Miquel Montero J. Stat. Mech. (2007) P04002 doi:10.1088/1742-5468/2007/04/P04002
Miquel Montero
Show affiliationsAmerican options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties—volatility and dividend policy—of the underlaying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because some of the most relevant facts that may potentially affect a firm will entail sharp predictable effects. We will analyse the consequences of this potential risk on perpetual American derivatives, a topic connected with a wide class of recurrent problems in physics: holders of American options must look for the fair price and the optimal exercise strategy at once, a typical question of free absorbing boundaries. We present explicit solutions to the most common contract specifications and derive analytical expressions concerning the mean and higher moments of the exercise time.
E-print Number: physics/0610047
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89.65.Gh Economics; econophysics, financial markets, business and management
02.50.-r Probability theory, stochastic processes, and statistics
91B24 Price theory and market structure
Issue 04 (April 2007)
Received 16 October 2006, accepted for publication 13 March 2007
Published 4 April 2007
Miquel Montero J. Stat. Mech. (2007) P04002
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