hard · FRM Part 1 Valuation and Risk Models

A risk manager computes 1-day 99% VaR for a long position in a deeply out-of-the-money written put option using the delta-normal (linear) method. The underlying has zero drift over the horizon. Compared with a full revaluation (Monte Carlo) VaR that captures the option's true convexity, the delta-normal VaR for this position will most likely be:

1. Understated, because the negative gamma of the written put makes losses on adverse underlying moves larger than the linear approximation predicts
2. Overstated, because the linear approximation ignores the limited liability that caps the option premium received
3. Understated, because vega risk from a volatility increase is omitted from a pure delta-normal calculation
4. Approximately unbiased, since for a deep-OTM option delta is near zero and the linear and full-revaluation results converge

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