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

Posted: 29 Mar 2001

See all articles by Dietmar Leisen

Dietmar Leisen

Johannes Gutenberg University Mainz - Department of Banking

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Abstract

This paper discusses the pitfalls in the pricing of barrier options using approximations of the underlying continuous processes via discrete lattice models. To prevent from numerical deficiencies, the space axis is discretized first, and not the time axis. In a Black-Scholes setup, models with improved convergence properties are constructed: a trinomial model and a randomized trinomial model where price changes occur at the jump times of a Poisson process. These lattice models are sufficiently general to handle options with multiple barriers: the numerical difficulties are resolved and extrapolation yields even more accurate results. In a last step, we extend the Black-Scholes setup and incorporate unpredictable discontinuous price movements. The randomized trinomial model can easily be extended to this case, inheriting its superior convergence properties.

Keywords: barrier option, binomial model, lattice-approach, option valuation

JEL Classification: C63, G12, G13

Suggested Citation

Leisen, Dietmar P. J., Valuation of Barrier Options in a Black-Scholes Setup with Jump Risk. Available at SSRN: https://ssrn.com/abstract=262130

Dietmar P. J. Leisen (Contact Author)

Johannes Gutenberg University Mainz - Department of Banking ( email )

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