Optimal Risk Management Using Options

45 Pages Posted: 25 May 2006

See all articles by Dong-Hyun Ahn

Dong-Hyun Ahn

University of North Carolina at Chapel Hill

Jacob Boudoukh

Interdisciplinary Center (IDC) Herzliyah; AQR Capital Management, LLC

Matthew P. Richardson

New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER); AQR Capital Management, LLC

Robert Whitelaw

New York University; National Bureau of Economic Research (NBER)

Multiple version iconThere are 3 versions of this paper

Date Written: September 1997

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.

Suggested Citation

Ahn, Dong-Hyun and Boudoukh, Jacob and Richardson, Matthew P. and Whitelaw, Robert F., Optimal Risk Management Using Options (September 1997). NBER Working Paper No. w6158. Available at SSRN: https://ssrn.com/abstract=225921

Dong-Hyun Ahn (Contact Author)

University of North Carolina at Chapel Hill ( email )

Kenan-Flagler Business School
Chapel Hill, NC 27599-3490
United States
919-962-3203 (Phone)
919-962-2068 (Fax)

Jacob Boudoukh

Interdisciplinary Center (IDC) Herzliyah ( email )

P.O. Box 167
Herzliya, 46150
Israel

AQR Capital Management, LLC ( email )

Greenwich, CT
United States

Matthew P. Richardson

New York University (NYU) - Department of Finance ( email )

44 West 4th Street
Suite 9-190
New York, NY 10012-1126
United States
212-998-0349 (Phone)
212-995-4233 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

AQR Capital Management, LLC ( email )

Greenwich, CT
United States

Robert F. Whitelaw

New York University ( email )

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States
212-998-0338 (Phone)
212-995-4233 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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