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Pricing American Options by Willow Tree Method Under Jump-Diffusion Process

Wei Xu and Yufang Yin
The Journal of Derivatives Fall 2014, 22 (1) 46-56; DOI: https://doi.org/10.3905/jod.2014.22.1.046
Wei Xu
is an associate professor in the Department of Mathematics at Tongji University in Shanghai, China.
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  • For correspondence: wdxu@tongji.edu.cn
Yufang Yin
is a master student in the Department of Mathematics at Tongji University in Shanghai, China.
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  • For correspondence: yinyufang8986@163.com
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Abstract

Numerical solution methods for option pricing fall into two broad classes, either the lattice framework or Monte Carlo simulation. Monte Carlo simulation is problematic for American options, while the Binomial and Trinomial approaches have difficulty incorporating stochastic jumps. The probability density at expiration that is generated by a lattice typically has different skewness and kurtosis than is embedded in option market prices. The Binomial can be fitted imposing a terminal density with the right moments, using the Johnson system of distributions for example, but the problem still remains that the number of distinct nodes to calculate increases quadratically with the number of time steps. This article proposes the “Willow Tree” method, which combines a small number of large time steps that connect to many possible next period nodes, with the constraint that the terminal density, constructed from the Johnson system, has the same mean, volatility, skewness, and kurtosis as the risk neutral density extracted from prices in the options market. The result is a much faster and more accurate valuation than may be achieved through existing approaches.

TOPICS: Options, simulations

  • © 2014 Institutional Investor, Inc.
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The Journal of Derivatives: 22 (1)
The Journal of Derivatives
Vol. 22, Issue 1
Fall 2014
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Pricing American Options by Willow Tree Method Under Jump-Diffusion Process
Wei Xu, Yufang Yin
The Journal of Derivatives Aug 2014, 22 (1) 46-56; DOI: 10.3905/jod.2014.22.1.046

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Pricing American Options by Willow Tree Method Under Jump-Diffusion Process
Wei Xu, Yufang Yin
The Journal of Derivatives Aug 2014, 22 (1) 46-56; DOI: 10.3905/jod.2014.22.1.046
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  • Article
    • Abstract
    • WILLOW TREE FOR BROWNIAN MOTION
    • WILLOW TREE FOR JUMP DIFFUSION PROCESS
    • NUMERICAL EXPERIMENTS
    • CONCLUSION
    • APPENDIX
    • ENDNOTE
    • REFERENCES
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