Abstract
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.
Original language | English (US) |
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Pages (from-to) | 457-486 |
Number of pages | 30 |
Journal | Mathematical Finance |
Volume | 19 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2009 |
Externally published | Yes |
Keywords
- Implied volatilities
- Multiple underlyings
- Numerical techniques
- Option valuation
- Singular perturbation theory
ASJC Scopus subject areas
- Accounting
- Finance
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Applied Mathematics