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Article

Pricing Variance, Gamma, and Corridor Swaps Using Multinomial Trees

Honglei Zhao, Zhe Zhao, Rupak Chatterjee, Thomas Lonon and Ionuţ Florescu
The Journal of Derivatives Winter 2017, 25 (2) 7-21; DOI: https://doi.org/10.3905/jod.2017.25.2.007
Honglei Zhao
is a PhD candidate in the Financial Engineering Division at Stevens Institute of Technology Castle Point on Hudson in Hoboken, NJ, and lab assistant in the Financials Systems Lab at Stevens Institute of Technology Babbio Center in Hoboken, NJ
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Zhe Zhao
is a PhD candidate in the Financial Engineering Division at Stevens Institute of Technology Castle Point on Hudson in Hoboken, NJ, and lab assistant in the Financials Systems Lab at Stevens Institute of Technology Babbio Center in Hoboken, NJ
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Rupak Chatterjee
is an industry professor and director in the Financial Engineering Division at Stevens Institute of Technology Castle Point on Hudson in Hoboken, NJ
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Thomas Lonon
is an assistant teaching professor in the Financial Engineering Division at Stevens Institute of Technology Castle Point on Hudson in Hoboken, NJ
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Ionuţ Florescu
is a research associate professor in the Financial Engineering Division at Stevens Institute of Technology Castle Point on Hudson in Hoboken, NJ, and director in the Hanlon Financial Systems Lab at Stevens Institute of Technology Babbio Center in Hoboken, NJ
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Abstract

Pricing and hedging real world derivatives requires approximation methods for all but the plainest of plain vanilla cases. The two standard classes of valuation tools are lattices (trees) and Monte Carlo simulation. Lattice methods start at maturity and work backward through the tree to compute the derivative value at the beginning. This works very well as long as the payoff at a given time step depends on the asset price at that date but not on the path the price followed to arrive there. There are many more paths through a tree than there are time steps, so path-dependent problems normally require Monte Carlo and calculations over a very large number of paths to achieve accuracy. This raises major problems for valuing derivatives based on volatility and other higher moments of the returns distribution, because realized values of these statistics do depend on the path and not just the terminal price. In this article, the authors present a new kind of lattice procedure for variance swaps and related contracts that achieves the accuracy of a Monte Carlo approximation in execution time that is very much less—more than two orders of magnitude faster in a basic example. The technique involves a single backward pass through the tree, with efficient calculations of conditional future variance through expiration at each intermediate node being built up along the way. The procedure does not depend on any specific returns process, and examples with several well-known stochastic volatility models show excellent performance on all of them.

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The Journal of Derivatives: 25 (2)
The Journal of Derivatives
Vol. 25, Issue 2
Winter 2017
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Pricing Variance, Gamma, and Corridor Swaps Using Multinomial Trees
Honglei Zhao, Zhe Zhao, Rupak Chatterjee, Thomas Lonon, Ionuţ Florescu
The Journal of Derivatives Nov 2017, 25 (2) 7-21; DOI: 10.3905/jod.2017.25.2.007

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Pricing Variance, Gamma, and Corridor Swaps Using Multinomial Trees
Honglei Zhao, Zhe Zhao, Rupak Chatterjee, Thomas Lonon, Ionuţ Florescu
The Journal of Derivatives Nov 2017, 25 (2) 7-21; DOI: 10.3905/jod.2017.25.2.007
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  • Article
    • Abstract
    • LITERATURE
    • VARIANCE SWAPS
    • SWAP PRICING METHODOLOGY
    • NUMERICAL EXPERIMENTS
    • CONCLUSION
    • APPENDIX
    • ENDNOTE
    • REFERENCES
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