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| {{Use dmy dates|date=November 2013}}
| | Irwin Butts is what my wife loves to call me though I don't really like being called like that. Since she was 18 she's been operating as a receptionist but her marketing by no means comes. One of the things she loves most is to study comics and she'll be starting some thing else along with it. North Dakota is our birth location.<br><br>Review my web blog; [http://www.pornextras.info/blog/129353 http://www.pornextras.info/blog/129353] |
| In [[finance]], the '''Chen model''' is a [[mathematical model]] describing the evolution of [[interest rate]]s. 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.
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| The dynamics of the instantaneous interest rate are specified by the [[stochastic differential equations]]:{{Clarify|needs to explain symbols in equations that follow|date=August 2009}}
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| :<math> dr_t = (\theta_t-\alpha_t)\,dt + \sqrt{r_t}\,\sigma_t\, dW_t,</math>
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| :<math> d \alpha_t = (\zeta_t-\alpha_t)\,dt + \sqrt{\alpha_t}\,\sigma_t\, dW_t,</math>
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| :<math> d \sigma_t = (\beta_t-\sigma_t)\,dt + \sqrt{\sigma_t}\,\eta_t\, dW_t.</math>
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| 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 C. Hull|John Hull]], Robert A. Jarrow, and [[Emanuel Derman]] as a major term structure model.
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| 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.
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| ==References==
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| *{{cite journal| author = Lin Chen |year= 1996 | title= 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 | journal=Financial Markets, Institutions, and Instruments |volume=5|pages=1–88}}
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| *{{cite book | author = Lin Chen | year = 1996 | title = Interest Rate Dynamics, Derivatives Pricing, and Risk Management | series=Lecture Notes in Economics and Mathematical Systems, 435|publisher = Springer| isbn=978-3-540-60814-1 }}
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| *{{cite book |author=Jessica James and Nick Webber |year=2000 |title=Interest Rate Modelling
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| |publisher=Wiley Finance |isbn=0-471-97523-0}}
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| *{{cite book |author=Rajna Gibson, [[François-Serge Lhabitant]] and Denis Talay |year=2001 |title=Modeling the Term Structure of Interest Rates: A Review of the Literature |publisher= RiskLab, ETH}}
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| *{{cite book |author= Frank J. Fabozzi and [[Moorad Choudhry]] |year=2007 |title=The Handbook of European Fixed Income Securities |publisher=Wiley Finance |isbn=0-471-43039-0}}
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| *{{cite book |author= Sanjay K. Nawalkha, Gloria M. Soto, Natalia A. Beliaeva |year=2007 |title=Dynamic Term Structure Modeling: The Fixed Income Valuation Course |publisher=Wiley Finance |isbn=0-471-73714-3}}
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| *{{cite journal |doi=10.1111/0022-1082.00261 |title=Continuous-Time Methods in Finance: A Review and an Assessment |author=Sundaresan, Suresh M. |journal=The Journal of Finance |volume=55 |year=2000|pages=1569–1622 |issue=54, number 4}}
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| *{{cite book |author= Andersen, T.G., L. Benzoni, and J. Lund |year=2004 |title=Stochastic Volatility, Mean Drift, and Jumps in the Short-Term Interest Rate, |publisher=Working Paper, Northwestern University}}
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| *{{cite book |author= Gallant, A.R., and G. Tauchen |year=1997 |title=Estimation of Continuous Time Models for Stock Returns and Interest Rates, |publisher=Macroeconomic Dynamics 1, 135-168.}}
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| *{{cite book |author= Cai, L.|year= 2008 |title=Specification Testing for Multifactor Diffusion Processes:An Empirical and Methodological Analysis of Model Stability Across Different Historical Episodes| publisher=Rutgers University |url=http://econweb.rutgers.edu/lcai/lili_files/JobMarketPaper.pdf
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| }}
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| *{{cite book |author=Wibowo A. |year= 2006 |title=Continuous-time identification of exponential-affine term structure models |publisher=Twente University | url = http://eprints.eemcs.utwente.nl
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| }}
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| {{Bond market}}
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| {{Stochastic processes}}
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| {{DEFAULTSORT:Chen Model}}
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| [[Category:Finance theories]]
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| [[Category:Interest rates]]
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| [[Category:Mathematical finance]]
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| [[Category:Fixed income analysis]]
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| [[Category:Short-rate models]]
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Irwin Butts is what my wife loves to call me though I don't really like being called like that. Since she was 18 she's been operating as a receptionist but her marketing by no means comes. One of the things she loves most is to study comics and she'll be starting some thing else along with it. North Dakota is our birth location.
Review my web blog; http://www.pornextras.info/blog/129353