We extend the short rate model of Vasicek (1977) to include jumps in the local mean. Conditions ensuring existence of a unique equivalent martingale measure are given, implying that the model is arbitrage-free and complete. We develop efficient numerical methods for computation of zero coupon...

By extending the GARCH option pricing model of Duan (1995) to more flexible volatility estimation it is shown that the prices of out-of-the-money options strongly depend on volatility features such as asymmetry. Results are provided for the properties of the stationary pricing distribution in...

This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be...

Stochastic flows and their Jacobians are used to show why, when the short rate process is described by Gaussian dynamics, (as in the Vasicek or Hull-White models), or square root, affine (Bessel) processes, (as in the Cox-Ingersoll-Ross, or Duffie-Kan models), the bond price is an exponential...

For a Markov process $x_t$, the forward measure $P^T$ over the time interval $[0,T]$ is defined by the Radon-Nikodym derivative $dP^T/dP = M\exp(-\int_0^Tc(x_s)ds)$, where $c$ is a given non-negative function and $M$ is the normalizing constant. In this paper, the law of $x_t$ under the forward...

The Market Models of the term structure of interest rates, in which forward LIBOR or forward swap rates are modelled to be lognormal under the forward probability measure of the corresponding maturity, are extended to a multicurrency setting. If lognormal dynamics are assumed for forward LIBOR...

We introduce a general class of interest rate models in which the value of pure discount bonds can be expressed as a functional of some (low-dimensional) Markov process. At the abstract level this class includes all current models of practical importance. By specifying these models in...

We analyze the joint convergence of sequences of discounted stock prices and Radon-Nicodym derivatives of the minimal martingale measure when interest rates are stochastic. Therefrom we deduce the convergence of option values in either complete or incomplete markets. We illustrate the general...

In this paper, a class of forward rate dependent Markovian transformations of the Heath-Jarrow-Morton [16] term structure model are obtained by considering volatility processes that are solutions of linear ordinary differential equations. These transformations generalise the Markovian systems...

A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among...