In practical applications, it is not uncommon for the hazard functions obtained for two groups to converge with time. We develop a procedure for testing the proportional odds assumption when the available data consists of two independent random samples of randomly right censored lifetimes.

This paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option price. It explicitly treats the fact that only a discrete data set can be observed in practice, The framework is general and allows for state dependent volatility and jumps.