# 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 economist Lin Chen, a Harvard doctorate, former US Federal Reserve Board economist, and professor of Yonsei University of Korea and Nanyang Tech University of Singapore.

The dynamics of the instantaneous interest rate are specified by the stochastic differential equations:[clarification needed]

$dr_t = (\theta_t-\alpha_t)\,dt + \sqrt{r_t}\,\sigma_t\, dW_t,$
$d \alpha_t = (\zeta_t-\alpha_t)\,dt + \sqrt{\alpha_t}\,\sigma_t\, dW_t,$
$d \sigma_t = (\beta_t-\sigma_t)\,dt + \sqrt{\sigma_t}\,\eta_t\, dW_t.$

In an authoritative review of modern finance (Continuous-Time Methods in Finance: A Review and an Assessment), 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

• Lin Chen (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, and Instruments 5: 1–88.
• Lin Chen (1996). Interest Rate Dynamics, Derivatives Pricing, and Risk Management. Lecture Notes in Economics and Mathematical Systems, 435. Springer. ISBN 978-3-540-60814-1.
• Jessica James and Nick Webber (2000). Interest Rate Modelling. Wiley Finance. ISBN 0-471-97523-0.
• Rajna Gibson, François-Serge Lhabitant and Denis Talay (2001). Modeling the Term Structure of Interest Rates: A Review of the Literature. RiskLab, ETH.
• Frank J. Fabozzi and Moorad Choudhry (2007). The Handbook of European Fixed Income Securities. Wiley Finance. ISBN 0-471-43039-0.
• Sanjay K. Nawalkha, Gloria M. Soto, Natalia A. Beliaeva (2007). Dynamic Term Structure Modeling: The Fixed Income Valuation Course. Wiley Finance. ISBN 0-471-73714-3.
• Sundaresan, Suresh M. (2000). "Continuous-Time Methods in Finance: A Review and an Assessment". The Journal of Finance 55 (54, number 4): 1569–1622. doi:10.1111/0022-1082.00261.
• Andersen, T.G., L. Benzoni, and J. Lund (2004). Stochastic Volatility, Mean Drift, and Jumps in the Short-Term Interest Rate,. Working Paper, Northwestern University.
• Gallant, A.R., and G. Tauchen (1997). Estimation of Continuous Time Models for Stock Returns and Interest Rates,. Macroeconomic Dynamics 1, 135-168.
• Wibowo A. (2006). Continuous-time identification of exponential-affine term structure models. Twente University.