Chen model

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In finance, the Chen model is a mathematical model describing the evolution of interest rates. It is a type of "one-factor model" (short rate model) as it describes interest rate movements as driven by only one source of market risk. It was the first stochastic mean and stochastic volatility model and it was introduced in 1996 by Lin Chen.

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

dr_t = (\theta_t-\alpha_t)\,dt + \sqrt{r_t}\,\sigma_t\, dW_t,

where

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.

[edit] References

  • Lin Chen (1996). Interest Rate Dynamics, Derivatives Pricing, and Risk Management. Springer. 
  • 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. Blackwell Publishers. 
  • Jessica James and Nick Webber (2000). Interest Rate Modelling. Wiely Finance. 
  • Rajna Gibson,François-Serge Lhabitant and Denis Talay (2001). Modeling the Term Structure of Interest Rates: A Review of the Literature. RiskLab, ETH. 
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