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Option pricing under jump diffusion model

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  • Qian Li
  • Li Wang

Abstract

We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series solution converges with a radius of convergence, and it is complemented by some numerical experiments to demonstrate its speed of convergence.

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  • Qian Li & Li Wang, 2023. "Option pricing under jump diffusion model," Papers 2305.10678, arXiv.org.
    • Handle: RePEc:arx:papers:2305.10678
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Bing‐Huei Lin & Shih‐Kuo Yeh, 1999. "Junp‐Diffusion Interest Rate Process: An Empirical Examination," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 26(7‐8), pages 967-995, September.
    3. Massoud Heidari & Liuren Wu, 2010. "Market Anticipation of Fed Policy Changes and the Term Structure of Interest Rates," Review of Finance, European Finance Association, vol. 14(2), pages 313-342.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, February.
    8. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    9. Bing-Huei Lin & Shih-Kuo Yeh, 1999. "Junp-Diffusion Interest Rate Process: An Empirical Examination," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 26(7&8), pages 967-995.
    10. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    11. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    12. 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 637-654, May-June.
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