Evaluating Interest Rate Derivatives with Discretely Observed Non-Gaussian Hull-White Models

• Activity Number: 683
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Takayuki Shiohama*
• Companies: Tokyo University of Science
• Keywords: asymptotic expansion ; Hull-White model ; zero-coupon bond option ; Japanese fixed income markets

Abstract

The short-term interest rate is one of the most important and fundamental variables in financial markets. There are essentially two approaches to model the term structure, the equilibrium model approach and the no-arbitrage approach. The Hull-White model is a no-arbitrage model and one of historically most important interest rate models, which has the closed formulas for prices of bonds, caplets and swaptions. In this paper, we price an interest rate derivatives under the discretely observed one-factor Hull-White models with non-Gaussian innovations. Higher order asymptotic expansion theory enables us to obtain the approximate prices of the zero-coupon bond option. We illustrate the analytical result by applying to the Japanese fixed income markets and then for valuing swaptions.