Before revision: In this paper we discuss sufficient conditions for weak convergence of the Euler approximation to general multi-dimensional stochastic differential equations (SDEs) driven by correlated Brownian motions and with discontinuous and path-dependent coefficients. We prove tightness of the approximating processes and the weak solution of the limiting process. Furthermore, motivated by a basket credit default swap (CDS ) pricing problem with counterparty risk and contagion risk, we show weak convergence for some functions of correlated first-passage times of the approximating processes.
After revision: We investigate the computational aspects of the basket CDS pricing with counterparty risk and contagion risk, we show weak convergence for some functions of correlated first-passage times of the approximating processes.