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Article

Range-Curtailing for Options with Discrete Dividend Payments under General Diffusions

Deeveya Thakoor and Muddun Bhuruth
The Journal of Derivatives Summer 2019, 26 (4) 9-34; DOI: https://doi.org/10.3905/jod.2019.26.4.009
Deeveya Thakoor
is a PhD student in the department of mathematics at the University of Mauritius in Reduit, Mauritius
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Muddun Bhuruth
is a professor of computational mathematics in the department of mathematics at the University of Mauritius in Reduit, Mauritius
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Abstract

Lattice methods are often employed to price contingent claims with discrete dividends under the lognormal diffusion, but they are inclined to suffer from large decreases in execution speed as the number of dividends increases. Heteroskedastic assumptions for the stock price dynamics in between ex-dividend dates exacerbate these difficulties, and the option pricing problem with discrete dividends has thus been limited to the lognormal framework. This article proposes strategies to speed up lattice-based approximations under these general diffusions.

A range-curtailing technique that bypasses superfluous computations of numerous subtrees at unrealistic stock prices is considered for European, American, and barrier options. The effect of discrete dividends on the premature exercise of American options is also studied. A benchmark method based on numerical integration is described to validate results obtained in the heteroskedastic framework.

TOPICS: Options, statistical methods

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The Journal of Derivatives: 26 (4)
The Journal of Derivatives
Vol. 26, Issue 4
Summer 2019
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Range-Curtailing for Options with Discrete Dividend Payments under General Diffusions
Deeveya Thakoor, Muddun Bhuruth
The Journal of Derivatives May 2019, 26 (4) 9-34; DOI: 10.3905/jod.2019.26.4.009

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Range-Curtailing for Options with Discrete Dividend Payments under General Diffusions
Deeveya Thakoor, Muddun Bhuruth
The Journal of Derivatives May 2019, 26 (4) 9-34; DOI: 10.3905/jod.2019.26.4.009
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  • Article
    • Abstract
    • OPTION PRICING UNDER PIECEWISE GENERAL DIFFUSIONS
    • NON-RECOMBINING TREES FOR PIECEWISE GENERAL DIFFUSIONS
    • RECOMBINING SHIFTED TRINOMIAL LATTICE
    • IMPROVEMENTS FOR NON-RECOMBINING AND RECOMBINING TREES
    • RANGE-CURTAILING WITH DISCRETE DIVIDENDS
    • OPTIMAL EXERCISE POLICY FOR AMERICAN OPTIONS
    • LOGARITHMIC BINOMIAL COEFFICIENT APPROACH
    • FEJÉR QUADRATURE FOR THE PIECEWISE CEV MODEL
    • ACCURACY AND EFFICIENCY COMPARISONS
    • THE PIECEWISE CEV MODEL
    • CONCLUSION
    • ACKNOWLEDGMENT
    • ENDNOTES
    • REFERENCES
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  • PDF (Subscribers Only)

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