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: (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.

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“…As there is not an analytical expression for the detection threshold, the standard Monte Carlo technique [ 34 ] is utilized. A similar approach was recently used to solve several problems from different areas, such as physics [ 35 ], decision theory [ 36 ], engineering [ 37 ], computational geometry [ 38 ], finance [ 39 ], etc. The rule of adaptive normalized matched filter (ANMF) is given as [ 40 ], where is the clutter covariance estimation.…”

Quantization Goes Polynomial

“…Remark 6.1. (Barrier and Asian options) In case of interest in different types of path dependent options, such as barrier or Asian, we refer the reader to the methodology developed in Bormetti et al (2017), where, on top of a grid for the underlying process at every intermediate date (together with transition probabilities from one time step to another) a backward Monte Carlo procedure is applied to price barrier, Asian and auto-callable options.…”

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