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A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks

Frédéric Godin
The Journal of Derivatives Spring 2019, 26 (3) 97-107; DOI: https://doi.org/10.3905/jod.2019.1.071
Frédéric Godin
is an assistant professor in the Department of Mathematics and Statistics at Concordia University in Montréal, Canada and affiliate professor at the École d’Actuariat of Université Laval in Québec, Canada
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Abstract

This study obtains a closed-form solution for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. This extends the work of Rémillard and Rubenthaler (2013), who obtained closed-form formulas for some components of the hedging problem solution. Coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm. The author also presents a brief sensitivity analysis to determine the impact of the underlying asset drift and the hedging portfolio rebalancing frequency on the optimal hedging capital and the initial hedge ratio.

TOPICS: Options, statistical methods, performance measurement

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The Journal of Derivatives: 26 (3)
The Journal of Derivatives
Vol. 26, Issue 3
Spring 2019
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A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks
Frédéric Godin
The Journal of Derivatives Feb 2019, 26 (3) 97-107; DOI: 10.3905/jod.2019.1.071

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A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks
Frédéric Godin
The Journal of Derivatives Feb 2019, 26 (3) 97-107; DOI: 10.3905/jod.2019.1.071
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  • Article
    • Abstract
    • MARKET MODEL FOR HEDGING
    • EXPLICIT SOLUTIONS
    • A BRIEF SENSITIVITY ANALYSIS
    • CONCLUSION
    • APPENDIX
    • REFERENCES
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