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

A portfolio of options has delta 0 and gamma -500 per unit change in share price squared. Over a short interval the share price moves by +2 (rupees) with no change in other variables. Using the second-order approximation, the change in portfolio value (ignoring time decay) is closest to:

The change is about -1,000 rupees. With zero delta, the change is half gamma times the squared price move: 0.5 x (-500) x 2^2 = -1,000. Negative gamma loses money for a move in either direction.

  1. A-1,000
  2. B+1,000
  3. C-2,000Correct
  4. D+2,000
  5. 0

Explanation

Change = delta x dS + 0.5 x gamma x dS^2 = 0 + 0.5 x (-500) x 4 = -1,000. Wait: 0.5 x -500 = -250; times 4 = -1,000. So the correct value is -1,000, which is the first option.

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