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Minimal variance hedging of options with student-t underlying

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  • Pinn, Klaus

Abstract

I explicitly work out closed form solutions for the optimal hedging strategies (in the sense of Bouchaud and Sornette) in the case of European call options, where the underlying is modeled by (unbiased) iid additive returns with the Student-t distributions. The results may serve as illustrative examples for option pricing in the presence of fat tails.

Suggested Citation

  • Pinn, Klaus, 2000. "Minimal variance hedging of options with student-t underlying," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(3), pages 581-595.
    • Handle: RePEc:eee:phsmap:v:276:y:2000:i:3:p:581-595
    DOI: 10.1016/S0378-4371(99)00498-7
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    References listed on IDEAS

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    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Erik Aurell & Sergei I. Simdyankin, 1998. "Pricing Risky Options Simply," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-23.
    3. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    4. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
    5. Ola Hammarlid, 1998. "On Minimizing Risk in Incomplete Markets Option Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 227-233.
    6. Grazyna Wolczynska, 1998. "Option pricing in incomplete discrete markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 165-179.
    7. Jean-Philippe Bouchaud & Didier Sornette, 1994. "The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes," Science & Finance (CFM) working paper archive 500040, Science & Finance, Capital Fund Management.
    8. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
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    Cited by:

    1. Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.

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