Optimal Risk Management Using Options

24 Pages Posted: 7 Nov 2008

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: October 1997

Abstract

This paper provides an analytical solution to the problem of how an institution might optimally manage the market risk of a given exposure, under the assumption that the institution wishes to minimize its Value at Risk (VaR) using options. The solution specifies the VaR-minimizing level of moneyness of the options as a function of the underlying parameters. We show that the optimal hedge consists of a position in a single option whose strike price is independent of the level of expense the institution is willing to incur for its hedging program. The optimal strike price is increasing in the asset's drift, decreasing in its volatility for most reasonable parameter, 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 percentile of the distribution relevant for the VaR). Finally, we also show that the costs associated with a suboptimal choice of exercise price are economically significant.

Suggested Citation

Ahn, Dong-Hyun and Boudoukh, Jacob and Richardson, Matthew P. and Whitelaw, Robert F., Optimal Risk Management Using Options (October 1997). NYU Working Paper No. FIN-98-001. Available at SSRN: https://ssrn.com/abstract=1296391

Dong-Hyun Ahn

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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