Exceptional accuracy and speed for option pricing are available via quadrature (Andricopoulos, Widdicks, Duck, and Newton, 2003), extending into multiple dimensions with complex path-dependency and early exercise (Andricopoulos, Widdicks, Newton, and Duck, 2007). However, the exposition is...

Option prices contain forward looking information about stock price volatility and, potentially, the probability of bankruptcy. We develop a risk-neutral density (RND) model consisting of a mixture of two lognormal densities with a probability of bankruptcy. We calibrate this model to daily...