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Algorithms to price American and European equity options, convertible bonds and a variety of other financial derivatives. It uses an extension of the usual Black-Scholes model in which jump to default may occur at a probability specified by a power-law link between stock price and hazard rate as found in the paper by Takahashi, Kobayashi, and Nakagawa (2001) doi:10.3905/jfi.2001.319302. We use ideas and techniques from Andersen and Buffum (2002) doi:10.2139/ssrn.355308 and Linetsky (2006) doi:10.1111/j.1467-9965.2006.00271.x.