Two-Factor Black-Karasinski Pricing Kernel

Turfus, Colin; Shubert, Alex

doi:10.2139/ssrn.3420977

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Two-Factor Black-Karasinski Pricing Kernel

15 Pages Posted: 17 Jul 2019 Last revised: 11 Aug 2021

See all articles by Colin Turfus

Alex Shubert

Independent

There are 2 versions of this paper

Date Written: August 6, 2019

Abstract

We present an analytic pricing kernel for a two-factor Black-Karasinski (lognormal) short rate model as a rapidly convergent perturbation expansion valid in the limit of low rates. Even the leading order expansion is found to be extremely accurate in most circumstances. We use this expansion to derive analytic formulae for conditional bond prices and thus for zero rates and forward rates. The model is equally applicable for the modelling of credit spreads and satisfies the important requirement of guaranteeing positive implied default probabilities. We suggest how these results could be used for interest rate and credit spread scenario generation in risk capital calculations and provide some representative scenario calculations.

Keywords: Black-Karasinski, pricing kernel, perturbation expansion, asymptotic, two-factor, risk capital, scenario generation, short rate model

Suggested Citation: Suggested Citation

Turfus, Colin and Shubert, Alex, Two-Factor Black-Karasinski Pricing Kernel (August 6, 2019). Available at SSRN: https://ssrn.com/abstract=3420977 or http://dx.doi.org/10.2139/ssrn.3420977