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

Part of: Mathematical finance

Published online by Cambridge University Press:  20 July 2016

Minseok Park ,
Kyungsub Lee  and
Geon Ho Choe
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:minseok.park@kaist.ac.kr (M. Park), ksublee@yu.ac.kr (K. Lee), choe@euclid.kaist.ac.kr (G. H. Choe)
*Corresponding author. Email addresses:minseok.park@kaist.ac.kr (M. Park), ksublee@yu.ac.kr (K. Lee), choe@euclid.kaist.ac.kr (G. H. Choe)
*Corresponding author. Email addresses:minseok.park@kaist.ac.kr (M. Park), ksublee@yu.ac.kr (K. Lee), choe@euclid.kaist.ac.kr (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.

Keywords

Delta-hedging errorsprofit and loss distributiondiscrete tradingjump-diffusion modeltransaction cost

MSC classification

Secondary: 91G20: Derivative securities 91G60: Numerical methods (including Monte Carlo methods)
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 3 , August 2016 , pp. 314 - 336
Copyright
Copyright © Global-Science Press 2016 

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