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Optimal Risk Management Using Options

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  • Dong-Hyun Ahn
  • Jacob Boudoukh
  • Matthew Richardson
  • Robert F. Whitelaw
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    Abstract

    This paper addresses the question of how an institution might optimally manage the market risk of a given exposure. We provide an analytical approach to optimal risk management under the assumption that the institution wishes to minimize its Value-at-Risk (VaR) using options follows a geometric Brownian. The optimal solution specifies the VaR-minimizing level of moneyness of the option as a function of the asset's distribution, the risk-free rate, and the VaR hedging period. We find that the optimal strike of the put is independent of the level of expense the institution is willing to incur for its hedging program. The costs associated with a suboptimal choice of exercise price, in terms of either the increased VaR for a fixed hedging cost or the increased cost to achieve a given VaR, are economically significant. Comparative static results show that the optimal strike price of these options is increasing in the asset's drift, decreasing in its volatility for most reasonable parameterizations, decreasing in the risk-free interest rate, nonmonotonic in the horizon of the hedge, and increasing in the level of protection desired by the institution (i.e., the percentage of the distribution relevant for the VaR). We show that the most important determinant is the conditional distribution of the underlying asset exposure; therefore, the optimal exercise price is very sensitive to the relative magnitude of the drift and diffusion of this exposure.

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    File URL: http://www.nber.org/papers/w6158.pdf
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    Bibliographic Info

    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 6158.

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    Date of creation: Sep 1997
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    Publication status: published as Journal of Finance, Vol. 54, no. 1 (February 1999): 359-375.
    Handle: RePEc:nbr:nberwo:6158

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    1. DeMarzo, Peter M & Duffie, Darrell, 1995. "Corporate Incentives for Hedging and Hedge Accounting," Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 743-71.
    2. Kenneth A. Froot & David S. Scharfstein & Jeremy C. Stein, 1992. "Risk Management: Coordinating Corporate Investment and Financing Policies," NBER Working Papers 4084, National Bureau of Economic Research, Inc.
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