3.3 Estimating VaR

3.3.1. Assigning Credit Ratings

With the purpose to perform Monte-Carlo simulation of possible portfolio values, 3305 random points were simulated from the modelled joint distribution. Figure 7 depicts pairplots of simulated points, where X1, X2 and X3 represent Lukoil, Gazprom and Nornickel respectively. Uniform marginal values of those points were transformed back using inverse CDFs of previously found respective t distributions. Then, those transformed randomly generated points represent possible asset returns of each company in comovement with other firms. For each scenario of possible asset returns appropriate credit rating was assigned to a firm based on which interval of return thresholds it lies. Let us continue with an illustration for Lukoil. Let the simulated asset return of Lukoil be equal to -0.8. From the example displayed in equation (35), it can be seen that -0.8 is in the interval (tDef , tC-). Therefore, in this particular possible case Lukoil will be assigned a credit rating of "C-". Following the same procedure, appropriate credit ratings were assigned to all 3 companies. 

3.3.2. Maping Credit Ratings to Bond values

As it was mentioned earlier, in 1 year time horizon the present values of the bonds might change depending on what credit rating an issuer company will be assigned. Now the simulated credit ratings of each company from the previous section were mapped to the appropriate bond values from the Table 8. As an example let us consider the case of a particular realization where in 1 year Lukoil and Gazprom downgraded to "CC", while Norilsk Nickel upgraded to "A". In this case, according to the Table 8, the value of our portfolio is 624.9620+829.4743+984.2259 = 2438.6622 dollars. 

3.3.3. Estimating VaR

By the algoritghm described above possible portfolio values in 1 year time horizon were calculated for all 3305 simulated scenarios. Figure 2 represents the histogram of possible values of our portfolio.