On Asian option pricing for NIG Lévy processes

In this paper, we derive approximations and bounds for the Esscher price of European-style arithmetic and geometric average options. The asset price process is assumed to be of exponential Levy type with normal inverse Gaussian (NIG) distributed log-returns. Numerical illustrations of the accuracy of these bounds as well as approximations and comparisons of the NIG average option prices with the corresponding Black-Scholes prices are given.

[1]  D. Madan,et al.  1option Pricing with V. G. Martingale Components , 1991 .

[2]  E. Eberlein,et al.  The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures , 2002 .

[3]  Edmond Levy.  Pricing European average rate currency options , 1992 .

[4]  Freddy Delbaen,et al.  No-arbitrage, change of measure and conditional Esscher transforms , 1996 .

[5]  A. Kemna,et al.  A pricing method for options based on average asset values , 1990 .

[6]  R. Jarrow,et al.  APPROXIMATE OPTION VALUATION FOR ARBITRARY STOCHASTIC PROCESSES , 1982 .

[7]  K. Prause.  The Generalized Hyperbolic Model: Estimation, Financial Derivatives, and Risk Measures , 1999 .

[8]  S. R. Pliska,et al.  Mathematical Finance, Bachelier Congres 2000 , 2002 .

[9]  Hans U. Gerber,et al.  Option pricing by Esscher transforms. , 1995 .

[10]  S. Turnbull,et al.  A Quick Algorithm for Pricing European Average Options , 1991, Journal of Financial and Quantitative Analysis.

[11]  O. Barndorff-Nielsen.  Exponentially decreasing distributions for the logarithm of particle size , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[12]  E. Eberlein,et al.  Hyperbolic distributions in finance , 1995 .

[13]  Pure Jump Levy Processes for Asset Price Modelling , 2002 .

[14]  E. Eberlein.  Application of Generalized Hyperbolic Lévy Motions to Finance , 2001 .

[15]  T. Vorst.  Prices and Hedge Ratios of Average Exchange Rate Options , 1992 .

[16]  O. Barndorff-Nielsen,et al.  Lévy processes : theory and applications , 2001 .

[17]  H. Geman.  Pure jump L'evy processes for asset price modeling , 2002 .

[18]  Tina Hviid Rydberg.  Generalized Hyperbolic Diffusion Processes with Applications in Finance , 1999 .

[19]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[20]  Jan Dhaene,et al.  An easy computable upper bound for the price of an arithmetic Asian option , 2000 .

[21]  Jan Dhaene,et al.  The Concept of Comonotonicity in Actuarial Science and Finance: Theory , 2002, Insurance: Mathematics and Economics.

[22]  O. Barndorff-Nielsen.  Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling , 1997 .

[23]  S. Raible,et al.  Lévy Processes in Finance: Theory, Numerics, and Empirical Facts , 2000 .

[24]  Peter Grandits,et al.  The p-optimal martingale measure and its asymptotic relation with the minimal-entropy martingale measure , 1999 .

[25]  Ole E. Barndorff-Nielsen,et al.  Processes of normal inverse Gaussian type , 1997, Finance Stochastics.

[26]  Tina Hviid Rydberg.  The normal inverse gaussian lévy process: simulation and approximation , 1997 .