Fast and simple method for pricing exotic options using Gauss–Hermite quadrature on a cubic spline interpolation

Xiaolin Luo () and Pavel V. Shevchenko ()
Additional contact information
Xiaolin Luo: The Commonwealth Scientific and Industrial Research Organisation, Australia
Pavel V. Shevchenko: The Commonwealth Scientific and Industrial Research Organisation, Australia

Journal of Financial Engineering (JFE), 2014, vol. 01, issue 04, 1-31

Abstract: There is a vast literature on numerical valuation of exotic options using Monte Carlo (MC), binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to calculate the required option price expectations in a backward time-stepping algorithm. This paper presents a simple, robust and efficient algorithm that can be applied for pricing many exotic options by computing the expectations using Gauss–Hermite integration quadrature applied on a cubic spline interpolation. The algorithm is fully explicit but does not suffer the inherent instability of the explicit finite difference counterpart. A "free" bonus of the algorithm is that it already contains the function for fast and accurate interpolation of multiple solutions required by many discretely monitored path dependent options. For illustrations, we present examples of pricing a series of American options with either Bermudan or continuous exercise features, and a series of exotic path-dependent options of target accumulation redemption note (TARN). Results of the new method are compared with MC and finite difference methods, including some of the most advanced or best known finite difference algorithms in the literature. The comparison shows that, despite its simplicity, the new method can rival with some of the best finite difference algorithms in accuracy and at the same time it is significantly faster. Virtually the same algorithm can be applied to price other path-dependent financial contracts such as Asian options and variable annuities.

Keywords: Exotic options; Gauss–Hermite quadrature; cubic spline; finite difference method; American option; Bermudan option; target accumulation redemption note; GMWB variable annuity (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S2345768614500330
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:jfexxx:v:01:y:2014:i:04:n:s2345768614500330

Ordering information: This journal article can be ordered from

DOI: 10.1142/S2345768614500330

Access Statistics for this article

Journal of Financial Engineering (JFE) is currently edited by George Yuan

More articles in Journal of Financial Engineering (JFE) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().