| The LIBOR (London InterBank Offered Rate) market model of interest rates introduced in 1997 can be an interest version of the well known Black-Scholes model, and is currently the most popular model for the pricing of interest rate derivatives. In the LIBOR market model, interest rates are subject to a continuous process called diffusion process. Our recent empirical study, however, rejects the LIBOR market model. Other empirical studies have suggested that most of financial processes including interest rates are better described by a combination of diffusion and jump processes, i.e. jump-diffusion process, which implies that the economy has jump-diffusion information. Based on these empirical studies, many researchers have studied security market models with jump-diffusion information. In most of these models, the jump magnitude is specified as a continuously distributed random variable at each jump time, and the following are explicitly or implicitly assumed: (1) Agents have time additive utilities. (2) There exists a GE (General Equilibrium). (3) CCAPM (Consumption-Based Capital Asset Pricing Model) is statistically acceptable. However, in such models, the number of sources of uncertainty is infinite, and no finite set of securities complete the markets. In an incomplete market economy with time additive utility agents, it is very difficult to show the existence of GE, and the CCAPM is statistically unacceptable, and leads us to the equity premium puzzle and the risk-free rate puzzle. The class of stochastic differential utilities, which is a generalization of the class of standard time additive utilities, is proposed for solving these puzzles. We present the existence of GE, and derive a CCAPM in a security market economy with jump-diffusion information in each case of time additive utilities and of stochastic differential utilities. Then we show a GE framework for jump-diffusion option pricing models, and finally construct jump-diffusion LIBOR rate models in the GE framework. |
