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A backward Monte Carlo approach to exotic option pricing†

Published online by Cambridge University Press:  12 April 2017

G. BORMETTI ,
G. CALLEGARO ,
G. LIVIERI  and
A. PALLAVICINI
G. BORMETTI
Affiliation:
Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy, email: giacomo.bormetti@unibo.it
G. CALLEGARO
Affiliation:
Department of Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy, email: gcallega@math.unipd.it
G. LIVIERI
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy email: giulia.livieri@sns.it
A. PALLAVICINI
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK, email: a.pallavicini@imperial.ac.uk Banca IMI, Largo Mattioli 3, 20121 Milano, Italy
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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: (i) in terms of the optimal grids originating from the Recursive Marginal Quantization algorithm, (ii) 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 methods (65C05)Markov chains (60J10)Computational methods in Markov chains (60J22)Derivative securities (91G20)Numerical methods (including Monte Carlo methods) (91G60)
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 1 , February 2018 , pp. 146 - 187
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

†

GB and GL acknowledge research support from the Scuola Normale Superiore Grant SNS_14_BORMETTI.

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