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

BEÁTA STEHLÍKOVÁ

Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská Dolina, 842 25 Bratislava, Slovakia

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and

LUCA CAPRIOTTI

Quantitative Strategies, Credit Suisse, Eleven Madison Avenue, New York, NY 10010, USA

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https://doi.org/10.1142/S021902491450037XCited by:13 (Source: Crossref)

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.

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References

Y. Aït Sahalia, Journal of Finance 54(4), 1361 (1999). Crossref, Web of Science, Google Scholar
L. B. G. Andersen and V. V. Piterbarg , Interest Rate Modeling ( Atlantic Financial Press , London , 2010 ) . Google Scholar
A. Antonov and M. Spector, Risk 24(5), 66 (2011). Google Scholar
F. Black and P. Karasinski, Financial Analysts Journal 47(4), 52 (1991). Crossref, Google Scholar
L. Capriotti, International Journal on Theoretical and Applied Finance 9(7), 1179 (2006). Link, Google Scholar
L. Capriotti, New Econometric Modelling Research, ed. W. N. Toggins (Nova Publishers, New York, 2007) pp. 187–215. Google Scholar
J. C. Cox, J. E. Ingersoll and S. A. Ross, Econometrica 53(2), 385 (1985). Crossref, Web of Science, Google Scholar
J. C. Cox and S. A. Ross, Journal of Financial Economics 3(1), 145 (1976). Crossref, Web of Science, Google Scholar
D. Duffie, J. Pan and K. Singleton, Econometrica 68(6), 1343 (2000). Crossref, Web of Science, Google Scholar
P. Glasserman , Monte Carlo Methods in Financial Engineering ( Springer-Verlag , New York , 2004 ) . Google Scholar
J. Gregory , Counterparty Credit Risk: The New Challenge for Global Financial Markets ( Wiley , New York , 2010 ) . Google Scholar
J. Hull and A. White, Review of Financial Studies 3(4), 573 (1990). Crossref, Web of Science, Google Scholar
N. Makri and W. H. Miller, Journal of Chemical Physics 90(2), 904 (1989). Crossref, Web of Science, Google Scholar
D. O'Kane , Modelling Single-Name and Multi-Name Credit Derivatives ( Wiley , New York , 2008 ) . Google Scholar
S. E. Shreve , Stochastic Calculus for Finance ( Springer-Verlag , New York , 2004 ) . Google Scholar
B. Stehlíková (2014) Approximating the zero coupon bond price in a general one factor model with constant coefficients. Preprint, available at , arXiv:1408.5673 . Google Scholar
F. Tourrucôo, P. S. Hagan and G. F. Schleiniger, Applied Mathematical Finance 14(3), 107 (2007). Crossref, Google Scholar
O. A. Vasicek, Journal of Financial Economics 5(2), 177 (1977). Crossref, Web of Science, Google Scholar