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VAR-BASED OPTIMAL PARTIAL HEDGING

Published online by Cambridge University Press:  29 July 2013

Jianfa Cong ,
Ken Seng Tan  and
Chengguo Weng
Jianfa Cong
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of Waterloo, Waterloo, N2L 3G1, ON, Canada E-Mail: jcong@uwaterloo.ca
Ken Seng Tan*
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of Waterloo, Waterloo, N2L 3G1, ON, Canada
Chengguo Weng
Affiliation:
Department of Statistics and Actuarial ScienceUniversity of Waterloo, Waterloo, N2L 3G1, ON, Canada E-Mail: c2weng@uwaterloo.ca
*
E-Mail: kstan@uwaterloo.ca
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Abstract

Hedging is one of the most important topics in finance. When a financial market is complete, every contingent claim can be hedged perfectly to eliminate any potential future obligations. When the financial market is incomplete, the investor may eliminate his risk exposure by superhedging. In practice, both hedging strategies are not satisfactory due to their high implementation costs, which erode the chance of making any profit. A more practical and desirable strategy is to resort to the partial hedging, which hedges the future obligation only partially. The quantile hedging of Föllmer and Leukert (Finance and Stochastics, vol. 3, 1999, pp. 251–273), which maximizes the probability of a successful hedge for a given budget constraint, is an example of the partial hedging. Inspired by the principle underlying the partial hedging, this paper proposes a general partial hedging model by minimizing any desirable risk measure of the total risk exposure of an investor. By confining to the value-at-risk (VaR) measure, analytic optimal partial hedging strategies are derived. The optimal partial hedging strategy is either a knock-out call strategy or a bull call spread strategy, depending on the admissible classes of hedging strategies. Our proposed VaR-based partial hedging model has the advantage of its simplicity and robustness. The optimal hedging strategy is easy to determine. Furthermore, the structure of the optimal hedging strategy is independent of the assumed market model. This is in contrast to the quantile hedging, which is sensitive to the assumed model as well as the parameter values. Extensive numerical examples are provided to compare and contrast our proposed partial hedging to the quantile hedging.

Keywords

Quantile hedgingpartial hedgingoptimal strategyvalue-at-risk (VaR)bull call spreadknock-out call
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 3 , September 2013 , pp. 271 - 299
Copyright
Copyright © ASTIN Bulletin 2013 

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