Risk-Neutral Distribution and Alternative Credit Exposure Modeling

Abstract

The paper develops a new modeling approach, termed "Risk-Neutral Distribution Method", for credit risk exposures. It provides an alternative to the Monte-Carlo simulation method in the financial industry. The method first derives the risk-neutral moments of the underlying security's return using the Bakshi-Kapadia-Madan (BKM) method, with option prices as inputs. It then translates such moments into risk-neutral distribution using Normal Inverse Gaussian distribution or Variance Gamma distribution. This study establishes that the Risk-Neutral Distribution Method can be used to value derivatives, and to measure the credit risk on such derivatives. Furthermore, we illustrate the Risk-Neutral Distribution Method using a simple equity forward to demonstrate its application with real world data. It is shown that the alternative method produces similar results to the simulation method with the underlying following a Heston or CEV process.