Correlated Random Walks and the Joint Survival Probability

13 Pages Posted: 7 Jul 2004

See all articles by Mark B. Wise

Mark B. Wise

California Institute of Technology

Vineer Bhansali

LongTail Alpha, LLC

Date Written: July 7, 2004

Abstract

First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations are small, i.e., of order a few percent, but nonetheless including correlations is very important for managing portfolio credit risk and pricing some credit derivatives (e.g. first to default baskets). In first passage models the exact dependence of the joint survival probability of more than two firms on their asset correlations is not known. We derive an expression for the dependence of the joint survival probability of n firms on their asset correlations using first order perturbation theory in the correlations. It includes all terms that are linear in the correlations but neglects effects of quadratic and higher order. For constant time independent correlations we compare the first passage model expression for the joint survival probability with what a multivariate normal Copula function gives. As a practical application of our results we calculate the dependence of the five year joint survival probability for five basic industrials on their asset correlations.

Keywords: Random walk , survival probability, first passage

JEL Classification: G13

Suggested Citation

Wise, Mark B. and Bhansali, Vineer, Correlated Random Walks and the Joint Survival Probability (July 7, 2004). Available at SSRN: https://ssrn.com/abstract=562207 or http://dx.doi.org/10.2139/ssrn.562207

Mark B. Wise (Contact Author)

California Institute of Technology ( email )

Pasadena, CA 91125
United States
626-395-6687 (Phone)
626-568-8473 (Fax)

Vineer Bhansali

LongTail Alpha, LLC ( email )

500 Newport Center Drive
Suite 820
Newport Beach, CA 92660
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
341
Abstract Views
1,566
rank
91,218
PlumX Metrics