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OPTIMAL LIQUIDATION OF DERIVATIVE PORTFOLIOS
Author(s) -
Henderson Vicky,
Hobson David
Publication year - 2011
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00455.x
Subject(s) - portfolio , derivative (finance) , asset (computer security) , tranche , mathematical economics , economics , infinitesimal , diversification (marketing strategy) , greeks , econometrics , financial economics , mathematics , actuarial science , computer science , business , mathematical analysis , computer security , marketing
We consider the problem facing a risk averse agent who seeks to liquidate or exercise a portfolio of (infinitely divisible) perpetual American style options on a single underlying asset. The optimal liquidation strategy is of threshold form and can be characterized explicitly as the solution of a calculus of variations problem. Apart from a possible initial exercise of a tranche of options, the optimal behavior involves liquidating the portfolio in infinitesimal amounts, but at times which are singular with respect to calendar time. We consider a number of illustrative examples involving CRRA and CARA utility, stocks, and portfolios of options with different strikes, and a model where the act of exercising has an impact on the underlying asset price.