equals N(d2)

Explanation

Call delta equals N(d1), which is a probability-like value between 0 and 1. Put delta equals N(d1) minus 1, which lies between -1 and 0. N(d2) is the risk-neutral probability of exercise, not delta.

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