A Backward Monte Carlo Approach to Exotic Option Pricing

Abstract

We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction of a discrete multinomial tree. The crucial feature of our approach is that -in a similar spirit to the Brownian Bridge -each random path runs backward from a terminal fixed point to the initial spot price. We characterize the tree in two alternative ways: in terms of the optimal grids originating from the Recursive Marginal Quantization algorithm and following an approach inspired by the finite difference approximation of the diffusion's infinitesimal generator. We assess the reliability of the new methodology comparing the performance of both approaches and benchmarking them with competitor Monte Carlo methods.JEL codes: C63, G12, G13

Recursive marginal quantization of higher-order schemes

“…Quantization techniques have been shown to be effective in a number of quantitative finance applications. In particular, this includes the pricing of contingent claims with path dependency and early exercise [Pàges and Wilbertz, 2009;Sagna, 2011;Bormetti et al, 2016], stochastic control problems [Pàges et al, 2004] and nonlinear filtering [Pàges and Pham, 2005]. To improve numerical efficiency, Pagès and Sagna [2015] introduced a technique known as recursive marginal quantization.…”

Fast Quantization of Stochastic Volatility Models

“…Quantization is a lossy compression technique that has been applied to many challenging problems in mathematical finance, including pricing options with path dependence and early exercise [Pagès and Wilbertz, 2009;Sagna, 2011;Bormetti et al, 2016], stochastic control problems [Pagès et al, 2004] and non-linear filtering [Pagès and Pham, 2005]. Pagès and Sagna [2015] introduced a technique known as Recursive Marginal Quantization (RMQ), which approximates the marginal distribution of a stochastic differential equation by recursively quantizing the Euler approximation of the process.…”

Recursive Marginal Quantization of Higher-Order Schemes

“…In particular, this includes the pricing of contingent claims with path dependency and early exercise [Pàges and Wilbertz, 2009;Sagna, 2011;Bormetti et al, 2016], stochastic control problems [Pàges et al, 2004] and nonlinear filtering [Pàges and Pham, 2005]. To improve numerical efficiency, Pagès and Sagna [2015] introduced a technique known as recursive marginal quantization.…”