A Backward Monte Carlo Approach to Exotic Option Pricing

47 Pages Posted: 5 Nov 2015 Last revised: 4 Oct 2016

See all articles by Giacomo Bormetti

Giacomo Bormetti

University of Bologna - Department of Mathematics

Giorgia Callegaro

University of Padua

Giulia Livieri

Scuola Normale Superiore

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Date Written: October 3, 2016

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.

Keywords: Monte Carlo, Variance Reduction, Quantization, Markov Generator, Local Volatility, Option Pricing

JEL Classification: C63, G12, G13

Suggested Citation

Bormetti, Giacomo and Callegaro, Giorgia and Livieri, Giulia and Pallavicini, Andrea, A Backward Monte Carlo Approach to Exotic Option Pricing (October 3, 2016). Available at SSRN: https://ssrn.com/abstract=2686115 or http://dx.doi.org/10.2139/ssrn.2686115

Giacomo Bormetti

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Giorgia Callegaro

University of Padua ( email )

Via 8 Febbraio, 2
Padova, Vicenza 35122
Italy

Giulia Livieri

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Andrea Pallavicini (Contact Author)

Banca IMI ( email )

Largo Mattioli 3
Milan, MI 20121
Italy
+39 02 7261 (Phone)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

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