Pricing Complex Barrier Options with General Features Using Sharp Large Deviation Estimates

  • Paolo Baldi
  • Lucia Caramellino
  • Maria Gabriella Iovino
Conference paper


In this paper we adapt the simulation procedures, already developed in a previous paper, in order to evaluate single and double barrier options with cash rebates and Parisian barrier options. Our method is based on Sharp Large Deviation estimates, which allow one to improve the usual Monte Carlo procedure. Numerical results are provided and show the validity of the proposed simulation algorithm.


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  1. Andersen, L., and Brotherton-Ratcliffe, R.: Exact Exotics. Risk 9 (1996) 85 – 89Google Scholar
  2. Baldi, P., Caramellino L. and Iovino M.G.: Pricing General Barrier Options: a Numerical Approach Using Sharp Large Deviations. To appear on Mathematical Finance (1998).Google Scholar
  3. Beaglehole, D.R.,Dybvig, P.H., and Zhou, G.: Going to Extremes: Correcting Simulation Bias in Exotic Option Valuation. Financial Analysts Journal 53(1997) 62 – 68CrossRefGoogle Scholar
  4. Black, F. and Scholes, M.: The Pricing of Options and Corporate Liabilities. Journal of Political Economy 81(1973) 637 – 654.CrossRefGoogle Scholar
  5. Boyle, P.P. and Tian, Y.: Pricing Path-Dependent Options under the CEV process. Working paper (1997).Google Scholar
  6. Broadie, M., Glasserman, P. and Kou, S.: A Continuity Correction for Discrete Barrier Options. Mathematical Finance 7(1997) 325 – 349.Google Scholar
  7. Chesney, M., Jeanblanc-Piqué, M. and Yor, M.: Brownian Excursion and Parisian Barrier Options. Advances in Applied Probability 29(1997) 165 – 184.CrossRefzbMATHMathSciNetGoogle Scholar
  8. Cox, J.C.: Notes on Option Pricing I: Constant Elasticity of Variance Diffusions. Unpublished note, Stanford University(1975).Google Scholar
  9. Linetsky, V.: Step Options (the Feynman-Kac Approach to Occupation Time Derivatives).University of Michigan, IOE Technical Report (1996) 96 – 18.Google Scholar
  10. Reiner, E. and Rubinstein, M.: Breacking Down the Barriers. Risk, September, 28–35.Google Scholar
  11. Revuz, D. and Yor, M.: Continuous Martingales and Brownian Motion. 2nd edition Springer Berlin (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Paolo Baldi
    • 1
  • Lucia Caramellino
    • 2
  • Maria Gabriella Iovino
    • 3
  1. 1.Dipartimento di MatematicaUniversity of Rome — Tor VergataRomaItaly
  2. 2.Dipartimento di MatematicaUniversity of Rome — Roma TreRomaItaly
  3. 3.Istituto di Matematica FinanziariaUniversity of PerugiaPerugiaItaly

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