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SINGULAR PERTURBATION TECHNIQUES APPLIED TO MULTIASSET OPTION PRICING
Author(s) -
Duck Peter W.,
Yang Chao,
Newton David P.,
Widdicks Martin
Publication year - 2009
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2009.00373.x
Subject(s) - curse of dimensionality , valuation of options , singular perturbation , valuation (finance) , mathematical optimization , monte carlo methods for option pricing , black–scholes model , perturbation (astronomy) , computer science , call option , mathematical economics , mathematics , econometrics , economics , artificial intelligence , finance , volatility (finance) , mathematical analysis , physics , quantum mechanics
It is well known that option valuation problems with multiple‐state variables are often problematic to solve. When valuing options using lattice‐type techniques such as finite‐difference methods, the curse of dimensionality ensures that additional‐state variables lead to exponential increases in computational effort. Monte Carlo methods are immune from this curse but, despite advances, require a great deal of adaptation to treat early exercise features. Here the multiunderlying asset Black–Scholes problem, including early exercise, is studied using the tools of singular perturbation analysis. This considerably simplifies the pricing problem by decomposing the multi‐dimensional problem into a series of lower‐dimensional problems that are far simpler and faster to solve than the full, high‐dimensional problem. This paper explains how to apply these singular perturbation techniques and explores the significant efficiency improvement from such an approach.