Two different probability measures are of importance when calculating the risk of a large portfolio: the risk-neutral measure for pricing, and the real measure to project true earnings. When using Monte Carlo, the natural method is to conduct two different simulations, one in each probability measure . We advocate to simulate portfolios only in the true measure, and for pricing, to adjust the results by the Radon-Nikodym derivative. This scheme leads to simulations that are signifficantly faster and whose results are easier to interpret. Our results can also be useful in the calibration of the BGM /J Libor model. It is well-known that calibrating this model to caps and swaptions results in a dispersion of risk-neutral rates that is much higher than the plausible dispersion of real rates. Our scheme uses mean-reversion to correct the real rate distribution while having the advantageof preserving the volatility structure coming from the calibration process. In orderto solve this problem we determined a new expression for the variance of the Radon-Nikodym derivative of Gaussian measures, which could be useful in other areas of finance.
