Convergence analysis for continuous-time Markov chain approximation of stochastic local volatility models: Option pricing and Greeks

This paper establishes the precise second order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing options under the general framework of stochastic local volatility (SLV) models. The stochastic local volatility models studied in this paper include Heston model, 4/2 model, α-Hypergeometric model, stochastic alpha beta rho (SABR) model, Heston-SABR model and quadratic SLV model. Using the stochastic flow theorem, the closed-form CTMC approximation formula for the Greeks are obtained and the second order convergence rates are proved. Numerical examples confirm the theoretical findings.