Title: Bond pricing under the generalised Black-Karasinski models

Authors: Nawdha Thakoor; Désiré Yannick Tangman; Muddun Bhuruth

Addresses: Department of Mathematics, University of Mauritius, Reduit, Mauritius ' Department of Mathematics, University of Mauritius, Reduit, Mauritius ' Department of Mathematics, University of Mauritius, Reduit, Mauritius

Abstract: Due to the lognormality of the short rate under the Black-Karasinski interest model, closed-form expressions for zero-coupon bond prices are not available. Existing methods for computing approximate prices include perturbation methods for solving the reaction-diffusion equation satisfied by the bond-price and the exponent expansion for computing the bond price via Arrow-Debreu prices. Perturbation methods are accurate for small volatility problems whereas the exponent expansion is accurate for small maturities. This work proposes a high-order computational method that works for all parameter settings. Several numerical examples are described to illustrate the high accuracy and rapid computation of bond prices.

Keywords: zero-coupon bond prices; generalised Black-Karasinski models; reaction-diffusion equation; fourth-order discretisations.

DOI: 10.1504/IJFMD.2017.086754

International Journal of Financial Markets and Derivatives, 2017 Vol.6 No.1, pp.57 - 73

Received: 24 Apr 2017
Accepted: 20 May 2017
Published online: 24 Sep 2017 *

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