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Distribution of Discrete Time Delta-Hedging Error via a Recursive Relation

Published online by Cambridge University Press:  20 July 2016

Minseok Park*
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon, Republic of Korea
Kyungsub Lee*
Affiliation:
Department of Statistics, Yeungnam University, Gyeongsan, Republic of Korea
Geon Ho Choe*
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon, Republic of Korea
*
*Corresponding author. Email addresses:[email protected] (M. Park), [email protected] (K. Lee), [email protected] (G. H. Choe)
*Corresponding author. Email addresses:[email protected] (M. Park), [email protected] (K. Lee), [email protected] (G. H. Choe)
*Corresponding author. Email addresses:[email protected] (M. Park), [email protected] (K. Lee), [email protected] (G. H. Choe)
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Abstract

We introduce a new method to compute the approximate distribution of the Delta-hedging error for a path-dependent option, and calculate its value over various strike prices via a recursive relation and numerical integration. Including geometric Brownian motion and Merton's jump diffusion model, we obtain the approximate distribution of the Delta-hedging error by differentiating its price with respect to the strike price. The distribution from Monte Carlo simulation is compared with that obtained by our method.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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