Numerical approximations for Heston-Hull-White type models

We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods

[1]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[2]  Cornelis W. Oosterlee,et al.  On the Heston Model with Stochastic Interest Rates , 2010, SIAM J. Financial Math..

[3]  Daniel B. Nelson,et al.  Simple Binomial Processes as Diffusion Approximations in Financial Models , 1990 .

[4]  L. Caramellino,et al.  A hybrid approach for the implementation of the Heston model , 2013, 1307.7178.

[5]  Francis A. Longstaff,et al.  Valuing American Options by Simulation: A Simple Least-Squares Approach , 2001 .

[6]  A robust tree method for pricing American options with CIR stochastic interest rate , 2013 .

[7]  John C. Hull,et al.  Numerical Procedures for Implementing Term Structure Models I , 1994 .

[8]  D. Brigo,et al.  Interest Rate Models , 2001 .

[9]  Aurélien Alfonsi,et al.  High order discretization schemes for the CIR process: Application to affine term structure and Heston models , 2010, Math. Comput..

[10]  L. Caramellino,et al.  A hybrid tree-finite difference approach for the Heston model , 2014 .

[11]  Jade Mitchell.  Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation , 2012 .

[12]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[13]  D. Lamberton,et al.  Sur l'approximation des réduites , 1990 .

[14]  Michel Vellekoop,et al.  A tree-based method to price American options in the Heston model , 2009 .

[15]  Donato Trigiante,et al.  Tridiagonal matrices: Invertibility and conditioning , 1992 .

[16]  S. Ethier,et al.  Markov Processes: Characterization and Convergence , 2005 .