I was reading the differences between Delta-Gamma and Delta-normal method for VaR. One of the difference I found is mentioned below, but I can't understand it's importance. Can anybody please explain this?

The improved accuracy by the Delta-Gamma method comes at the cost of at least some reduced tractability relative to the Delta-Normal model. In using Delta- Gamma approach we might lose normality in our portfolio return even if changes in the underlying risk factors are normally distributed



1 Answer 1


Delta-Normal VaR means the portfolio is approximated as a linear function $a + \Delta^T X$ of gaussian risk factors $X$ with variance covariance $V$, so the portfolio distribution is also Gaussian, with variance $\Delta^T V \Delta$, and its VaR is computed explicitly as a percentile on the Gaussian probability distribution function.

Delta-Gamma VaR means the portfolio is approximated as a quadratic function $a + \Delta^T X + \frac{1}{2} X^T \Gamma X$ of gaussian risk factors $X$. The portfolio distribution is no longer Gaussian (because of the quadratic term) and its probability distribution function must be computed trough a semi-explicit numerical method such as a fast Fourier Transform applied to its moment generating function.

See Stefan R. Jaschke risk management for financial institutions http://citeseerx.ist.psu.edu/viewdoc/download?doi= for a good overview of this topic.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.