A case study on pricing foreign exchange options using the modified Craig–Sneyd ADI scheme

ABSTRACT

One of the prominent alternating direction implicit (ADI) schemes for numerically pricing financial options, the modified Craig–Sneyd scheme, is put to test for its reliability and efficiency for solving non-trivial problems with empirical market data. The Heston equation for pricing foreign exchange options of European style, a two-dimensional convection–diffusion–reaction equation with a mixed derivative term, is numerically solved for various parameter values observed in the market by employing the said scheme. Numerical stability and convergence issues of this scheme is compared with another popular Hundsdorfer–Verwer ADI scheme. From among a total of 56 options on 8 currency pairs, it is observed that some interesting ones for which the so-called Feller condition is strongly violated, create additional computational challenges. Suggestions on successful implementation of the MCS scheme are made in order to tackle these challenging test cases.

KEYWORDS:

• Foreign exchange options
• convection–diffusion equations
• initial-boundary value problems
• ADI schemes
• stability

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 35

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Xiaoping Lu http://orcid.org/0000-0003-1090-8437

Notes

1 Thanks to Dr Sven Foulon for providing us an exact Heston pricer code.