Bond pricing under the generalised Black-Karasinski models. (2017) - Thakoor, Nawdha; Tangman, Désiré Yannick; Bhuruth, Muddun
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.