The beta-Meixner model

We propose to approximate the Meixner model by a member of the @b-family introduced by Kuznetsov (2010) in [2]. The advantage of the approximation is the semi-explicit formulae for the running extrema under the @b-family processes which enables us to produce more efficient algorithms for pricing path dependent options through the Wiener-Hopf factors. We will explore the performance of the approximation both in an equity framework and in the credit risk setting, where we use the approximation to calibrate a surface of credit default swaps. The paper follows the approach of the study made by Schoutens and Damme (2010) in [1], where the aim was to approximate the variance gamma. We will contextualize the results by Schoutens and Damme (2010) in [1] and the ones here with respect to the approach taken by Jeannin and Pistorius (2010) in [15]. An asymptotic expression for the rate of convergence of the approximation is derived.

[1]  Yurii Lyubarskii,et al.  Lectures on entire functions , 1996 .

[2]  Wim Schoutens,et al.  The β-variance gamma model , 2011 .

[3]  D. Hunter.  Pricing equity default swaps under an approximation to the CGMY Levy model , 2007 .

[4]  Sergei Levendorskii,et al.  Fast and accurate pricing of barrier options under Lévy processes , 2009, Finance Stochastics.

[5]  Sergei Levendorskii,et al.  Fast and Accurate Pricing of Barrier Options Under Levy Processes , 2007 .

[6]  Cornelis W. Oosterlee,et al.  Fast Valuation and Calibration of Credit Default Swaps Under Levy Dynamics , 2009 .

[7]  Aleksandar Mijatovic,et al.  Approximating Levy Processes with a View to Option Pricing , 2009 .

[8]  Alexey Kuznetsov,et al.  Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes , 2010, 1011.1790.

[9]  L. C. G. Rogers.  Evaluating first-passage probabilities for spectrally one-sided Lévy processes , 2000, Journal of Applied Probability.

[10]  Ernesto Mordecki,et al.  WIENER-HOPF FACTORIZATION FOR LEVY PROCESSES HAVING POSITIVE JUMPS WITH RATIONAL TRANSFORMS , 2005 .

[11]  Alexey Kuznetsov.  Wiener-Hopf Factorization for a Family of Lévy Processes Related to Theta Functions , 2010, Journal of Applied Probability.

[12]  W. Schoutens.  Lévy Processes in Finance: Pricing Financial Derivatives , 2003 .

[13]  Anja Feldmann,et al.  Fitting Mixtures of Exponentials to Long-Tail Distributions to Analyze Network , 1998, Perform. Evaluation.

[14]  J. C. Pardo,et al.  On the Lamperti stable processes , 2008, 0802.0851.

[15]  Andreas E. Kyprianou,et al.  Meromorphic Lévy processes and their fluctuation identities. , 2010, 1004.4671.

[16]  M. Pistorius,et al.  A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes , 2008, 0812.3128.

[17]  P. Carr,et al.  Option valuation using the fast Fourier transform , 1999 .

[18]  Hui Wang,et al.  First passage times of a jump diffusion process , 2003, Advances in Applied Probability.

[19]  W. Schoutens,et al.  Levy Processes in Credit Risk , 2009 .

[20]  S. Levendorskii,et al.  Barrier options and touch- and-out options under regular Lévy processes of exponential type , 2002 .

[21]  Cornelis W. Oosterlee,et al.  Pricing early-exercise and discrete barrier options by fourier-cosine series expansions , 2009, Numerische Mathematik.

[22]  Cornelis W. Oosterlee,et al.  A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions , 2008, SIAM J. Sci. Comput..

[23]  F. Utzet,et al.  Inversion of Analytic Characteristic Functions and Infinite Convolutions of Exponential and Laplace Densities , 2010, 1009.1543.

[24]  J. C. Pardo,et al.  A Wiener–Hopf Monte Carlo simulation technique for Lévy processes , 2009, 0912.4743.

[25]  M. Caballero,et al.  Conditioned stable Lévy processes and the Lamperti representation , 2006, Journal of Applied Probability.

[26]  O. Kudryavtsev,et al.  Efficient Pricing Options with Barrier and Lookback Features Under Levy Processes , 2011 .