medium · 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 premium originally received by the option writer
3. Understated, because vega risk arising from a rise in implied volatility is entirely omitted from a purely linear delta-normal VaR calculation method
4. Approximately unbiased, since for a deep out-of-the-money option the delta is near zero and the linear and full-revaluation results nearly converge together

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