Lech A. Grzelak

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We discuss the Heston [Heston-1993] model with stochastic interest rates driven by Hull-White [Hull,White-1996] (HW) or Cox-Ingersoll-Ross [Cox, et al.-1985] (CIR) processes. Two projection techniques to derive affine approximations of the original hybrid models are presented. In these approximations we can prescibe a non-zero correlation structure between(More)
We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump diffusion-linear quadratic jump-diffusion processes (Duffie, Pan and Singleton [13],(More)
The aim of the study was to evaluate the intensity of oxygen-derived free radicals generation (expressed as the lipid peroxidation process), as well as antioxidant potential changes in patients with cervical spinal cord injury. Subjects in the study were 32 patients treated in the Neurosurgery and Neurotraumatology Clinic, Medical University in Bydgoszcz.(More)
We analyze the efficiency properties of a numerical pricing method based on Fourier-cosine expansions for early-exercise options. We focus on variants of Schwartz' model based on a mean reverting Ornstein-Uhlenbeck process, which is commonly used for modeling commodity prices. This process however does not possess favorable properties for the option pricing(More)
We consider a Heston type inflation model in combination with a Hull-White model for nominal and real interest rates, in which all the correlations can be non-zero. Due to the presence of the Heston dynamics our derived inflation model is able to capture the implied volatility skew/smile, which is present in the inflation option market data. We derive an(More)
For European plain vanilla options, we investigate the difference between solutions obtained by the full-scale and an approximate Heston-Hull-White (HHW) model. Based on the corresponding two option pricing PDEs, we analyze the quality of the approximation. To confirm the accuracy of the analysis, we solve the HHW PDE, its approximating PDE as well as the(More)
In this article we define a multi-factor equity-interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model [24] and we use a Gaussian multi-factor short-rate process [7; 25]. By construction, the model fits in the framework of affine diffusion processes [11] allowing fast(More)
We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main processes. By an appropriate change of measure the dimension of(More)
Author: please check running head on odd pages – abbreviated form of title OK? Please provide a full postal address for the Rabobank International affiliation. We model the joint dynamics of stock prices and interest rates using a hybrid Direct citations removed from abstract according to journal style – OK? Also, changes to first sentence of text OK?(More)
In this article we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston [14] enhanced by a non-parametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire [8] and Derman & Kani [7]. In particular, the additional local(More)