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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

A risk manager uses the delta-normal method to estimate the one-day VaR of a portfolio consisting only of long positions in call options on a single stock. Compared with the VaR from full revaluation, the delta-normal VaR will most likely be:

Delta-normal VaR will be too high for long calls. Long options have positive gamma, so their value is convex. When the stock falls, the true option loss is smaller than the straight-line delta estimate, so ignoring gamma overstates the loss and the VaR.

  1. AToo high, because positive gamma makes actual losses smaller than the linear approximation predictsCorrect
  2. BToo low, because positive gamma makes actual losses larger than the linear approximation predicts
  3. CAccurate, because option payoffs are symmetric around the current price
  4. DToo low, because delta-normal ignores the time value of the options

Explanation

A long option has positive gamma, so its value is convex in the underlying. When the underlying falls, the option loses less than the linear delta estimate suggests. The delta-normal method therefore overstates the loss, and so overstates VaR, for long-gamma positions, especially for large moves.

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