First Passage Time for Tempered Stable Process and Its Application to Perpetual American Option and Barrier Option Pricing

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Kim, Young Shin (2018)

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.
  • References (22)
    22 references, page 1 of 3

    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

    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.

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

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

    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.

    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.

    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.

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