A Joint Stock and Bond Market based on the Hyperbolic Gaussian Model

Abstract

In this paper, we introduce a joint bond and stock market model based on the state price density approach as a mean to discount future payments—whether these are stochastic dividend payments or secure repayments of government zerobonds. Based upon a recipe of Rogers [20], we define a state price density model, the so-called Hyperbolic Gaussian model which allows for closed form zerobond prices and stock prices in an arbitrage-free way. It is particularly useful for insurance applications where large time horizons are considered. We estimate the joint factor model using the extended Kalman filter. The model we propose here is computationally much simpler than other models which have been considered in the literature.