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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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References

[1]Bakshi, G. and Kapadia, N., Delta-hedged gains and the negative market volatility risk premium, Rev. Financ. Stud. 16, 527–566 (2003).CrossRefGoogle Scholar
[2]Bertsimas, D., Kogan, L. and Lo, A.W., When is time continuous, J. Financ. Econ. 55, 173–204 (2000).Google Scholar
[3]Black, F. and Scholes, M., The pricing of options and corporate liabilities, J. Polit. Econ. 81, 637–659 (1973).Google Scholar
[4]Boyle, P. and Vorst, T., Option replication in discrete time with transaction costs, J. Financ. 47, 271–293 (1992).Google Scholar
[5]Carr, P. and Wu, L., Static hedging of standard options, J. Financ. Econom. 12, 3–46 (2014).Google Scholar
[6]Cont, R. and Tankov, P., Financial Modelling with Jump Processes, Chapman & Hall, London (2004).Google Scholar
[7]Derman, E., When you cannot hedge continuously. The corrections of Black–Scholes, Risk Books 1, 82–85 (1999).Google Scholar
[8]Hayashi, T. and Myklana, P.A., Evaluating hedging errors: An asymptotic approach, Math. Financ. 15, 309–343 (2005).Google Scholar
[9]Leland, H.E., Option pricing and replication with transaction costs, J. Financ. 5, 1283–1301 (1985).CrossRefGoogle Scholar
[10]Merton, R., Theory of rational option pricing, Bell J. Econ. Manag. Sci. 4, 141–183 (1973).Google Scholar
[11]Merton, R., Option pricing when underlying stock returns are discontinuous, J. Financ. Econ. 3, 125–144 (1976).Google Scholar
[12]Mina, K.F., Cheang, G.H.L. and Chiarella, C., Approximate hedging of options under jump-diffusion processes, Int. J. Theor. Appl. Finan. 18, 1550024-1-1550024-26 (2015).Google Scholar
[13]Primbs, A. and Yamada, Y., A new computational tool for analysing dynamic hedging under transaction costs, Quant. Financ. 4, 405–413 (2008).Google Scholar
[14]Sepp, A., An approximate distribution of delta-hedging errors in a jump-diffusion model with discrete trading and transaction costs, Quant. Financ. 12, 1119–1141 (2012).CrossRefGoogle Scholar
[15]Tankov, P. and Voltchkova, E., Asymptotic analysis of hedginig errors in models with jumps, Stoch. Process. Their Appl. 119, 2004–2027 (2009).Google Scholar
[16]Toft, B.K., On the mean-variance tradeoff in option replication with transactions costs, J. Financ. Quant. Anal. 2, 233–263 (1996).Google Scholar