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Perpetual American options are financial instruments that can be readilyexercised and do not mature. In this paper we study in detail the problem ofpricing this kind of derivatives, for the most popular flavour, within aframework in which some of the properties |volatility and dividend policy| ofthe underlying stock can change at a random instant of time, but in such a waythat we can forecast their final values. Under this assumption we can modelactual market conditions because most relevant facts usually entail sharppredictable consequences. The effect of this potential risk on perpetualAmerican vanilla options is remarkable: the very equation that will determinethe fair price depends on the solution to be found. Sound results are foundunder the optics both of finance and physics. In particular, a parallelismamong the overall outcome of this problem and a phase transition isestablished.

Perpetual American vanilla option pricing under single regime change risk. An exhaustive study