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Analysis of Error with Malliavin Calculus: Application to Hedging

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  • E. Temam

Abstract

The aim of this paper is to compute the quadratic error of a discrete time‐hedging strategy in a complete multidimensional model. This result extends that of Gobet and Temam (2001) and Zhang (1999). More precisely, our basic assumption is that the asset prices satisfy the d‐dimensional stochastic differential equation dXit=Xit(bi(Xt)dt+σi,j(Xt)dWjt). We precisely describe the risk of this strategy with respect to n, the number of rebalancing times. The rates of convergence obtained are for any options with Lipschitz payoff and 1/n1/4 for options with irregular payoff.

Suggested Citation

  • E. Temam, 2003. "Analysis of Error with Malliavin Calculus: Application to Hedging," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 201-214, January.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:1:p:201-214
    DOI: 10.1111/1467-9965.00014
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    Cited by:

    1. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833, arXiv.org, revised Jul 2017.
    2. Jirô Akahori & Takafumi Amaba & Kaori Okuma, 2017. "A Discrete-Time Clark–Ocone Formula and its Application to an Error Analysis," Journal of Theoretical Probability, Springer, vol. 30(3), pages 932-960, September.
    3. Tsubasa Nishimura & Kenji Yasutomi & Tomooki Yuasa, 2022. "Higher-Order Error Estimates of the Discrete-Time Clark–Ocone Formula," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2518-2539, December.
    4. Takafumi Amaba, 2014. "A Discrete-Time Clark-Ocone Formula for Poisson Functionals," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(2), pages 97-120, May.

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