Subordination JDCEV Processes And Its Application In Finance

In this paper we firstly study Levy subordinator and additive subordinator,and give a rich class of subordination diffusion processes through the combination of subor-dinator and diffusion process,and then obtain their spectral decomposition.Secondly,in this paper we develop a novel class of equity derivatives pricing models with state-dependent jumps and default intensity based on time changes of Markov processes with killing.When the time change is a Levy subordinator,we model the defaultable stock price process as a time-homogeneous Markov diffusion process with state-dependent jumps and killing rate(default intensity).When the time change is a additive subor-dinator,we model it as a time-inhomogeneous Markov diffusion process with state and time dependent jumps.We develop an approach to the pricing of equity derivatives in this class of models,based on the spectral expansion approach.If the spectral decompo-sition of the transition semigroup of the Markov process and the Laplace transform of the time change are both available in closed form,the expectation operator of the time changed process is expressed in closed form,i.e.,spectral decomposition.To illustrate our general framework,we time change the jump-to-default extended CEV model(JDCEV)and obtain a rich class of analytically tractable models with jumps and default intensity.These methods can be used to jointly price and hedge equity and credit derivatives,as well as be applied to many other processes in a variety of areas besides finance.