AN EFFECTIVE APPROXIMATION FOR ZERO-COUPON BONDS AND ARROW–DEBREU PRICES IN THE BLACK–KARASINSKI MODEL

Beáta Stehlíková () and Luca Capriotti ()
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Beáta Stehlíková: Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská Dolina, 842 25 Bratislava, Slovakia
Luca Capriotti: Quantitative Strategies, Credit Suisse, Eleven Madison Avenue, New York, NY 10010, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 06, 1-16

Abstract: We present an accurate and easy-to-compute approximation of zero-coupon bonds and Arrow–Debreu (AD) prices for the Black–Karasinski (BK) 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 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S021902491450037X

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