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.

A backward Monte Carlo approach to exotic option pricing

BORMETTI, G.;LIVIERI, G.
;
2017

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.
2017
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore SECS-P/07 - Economia Aziendale
Settore SECS-P/08 - Economia e Gestione delle Imprese
Settore SECS-P/10 - Organizzazione Aziendale
Settore SECS-P/11 - Economia degli Intermediari Finanziari
Settore SECS-P/09 - Finanza Aziendale
Settore SECS-P/13 - Scienze Merceologiche
Settore SECS-S/01 - Statistica
Settore SECS-S/02 - Statistica per La Ricerca Sperimentale e Tecnologica
Settore SECS-S/03 - Statistica Economica
Settore SECS-S/04 - Demografia
Settore SECS-S/05 - Statistica Sociale
Monte Carlo methods; Markov chains; Computational methods in Markov chains; Derivative securities; Numerical methods (including Monte Carlo methods)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/90738
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