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Geometric Lévy Process Pricing Model

  • Yoshio Miyahara
  • Alexander Novikov
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    We consider models for stock prices which relates to random processes with independent homogeneous increments (Levy processes). These models are arbitrage free but correspond to the incomplete financial market. There are many different approaches for pricing of financial derivatives. We consider here mainly the approach which is based on minimal relative entropy. This method is related to an utility function of exponential type and the Esscher transformation of probabilistic measures.

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    File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp66.pdf
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    Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 66.

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    Date of creation: 01 Dec 2001
    Date of revision:
    Handle: RePEc:uts:rpaper:66
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    1. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52.
    3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    4. Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer, vol. 4(2), pages 97-124, May.
    5. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    6. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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