Bond pricing under the generalised Black-Karasinski models. (2017)

• Record Type: Journal Article
• Authors: Thakoor, Nawdha; Tangman, Désiré Yannick; Bhuruth, Muddun
• Is Part Of: International journal of financial markets and derivatives. Volume 6:Number 1(2017)
• Page Start: 57
• Page End: 73
• Publication Date: 2017
• Subjects: zero-coupon bond prices -- generalised Black-Karasinski models -- reaction-diffusion equation -- fourth-order discretisations; Derivative securities -- Mathematical models -- Periodicals; Capital market -- Periodicals; 332.605
• Languages: English
• ISSNs: 1756-7130

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.