Dong-Hyun Ahn, Jacob Boudoukh, Matthew Richardson, Robert F Whitelaw
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.
Subject: Hedging (Theoretical)
Ahn: (919) 962 3203
Boudoukh: jboudoukh@stern.nyu.edu
Richardson: (212) 998 0349 mrichar0@stern.nyu.edu
Whitelaw: (212) 998 0338 rwhitla@stern.nyu.edu
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