The Adaptive Mesh Model: A New Approach to Efficient Option Pricing
Exact closed-form valuation equations for traded derivative securities are rare. Numerical approximation, most commonly with Binomial and Trinomial lattice models, gives exact valuation in the limit, but convergence is non-monotonic and often slow, due to 'distribution error' and 'truncation error.' This paper explains how truncation error arises and describes the Adaptive Mesh Model (AMM), a new approach that sharply reduces it by grafting one or more small sections of fine high-resolution lattice onto a tree with coarser time and price steps. Three different AMM structures are presented, one for pricing ordinary options, one for barrier options, and one for computing delta and gamma efficiently. The AMM approach can be adapted to a wide variety of contingent claims, yielding significant improvement in efficiency with very little increase in computational effort. For some common problems, including calculating delta, accuracy increases by several orders of magnitude relative to the standard models with no measurable increase in execution time at all.
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|Date of creation:||15 Mar 1998|
|Date of revision:|
|Contact details of provider:|| Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126|
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- Mark Rubinstein., 1991. "Exotic Options," Research Program in Finance Working Papers RPF-220, University of California at Berkeley.
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
- Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May.
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(01), pages 87-100, March.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-81.
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