Managerial Finance

Purpose – The purpose of this paper is to derive semi-closed-form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine-term structure models.

Design/methodology/approach – The paper first derives the Frobenius series solution to the cross-moment generating function, and then inverts the related characteristic function using the Gauss-Laguerre quadrature rule for the corresponding cumulative probabilities.

Findings – This paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.

Research limitations/implications – Future research could extend the approach adopted in this paper to some non-affine-term structure models such as quadratic models.

Practical implications – The valuation approach in this study can be used to price mortgage-backed securities, asset-backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed-income portfolios.

Originality/value – This paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.