Fast Computation of Securities Financing Loss Distribution in Joint Lognormal Credit and Jump Diffusion Asset Model

Abstract

At the core of securities financing transaction modeling is computing the distribution of the borrower default contingent market losses. Typically, the borrower’s credit spread is modeled after the lognormal model and the asset price dynamics is governed by a correlated jump diffusion model. While essential and realistic, this type of joint spread and asset model requires intensive numerical computation, often via the Monte Carlo simulation. This paper applies the Karhunen-Loeve decomposition of the Ornstein-Uhlenbeck process in such a cross-asset setting. It is shown that the first few orders of the decomposition can produce accurate repo and securities lending haircuts. A fast numerical approximation to the loss distribution is thus developed at a small fractional cost of the simulation method.