Valuation of Barrier Options in a Black--Scholes Setup with Jump Risk

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Valuation of Barrier Options in a Black--Scholes Setup with Jump Risk

Author Info

Dietmar P.J. Leisen

Abstract

This paper discusses the pitfalls in the pricing of barrier options a pproximations of the underlying continuous processes via discrete lattice models. These problems are studied first in a Black-Scholes model. Improvements result from a trinomial model and a further modified model where price changes occur at the jump times of a Poisson process. After the numerical difficulties have been resolved in the Black-Scholes model, unpredictable discontinuous price movements are incorporated.

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Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 446.

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Length: pages
Date of creation: Jan 1999
Date of revision:
Handle: RePEc:bon:bonsfb:446

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Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

NEP-ALL-1999-02-08 (All new papers)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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. [Downloadable!]
Other versions:
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Victor E. Vaugirard, 2001. "Monte Carlo applied to exotic digital options," Applied Mathematical Finance, Taylor and Francis Journals, vol. 8(3), pages 183-196, September. [Downloadable!] (restricted)

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