Bond pricing under the generalised Black-Karasinski models
by Nawdha Thakoor; Désiré Yannick Tangman; Muddun Bhuruth
International Journal of Financial Markets and Derivatives (IJFMD), Vol. 6, No. 1, 2017

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.

Online publication date: Sun, 24-Sep-2017

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