An Effective Approximation for Zero-Coupon Bonds and Arrow-Debreu Prices in the Black-Karasinski Model

15 Pages Posted: 27 Jan 2014

See all articles by Beata Stehlikova

Beata Stehlikova

Comenius University - Department of Applied Mathematics and Statistics

Luca Capriotti

University College London; NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Date Written: January 19, 2014

Abstract

We present an accurate and easy-to-compute approximation of zero-coupon bonds and Arrow-Debreu (AD) prices for the Black-Karasinski model of interest rates or default intensities. Through this procedure, dubbed exponent expansion, AD prices are obtained as a power series in time to maturity. This provides remarkably accurate results - for time horizons up to several years - even when truncated to the first few terms. For larger time horizons the exponent expansion can be combined with a fast numerical convolution to obtain extremely accurate results.

Keywords: Stochastic processes, Black-Karasinski, derivative pricing, power series expansions

Suggested Citation

Stehlikova, Beata and Capriotti, Luca, An Effective Approximation for Zero-Coupon Bonds and Arrow-Debreu Prices in the Black-Karasinski Model (January 19, 2014). Available at SSRN: https://ssrn.com/abstract=2385202 or http://dx.doi.org/10.2139/ssrn.2385202

Beata Stehlikova

Comenius University - Department of Applied Mathematics and Statistics ( email )

Mlynská dolina
SK-842 48 Bratislava, 842 48
Slovakia

Luca Capriotti (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States

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