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FRM Part II · FRM Exam Part II · VaR Mapping

A risk manager maps a long position in a call option on a stock to the underlying stock for a delta-normal VaR calculation. Which approach correctly represents the option's exposure?

The option is mapped to the underlying using delta times the market value of the underlying position. This delta-equivalent exposure captures the first-order sensitivity to the stock price. The option premium would understate exposure, and gamma measures curvature, not linear sensitivity.

  1. AUse the option's market value as the exposure to the stock
  2. BUse the option's delta multiplied by the market value of the underlying shares controlledCorrect
  3. CUse the option's gamma multiplied by the stock price
  4. DUse the strike price multiplied by the number of options

Explanation

In the delta-normal approach the option is replaced by an equivalent position in the underlying, equal to delta times the underlying notional. Using the option premium understates the exposure because the premium is only a fraction of the underlying value. Gamma only captures curvature and is not the first-order exposure.

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