Weak Convergence of Path-Dependent SDEs in Basket Credit Default Swap Pricing with Contagion Risk

We investigate computational aspects of basket credit default swap pricing with counterparty credit risk under a multiname contagion model. This model enables us to capture systematic volatility increases in the market triggered by particular bankruptcies. A drawback of this model is its analytical intractability due to a combination of path-dependent coefficients and a path-dependent functional, which furthermore causes potential failure of convergence of numerical approximations under standing assumptions. In this paper, we find sufficient conditions for the desired convergence of functionals associated with approximated solution of certain path-dependent stochastic differential equations.