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 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)
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? SABR–Hull–White model. The asset price dynamics are modeled by the SABR model of Hagan et al and the interest rate dynamics are modeled by the Hull– White short-rate(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)
ANTHONIE W. VAN DER STOEP†,‡,§, LECH A. GRZELAK†,‡ and CORNELIS W. OOSTERLEE∗,‡ ∗Delft Institute of Applied Mathematics, Delft University of Technology Mekelweg 4, 2628 CD, Delft, The Netherlands †Derivatives Research and Validation Group, Rabobank Graadt van Roggenweg 400, 3531 AH, Utrecht, The Netherlands ‡CWI — National Research Institute for Mathematics(More)
We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull-White [HW96]. We then extend the framework by modeling 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)
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)
Extension of stochastic volatility equity models with the Hull–White interest rate process Lech A. Grzelak a b , Cornelis W. Oosterlee a c & Sacha Van Weeren b a Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands b Derivatives Research and Validation Group, Rabobank, Jaarbeursplein 22, 3521 AP(More)