publication . Article . Preprint . 2018

Tempered stable process, first passage time, and path-dependent option pricing

Young Shin Kim;
Open Access
  • Published: 29 Jan 2018 Journal: Computational Management Science, volume 16, pages 187-215 (issn: 1619-697X, eissn: 1619-6988, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
In this paper, we will discuss an approximation of the characteristic function of the first passage time for a Levy process using the martingale approach. The characteristic function of the first passage time of the tempered stable process is provided explicitly or by an indirect numerical method. This will be applied to the perpetual American option pricing and the barrier option pricing. Numerical illustrations are provided for the calibrated parameters using the market call and put prices.
Subjects
free text keywords: Management Information Systems, Information Systems, Valuation of options, Numerical analysis, Martingale (probability theory), First-hitting-time model, Mathematics, Characteristic function (probability theory), Barrier option, Stable process, Mathematical optimization, Lévy process, Quantitative Finance - Pricing of Securities
Related Organizations
22 references, page 1 of 2

D. Applebaum. Le´vy process and stochastic calculus. Cambridge Univ. Press, New York, 2004.

O. Barndorff-Nielsen. Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 353(1674): 401-419, 1977. ISSN 0080-4630. doi: 10.1098/rspa.1977.0041. URL http://rspa.royalsocietypublishing.org/content/353/1674/401.

O. E. Barndorff-Nielsen and S. Levendorskii. Feller processes of normal inverse gaussian type. Quantitative Finance, 1:318 - 331, 2001.

O. E. Barndorff-Nielsen and N. Shephard. Normal modified stable processes. Economics Series Working Papers from University of Oxford, Department of Economics, 72, 2001. [OpenAIRE]

F. Black and M. Scholes. The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3):637-654, 1973. [OpenAIRE]

E. Boguslavskaya. Solving optimal stopping problems for Le´vy processes in infinite horizon via A-transform. ArXiv e-prints, March 2014. [OpenAIRE]

S. I. Boyarchenko and S. Z. Levendorski˘i. Option pricing for truncated Le´vy processes. International Journal of Theoretical and Applied Finance, 3:549-552, 2000.

S. I. Boyarchenko and S. Z. Levendorski˘i. Non-Gaussian Merton-Black-Scholes Theory. World Scientific, 2002a. [OpenAIRE]

S. I. Boyarchenko and S. Z. Levendorski˘i. Perpetual american options under Le´vy processes. SIAM Journal on Control and Optimization, 40(6):1663-1696, 2002b. [OpenAIRE]

S. I. Boyarchenko and S. Z. Levendorski˘i. Barrier options and touch-and-out options under regular lvy processes of exponential type. The Annals of Applied Probability, 12(4): 1261-1298, 2002c. [OpenAIRE]

P. Carr and D. Madan. Option valuation using the fast fourier transform. Journal of Computational Finance, 2(4):61-73, 1999.

P. Carr, H. Geman, D. Madan, and M. Yor. The fine structure of asset returns: An empirical investigation. Journal of Business, 75(2):305-332, 2002. [OpenAIRE]

S. R. Chandra and D Mukherjee. Barrier option under lvy model : A pide and mellin transform approach. Mathematics, 4(1), 2016.

R. Cont and P. Tankov. Financial Modelling with Jump Processes. Chapman & Hall / CRC, 2004.

H. U. Gerber and E. S. W. Shiu. Martingale approach to pricing perpetual american options. Astin Bulletin, 24:195-220, 1994.

22 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . Preprint . 2018

Tempered stable process, first passage time, and path-dependent option pricing

Young Shin Kim;