Computing MVA

MVA is today’s price of the future costs generated by future initial margin postings. Computing MVA requires long-term risk neutral simulations of future initial margin amounts. The ISDA SIMM1 computes initial margin based on the portfolio’s sensitivity with respect to a highdimensional vector of risk factors. In this note, we describe a way to approximate future SIMM based initial margin amounts in terms of regression functions with respect to a small number of explanatory variables. Our method uses principal components analysis, and it fits in naturally with American Monte Carlo techniques.