In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method...

This paper proposes a framework for pricing credit derivatives within the defaultable Markovian HJM framework featuring unspanned stochastic volatility. Motivated by empirical evidence, hump-shaped level dependent stochastic volatility specifications are proposed, such that the model admits...

The paper derives a parsimonious two-component affine diffusion model for a world stock index to capture the dynamics of aggregate wealth. The observable state variables of the model are the normalized index and the inverse of the stochastic market activity, both modeled as square root...

In this paper we consider the evaluation of American call options on dividend paying stocks in the case where the underlying asset price evolves according to Heston’s (1993) stochastic volatility model. We solve the Kolmogorov partial differential equation associated with the driving...

This paper builds upon the authors' previous work on transformation of the Heath-Jarrow-Morton (HJM) model of the term structure of interest rates to state space form for a fairly general class of volatility specification including stochastic variables. Estimation of this volatility function is...

This paper studies the impact of stochastic volatility (SV) on optimal investment decisions. We consider three different SV models: an extended Stein/Stein model, the Heston Model and an extended Heston Model with a constant elasticity variance (CEV) process and derive the the long-term optimal...

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square root process as used by Heston (1993), and by a Poisson jump process as introduced by Merton (1976). Probability arguments are invoked to...

This paper derives a unified framework for portfolio optimization, derivative pricing, financial modeling and risk measurement. It is based on the natural assumption that investors prefer more or less, in the sense that the higher drift is preferred. Each such investor is shown to hold an...

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is...

A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the...