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The Journal of Derivatives

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Article

Easy Gram–Charlier Valuations of Options

Ray Popovic and David Goldsman
The Journal of Derivatives Winter 2012, 20 (2) 79-97; DOI: https://doi.org/10.3905/jod.2012.20.2.079
Ray Popovic
is a consultant to the financial industry, and is based in Atlanta, GA.
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  • For correspondence: r.popovic@gmail.com
David Goldsman
is a professor at the H. Milton Stewart School of Industrial and Systems Engineering at the Georgia Institute of Technology in Atlanta, GA.
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  • For correspondence: sman@gatech.edu
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Abstract

The Black–Scholes model for pricing a European option written on a lognormal returns process was easy. Unfortunately, real world markets don’t try to make life easy for financial econometricians. Returns processes are more complicated than lognormal diffusions, and an array of derivative products with much more complex payoffs than European calls are now traded. Many of those are path dependent, making Monte Carlo simulation the only viable valuation technique. But, Monte Carlo can require many replications and substantial execution time to achieve reasonable accuracy for a single set of parameters. In this article, Popovic and Goldsman offer a hybrid approach that can achieve accurate pricing very efficiently. A base set of Monte Carlo runs is constructed and then a Gram–Charlier density approximation is fitted to the histogram of simulation results (which may first need to be transformed to be better adapted to the approximation). A series of examples based on pricing Asian options illustrates how the procedure performs and demonstrates its flexibility in handling non-lognormal underlying returns processes.

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The Journal of Derivatives: 20 (2)
The Journal of Derivatives
Vol. 20, Issue 2
Winter 2012
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Easy Gram–Charlier Valuations of Options
Ray Popovic, David Goldsman
The Journal of Derivatives Nov 2012, 20 (2) 79-97; DOI: 10.3905/jod.2012.20.2.079

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Easy Gram–Charlier Valuations of Options
Ray Popovic, David Goldsman
The Journal of Derivatives Nov 2012, 20 (2) 79-97; DOI: 10.3905/jod.2012.20.2.079
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  • Article
    • Abstract
    • ARITHMETIC AVERAGES OF GBM
    • THE GRAM–CHARLIER ESTIMATOR EXPLAINED
    • ARITHMETIC AVERAGES ON RELATED DIFFUSIONS
    • THE VARIANCE–GAMMA PROCESS
    • CONCLUSION
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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