Jirô Akahori

On a symmetrization of diffusion processes

The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion processes. The present paper aims to give a basis to the use of the numerical scheme for Heston and SABR-type stochastic volatility models. This will be done by showing a fairly general result on the symmetrization (in multi-dimension/multi-reflections). Further applications (to time-inhomogeneous diffusions/ to time-dependent boundaries/to curved boundaries) are also discussed.

HEAT KERNEL INTEREST RATE MODELS WITH TIME-INHOMOGENEOUS MARKOV PROCESSES

We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over time. The result is a so-called weighted heat kernel that by construction is a supermartingale with respect to the filtration generated by the time-inhomogeneous Markov processes. As an application, we show how this framework naturally fits the information-based asset pricing framework where time-inhomogeneous Markov processes are utilized to model partial information about random economic factors. We present examples of pricing kernel models which lead to analytical formulae for bond prices along with explicit expressions for the associated interest rate and market price of risk. Furthermore, we also address the pricing of fixed-income derivatives within this framework.

Tau functions of KP solitons realized in Wiener space

In this paper, a probabilistic representation of the tau functions of KP (Kadomtsev-Petviashvili) solitons in terms of stochastic areas will be presented.

On the Quasi Gaussian Interest Rate Models

In this paper some remarks on the interest rate model proposed by Jamishidian (1991) and Ritchken and Sankarasubramanian (1995b) are presented.