Efficient recursion-quadrature algorithms for pricing Asian options and variance derivatives under stochastic volatility and Lévy jumps

Abstract

We propose efficient algorithms for pricing discretely monitored arithmetic Asian options and variance derivatives, which utilize the recursion of characteristic functions, quadrature over the variance/activity rate dimension, and frame projection method of approximating the density function of the log-asset price. The classes of dynamic asset price models include the stochastic volatility models with Lévy jumps and time-changed Lévy models. Numerical tests reveal that our proposed recursion-quadrature algorithms compete favorably well in terms of efficiency, accuracy, and reliability.