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Volatility and Dividend Risk in Perpetual American Options

21 Pages Posted: 9 Nov 2006  

Miquel Montero

University of Barcelona - Department de Física Fonamental

Date Written: March 5, 2007

Abstract

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.

Suggested Citation

Montero, Miquel, Volatility and Dividend Risk in Perpetual American Options (March 5, 2007). Available at SSRN: https://ssrn.com/abstract=943045 or http://dx.doi.org/10.2139/ssrn.943045

Miquel Montero (Contact Author)

University of Barcelona - Department de Física Fonamental ( email )

Diagonal 647
Barcelona, Catalonia 08028
Spain
+34 93 403 92 07 (Phone)
+34 93 402 11 49 (Fax)

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