We first discuss some mathematical tools used to compute the intensity of a single jump process, in its canonical filtration. In the second part, we try to clarify the meaning of default and the links between the default time, the asset's filtration, and the intensity of the default time. We...

The price of a risky asset § is described by a Markov diffusion with jumps. In general there may be many equivalent martingale measures. Contingent claims which depend on the price of § at some time "T" may not be attainable, and the market may not be complete. However, using a martingale...

In this paper we use the Cox, Ingersoll, and Ross (1985b) single-factor, term structure model and extend it to the pricing of American default-free bond puts. We provide a quasi-analytical formula for these option prices based on recently established mathematical results for Bessel bridges,...

The exponential of a scalar diffusion is considered. Point estimates of the diffusion coefficient can be obtained by considering proportional increments of different powers of the exponential. an investigation of the minimum variance estimator gives unique optimal power. Copyright 1993 Blackwell...

It is shown how, even when the market is incomplete, certain contingent claims are attainable: that is, they can be represented as stochastic integrals with respect to the process which describes the evolution of the asset prices. Copyright 1995 Blackwell Publishers.

An equivalent martingale measure selection strategy for discrete time, continuous state, asset price evolution models is proposed. The minimal martingale law is shown to generally fail to produce a probability law in this context. The proposed strategy, termed the extended Girsanov principle,...