# How to calculate the gaussian VaR for a portfolio with 3 corporate bonds and 1 IRS payer?

As data I have the daily change of zero coupon spot rates for some vertex (0.25, 0.5, 1, 2..) and the daily change of z-spread for corporate bonds, also by vertex

• What have you tried so far? What is the Gaussian VaR? Do you also have so-called sensitivities at hand? May 23 at 19:51
• Thank you for you comment. For gaussian VaR I intend the VaR computation with montecarlo simulations. I don't have sensitivites at hand. I only know the composition of the portfolio and two time series: the daily change for zero coupon spot rates and the daily change of z-spreads for AA corporate bonds. Up to now i created a covariance matrix for the zero coupon rates changes. I don't know how to use this data to compute the VaR. May 23 at 20:59
• You need information to generate draws for your risk factors, i.e. you translate the rates and spread changes into a covariance matrix, that's a starting point. You then 1) simulate a draw from the multivariate normal distribution, $z_i$, and 2) calculate a new level of rates / spreads, $s_i = s_0 + z_i$. 3) You then apply this scenario in a valuation function and obtain new theoretical values, $V_i=f(s_i)$. 4) Subtracting the initial value results in one pnl sample, $V_i-V0$. 5) Repeat $N$ times and calculate the corresponding quantile from the simulated pnl distribution. May 24 at 6:08
• Why do you want to use Monte Carlo - is it an explicit requirement for the homework? Otherwise, once you have a covariance matrix, and the sensitivities (assuming the sensitivities are linear, ignoring convexity), you can just perform a matrix multiplication. See my answers quant.stackexchange.com/questions/69468/… and quant.stackexchange.com/questions/65940/… . But if you don't want to ignore the convexity, and want to do full revaluation of your portfolio (continued) May 24 at 12:45
• then: it sounds like you have sufficiently long historical time series of market factor changes. Instead of assuming normal (or any) distribution, you may want to consider revaluing your portfolo under historical scenarios. Then you don't need a covariance matrix. May 24 at 12:49