Chen model

In finance, the Chen model is a mathematical model describing the evolution of interest rates. It is a type of "three-factor model" (short-rate model) as it describes interest rate movements as driven by three sources of market risk. It was the first stochastic mean and stochastic volatility model and it was published in 1994 by Lin Chen, economist, theoretical physicist and former lecturer/professor at Beijing Institute of Technology, American University of Beirut, Yonsei University of Korea, and SunYetSan University .

The dynamics of the instantaneous interest rate are specified by the stochastic differential equations:

$dr_{t}=\kappa (\theta _{t}-r_{t})\,dt+{\sqrt {r_{t}}}\,{\sqrt {\sigma _{t}}}\,dW_{1},$

$d\theta _{t}=\nu (\zeta -\theta _{t})\,dt+\alpha \,{\sqrt {\theta _{t}}}\,dW_{2},$

$d\sigma _{t}=\mu (\beta -\sigma _{t})\,dt+\eta \,{\sqrt {\sigma _{t}}}\,dW_{3}.$

In an authoritative review of modern finance (Continuous-Time Methods in Finance: A Review and an Assessment), the Chen model is listed along with the models of Robert C. Merton, Oldrich Vasicek, John C. Cox, Stephen A. Ross, Darrell Duffie, John Hull, Robert A. Jarrow, and Emanuel Derman as a major term structure model.

Different variants of Chen model are still being used in financial institutions worldwide. James and Webber devote a section to discuss Chen model in their book; Gibson et al. devote a section to cover Chen model in their review article. Andersen et al. devote a paper to study and extend Chen model. Gallant et al. devote a paper to test Chen model and other models; Wibowo and Cai, among some others, devote their PhD dissertations to testing Chen model and other competing interest rate models.

References

• Andersen, T. G.; Benzoni, L.; Lund, J. (2004). Stochastic Volatility, Mean Drift, and Jumps in the Short-Term Interest Rate (Report). Econometric Society 2004 North American Winter Meetings.
• Cai, L. (2008). "Specification Testing for Multifactor Diffusion Processes:An Empirical and Methodological Analysis of Model Stability Across Different Historical Episodes" (PDF). Rutgers University.
• Chen, Lin (1996). "Stochastic Mean and Stochastic Volatility — A Three-Factor Model of the Term Structure of Interest Rates and Its Application to the Pricing of Interest Rate Derivatives". Financial Markets, Institutions & Instruments. 5: 1–88.
• Chen, Lin (1996). Interest Rate Dynamics, Derivatives Pricing, and Risk Management. Lecture Notes in Economics and Mathematical Systems. Vol. 435. Springer. ISBN 978-3-540-60814-1.
• Fabozzi, Frank J.; Choudhry, Moorad (2007). The Handbook of European Fixed Income Securities. Wiley Finance. ISBN 978-0-471-43039-1.
• Gallant, A. R.; Tauchen, G. (1997). "Estimation of Continuous Time Models for Stock Returns and Interest Rates". Macroeconomic Dynamics. 1 (1): 135–168. doi:10.1017/S1365100597002058.
• Gibson, Rajna; Lhabitant, François-Serge; Talay, Denis (2001). "Modeling the Term Structure of Interest Rates: A Review of the Literature". Foundations and Trends in Finance. 5 (1–2): 1–156. doi:10.1561/0500000032. ISBN 978-1-60198-372-5. ISSN 1567-2409.
• James, Jessica; Webber, Nick (2000). Interest Rate Modelling. Wiley Finance. ISBN 978-0-471-97523-6.
• Nawalkha, Sanjay K.; Soto, Gloria M.; Beliaeva, Natalia A. (2007). Dynamic Term Structure Modeling: The Fixed Income Valuation Course. Wiley Finance. ISBN 978-0-471-73714-8.
• Sundaresan, Suresh M. (2000). "Continuous-Time Methods in Finance: A Review and an Assessment". The Journal of Finance. 55 (4): 1569–1622. CiteSeerX 10.1.1.194.3963. doi:10.1111/0022-1082.00261.
• Wibowo, Arianto (2006). Continuous-time identification of exponential-affine term structure models (PhD thesis). Twente University.