Weak Convergence of Path-Dependent SDEs in Basket CDS Pricing with Contagion Risk

TL;DR

This paper establishes conditions for the weak convergence of numerical solutions to path-dependent stochastic differential equations used in basket CDS pricing with contagion risk, addressing analytical challenges in modeling systematic market volatility.

Contribution

It provides new sufficient conditions ensuring the convergence of numerical approximations for path-dependent SDEs in credit risk modeling, improving computational reliability.

Findings

Identified conditions for weak convergence of path-dependent SDE solutions.

Addressed convergence issues in basket CDS pricing models with contagion risk.

Enhanced understanding of numerical approximation stability in complex credit models.

Abstract

We investigate the computational aspects of the basket CDS pricing with counterparty risk under a credit contagion model of multinames. This model enables us to capture the systematic volatility increases in the market triggered by a particular bankruptcy. The drawback of this problem is its analytical complication due to its path-dependent functional, which bears a potential failure in its convergence of numerical approximation under standing assumptions. In this paper we find sufficient conditions for the desired convergence of the functionals associated with a class of path-dependent stochastic differential equations. The main ingredient is to identify the weak convergence of the approximated solution to the underlying path-dependent stochastic differential equation.