Physics – Physics and Society
Scientific paper
2006-10-09
J. Stat. Mech. (2007) P04002
Physics
Physics and Society
21 pages, 5 figures, iopart, submitted for publication; deep revision, two new appendices
Scientific paper
10.1088/1742-5468/2007/04/P04002
American 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.
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