In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing PDE. This can be done in a very elegant way, due to the fact that in our tradable based formulation there appear no drift terms in the PDE. We construct a mixed scheme based on this idea and apply it to price various types of arithmetic Asian options, as well as plain vanilla options (both european and american style) on stocks paying known cash dividends. We find prices which are accurate to ~0.1% in about 10ms on a Pentium 233MHz computer and to ~0.001% in a second. The scheme can also be used for market conform pricing, by fitting it to observed option prices.
|Date of creation:||21 May 2001|
|Date of revision:|
|Note:||Type of Document - Acrobat PDF; prepared on NT/LaTeX; to print on PostScript; pages: 12 ; figures: None|
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- Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing," Finance 9907002, EconWPA.
- Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
- Jiri Hoogland & Dimitri Neumann, 2001. "Asians and cash dividends: Exploiting symmetries in pricing theory," Finance 0105002, EconWPA.
- Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
- Jiri Hoogland & Dimitri Neumann, 1999. "Scale invariance and contingent claim pricing II: Path-dependent contingent claims," Finance 9907003, EconWPA.
- Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
- Jiri Hoogland & Dimitri Neumann, 2000. "Asians and cash dividends: Exploiting symmetries in pricing theory," Papers cond-mat/0006133, arXiv.org.
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