Stochastic Mean and Stochastic Volatility: A Four-Dimensional Term Structure of Interest Rates and its Application to the Pricing of Derivative Securities

Posted: 14 Sep 1999  

Lin Chen

Harvard University - Harvard Kennedy School (HKS)

Date Written: March 1, 1994

Abstract

In this paper a three-factor model of the term structure of interest rates is developed. In the model the future short rate depends on 1) the current short rate, 2) the short-term mean of the short rate, and 3) the current volatility of the short rate. Furthermore, it is assumed that both the short term mean of the short rate and the volatility of the short rate are stochastic and follow square-root process. The model is a substantial extension the seminal Cox-Ingersoll-Ross model of interest rates. A general formula for evaluating interest rate derivatives is presented. Closed-form solutions for prices of bond, bond option, futures, futures option, swap and cap are derived. The model can fit into the Heath-Jarrow-Morton arbitrage framework. The model is also useful for other practical purposes such as managing interest rate risks and formulating fixed income arbitrage strategies.

JEL Classification: G12

Suggested Citation

Chen, Lin, Stochastic Mean and Stochastic Volatility: A Four-Dimensional Term Structure of Interest Rates and its Application to the Pricing of Derivative Securities (March 1, 1994). Available at SSRN: https://ssrn.com/abstract=5515

Lin Chen (Contact Author)

Harvard University - Harvard Kennedy School (HKS) ( email )

79 John F. Kennedy Street
Cambridge, MA 02138
United States
617-628-2657 (Phone)
617-495-9285 (Fax)

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