Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

APPROXIMATIONS OF OPTION PRICES FOR A JUMP-DIFFUSION MODEL

  • Wee, In-Suk (Department of Mathematics Korea University)
  • Published : 2006.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

Keywords

References

  1. S. Asmussen and J. Rosinski, Approximations of small jumps of Levy processes with a view towards simulation, J. Appl. Probab. 38 (2001), no. 1, 482-493 https://doi.org/10.1239/jap/996986757
  2. T. Chan, Pricing contingent claims on stocks driven by Levy process, Ann. Appl. Probab. 9 (1999), no. 2, 504-528 https://doi.org/10.1214/aoap/1029962753
  3. H. Follmer and M. Schweizer, Hedging of contingent claims under incomplete information, Applied stochastic analysis (London, 1989), 389-414, Stochastics Monogr., 5, Gordon and Breach, New York, 1991
  4. M. G. Garroni and J. L. Menaldi, Green Functions for Second Order Parabolic Integro-differential Problems, Longman Scientific and Technical, England, 1992
  5. I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations, Springer- Verlag, New York, 1972
  6. D. Heath and M. Schewizer, Martingales versus PDEs in finance: An equivalence result with examples, J. Appl. Prob. 37 (2000), 947-957 https://doi.org/10.1239/jap/1014843075
  7. D. Hong and I.-S.Wee, Convergence of jump-diffusion models to the Black-Scholes model, Stoch. Anal. Appl. 21 (2003), no. 1, 141-160 https://doi.org/10.1081/SAP-120017536