Option pricing and hedging under a stochastic volatility Lévy process model

被引:0
作者
Young Shin Kim
Frank J. Fabozzi
Zuodong Lin
Svetlozar T. Rachev
机构
[1] Karlsruhe Institute of Technology,Department of Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering
[2] EDHEC Business School,HECTOR School of Engineering and Management, International Department
[3] Karlsruhe Institute of Technology,Department of Applied Mathematics and Statistics
[4] Stony Brook University,undefined
[5] FinAnalytica,undefined
来源
Review of Derivatives Research | 2012年 / 15卷
关键词
Option pricing; Hedging; Stochastic volatility; Continuous Markov chain; Regime-switching model; Lévy process; Esscher transform; C6; G11; G12; G13;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper, we discuss a stochastic volatility model with a Lévy driving process and then apply the model to option pricing and hedging. The stochastic volatility in our model is defined by the continuous Markov chain. The risk-neutral measure is obtained by applying the Esscher transform. The option price using this model is computed by the Fourier transform method. We obtain the closed-form solution for the hedge ratio by applying locally risk-minimizing hedging.
引用
收藏
页码:81 / 97
页数:16
相关论文
共 35 条
  • [1] Bates D. S.(1996)Jumps and stochastic volatility: The exchange rate processes implicit in deutschemark options Review of Financial Studies 9 69-107
  • [2] Black F.(1973)The pricing of options and corporate liabilities Journal of Political Economy 81 637-654
  • [3] Scholes M.(2002)American options with regime switching International Journal of Theoretical and Applied Finance 5 497-514
  • [4] Buffington J.(2003)Stochastic volatility for Lévy processes Mathematical Finance 3 345-382
  • [5] Elliott R. J.(1999)Option valuation using the fast Fourier transform Journal of Computational Finance 2 61-73
  • [6] Carr P.(1995)The GARCH option pricing model Mathematical Finance 5 13-32
  • [7] Geman H.(2005)Option pricing and Esscher transform under regime switching Annals of Finance 1 423-432
  • [8] Madan D.(2003)The minimal entropy martingale measures for geometric Lévy processes Finance & Stochastics 7 509-531
  • [9] Yor M.(1994)Option pricing by Esscher transforms Transactions of the Society of Actuaries XLVI 99-140
  • [10] Carr P.(1993)A closed form solution for options with stochastic volatility with applications to bond and currency options Review of Financial Studies 6 327-343