A Preference Free Partial Differential Equation for the Term Structure of Interest Rates
|Author(s):||Carl Chiarella & Nadima El-Hassan|
|Date of publication:||May 1996|
|Working paper number:||63|
The objectives of this paper are twofold: the first is the reconciliation of the differences between the Vasicek and the Heath-Jarrow-Morton approaches to the modelling of term structure of interest rates. We demonstrate that under certain (not empirically unreasonable) assumptions prices of interest-rate sensitive claims within the Heath-Jarrow-Morton framework can be expressed as a partial differential equation which both is preference-free and matches the currently observed yield curve. This partial differential equation is shown to be equivalent to the extended Vasicek model of Hull and White. The second is the pricing of interest rate claims in this framework. The preference free partial differential equation that we obtain has the added advantage that it allows us to bring to bear on the problem of evaluating American style contingent claims in a stochastic interest rate environment the various numerical techniques for solving free boundary value problems which have been developed in recent years such as the method of lines.
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|Comments:||Published as: Chiarella, C. and El-Hassan, N., 1996, "A Preference Free Partial Differential Equation for the Term Structure of Interest Rates", Financial Engineering and the Japanese Markets, 3(3), 217-238.|
Bhar, R., 2010, Stochastic Filtering With Applications in Finance, World Scientific.
Bhar. R. and Chiarella, C., 1997, "Interest Rate Futures: Estimation of Volatility Parameters in an Arbitrage-Free Framework", Applied Mathematical Finance, 4(4),181-199.
Bhar. R. and Chiarella, C., 2000, "Approximating Heath-Jarrow-Morton Non-Markovian Term Structure of Interest Rate Models with Markovian Systems", Working Paper: 76, Finance Discipline Group, University of Technology, Sydney
Bhar, R., Chiarella, C., El-Hassan, N. and Zheng, X., 2000, "The Reduction of Forward Rate Dependent Volatility HJM Models to Markovian Form: Pricing European Bond Options", Research Paper: 36, Quantitative Finance Research Centre, University of Technology, Sydney.
Chiarella, C. and El-Hassan, N., 1997, "Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques", Journal of Financial Engineering, 6(2), 121-147
Chiarella, C. and El-Hassan, N., 1999, "Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines", Research Paper: 12, Quantitative Finance Research Centre, University of Technology, Sydney.
Chiarella, C. and Nikitopoulos Sklibosios, C., 2003, "A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework", Asia-Pacific Financial Markets, 10(2-3), 87-127.