Pricing American Options in a Jump Diffusion Model

In this study, we use the McKean's integral equation to evaluate the American option price for the constant jump diffusion models. The early exercise boundary is ap- proximated by a multipiece exponential function. Approximate closed-form solution of the no arbitrage American option prices are obtained . Simulation studies are performed to evaluate accuracy of the derived formula. The results show that the proposed method improves the pricing of American option for larger dividend rates. Keywords-American options; early exercise boundary; early exercise premium; jump diffusion model; McKean's equation.

[2]  McKean's Methods Applied to American Call Options on Jump-Diffusion Processes , 2004 .

[3]  A Survey of the Integral Representation of American Option Prices , 2004 .

[4]  Steven Kou,et al.  A Jump Diffusion Model for Option Pricing , 2001, Manag. Sci..

[5]  Chandrasekhar Reddy Gukhal.  Analytical Valuation of American Options on Jump-Diffusion Processes , 2001 .

[6]  M. Jeanblanc,et al.  Pricing American currency options in an exponential Lévy model , 2004 .

[7]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[8]  P. Carr,et al.  ALTERNATIVE CHARACTERIZATIONS OF AMERICAN PUT OPTIONS , 1992 .

[9]  Antonella Basso,et al.  Optimal exercise of American options , 2002 .

[10]  Byung Chun Kim,et al.  The Analytical Valuation of American Average Rate Options , 2004 .

[11]  I. Kim.  The Analytic Valuation of American Options , 1990 .

[12]  H. Johnson,et al.  The American Put Option Valued Analytically , 1984 .

[13]  David S. Bates.  The Crash of ʼ87: Was It Expected? The Evidence from Options Markets , 1991 .

[14]  McKean’s Method applied to American Call Options on Jump-Diffusion Processes , 2003 .

[15]  Tze Leung Lai,et al.  Exercise boundaries and efficient approximations to American option prices and hedge parameters , 2000 .

[16]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[17]  Rui Zhong,et al.  An Approximate Formula for Pricing American Options , 1999 .

[18]  G. Barone-Adesi,et al.  Efficient Analytic Approximation of American Option Values , 1987 .

[19]  Marti G. Subrahmanyam,et al.  Pricing and Hedging American Options: A Recursive Integration Method , 1995 .