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Value-At-Risk Estimation For Dynamic Hedging

Author

Listed:
  • YUJI YAMADA

    (Graduate School of Business Sciences, University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan)

  • JAMES A. PRIMBS

    (Management Science and Engineering, Stanford University, Terman Engineering Center 700-327, CA 94305-4026, USA)

Abstract

In this work, we develop an efficient methodology for analyzing risk in the wealth balance (hedging error) distribution arising from a mean square optimal dynamic hedge on a European call option, where the underlying stock price process is modeled on a multinomial lattice. By exploiting structure in mean square optimal hedging problems, we show that moments of the resulting wealth balance may be computed directly and efficiently on the stock lattice through the backward iteration of a matrix. Based on this moment information, convex optimization techniques are then used to estimate the Value-at-Risk of the hedge. This methodology is applied to a numerical example where the Value-at-Risk is estimated for a hedged European call option on a stock modeled on a trinomial lattice.

Suggested Citation

  • Yuji Yamada & James A. Primbs, 2002. "Value-At-Risk Estimation For Dynamic Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 333-354.
    • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:04:n:s0219024902001468
    DOI: 10.1142/S0219024902001468
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    Cited by:

    1. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.

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