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, financial economist and environmental economist, professor of American University, Yonsei University and Nanyang Tech University of Singapore.

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

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 & 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.
Cai, L. (2008). Specification Testing for Multifactor Diffusion Processes:An Empirical and Methodological Analysis of Model Stability Across Different Historical Episodes (PDF). Rutgers University.
Wibowo A. (2006). Continuous-time identification of exponential-affine term structure models. Twente University.

Bond market

Bond Debenture Fixed income

Types of bonds by issuer	Agency bond Corporate bond Senior debt Subordinated debt Distressed debt Emerging market debt Government bond Municipal bond

Types of bonds by payout	Accrual bond Auction rate security Callable bond Commercial paper Contingent convertible bond Convertible bond Exchangeable bond Extendible bond Fixed rate bond Floating rate note High-yield debt Inflation-indexed bond Inverse floating rate note Perpetual bond Puttable bond Reverse convertible securities Zero-coupon bond

Bond valuation	Clean price Convexity Coupon Credit spread Current yield Dirty price Duration I-spread Mortgage yield Nominal yield Yield to maturity Z-spread

Securitized products	Asset-backed security Collateralized debt obligation Collateralized mortgage obligation Commercial mortgage-backed security Mortgage-backed security Yield-curve spread

Bond options	Callable bond Convertible bond Embedded option Exchangeable bond Extendible bond Option-adjusted spread Puttable bond

Institutions	Commercial Mortgage Securities Association (CMSA) International Capital Market Association (ICMA) Securities Industry and Financial Markets Association (SIFMA)

Stochastic processes

Discrete time	Bernoulli process Branching process Chinese restaurant process Galton–Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding

Continuous time	Bessel process Birth–death process Brownian motion Bridge Excursion Fractional Geometric Meander Cauchy process Contact process Continuous-time random walk Cox process Diffusion process Empirical process Feller process Fleming–Viot process Gamma process Hunt process Interacting particle systems Itô diffusion Itô process Jump diffusion Jump process Lévy process Local time Markov additive process McKean–Vlasov process Ornstein–Uhlenbeck process Poisson process Compound Non-homogeneous Point process Schramm–Loewner evolution Semimartingale Sigma-martingale Stable process Superprocess Telegraph process Variance gamma process Wiener process Wiener sausage

Both	Branching process Gaussian process Hidden Markov model (HMM) Markov process Martingale Differences Local Sub- Super- Random dynamical system Regenerative process Renewal process White noise

Fields and other	Dirichlet process Gaussian random field Gibbs measure Hopfield model Ising model Potts model Boolean network Markov random field Percolation Pitman–Yor process Point process Cox Poisson Random field Random graph

Time series models	Autoregressive conditional heteroskedasticity (ARCH) model Autoregressive integrated moving average (ARIMA) model Autoregressive (AR) model Autoregressive–moving-average (ARMA) model Generalized autoregressive conditional heteroskedasticity (GARCH) model Moving-average (MA) model

Financial models	Black–Derman–Toy Black–Karasinski Black–Scholes Chen Constant elasticity of variance (CEV) Cox–Ingersoll–Ross (CIR) Garman–Kohlhagen Heath–Jarrow–Morton (HJM) Heston Ho–Lee Hull–White LIBOR market Rendleman–Bartter SABR volatility Vašíček Wilkie

Actuarial models	Bühlmann Cramér–Lundberg Risk process Sparre–Anderson

Queueing models	Bulk Fluid Generalized queueing network M/G/1 M/M/1 M/M/c

Properties	Càdlàg paths Continuous Continuous paths Ergodic Exchangeable Feller-continuous Gauss–Markov Markov Mixing Piecewise deterministic Predictable Progressively measurable Self-similar Stationary Time-reversible

Limit theorems	Central limit theorem Donsker's theorem Doob's martingale convergence theorems Ergodic theorem Fisher–Tippett–Gnedenko theorem Large deviation principle Law of large numbers (weak/strong) Law of the iterated logarithm Maximal ergodic theorem Sanov's theorem

Inequalities	Burkholder–Davis–Gundy Doob's martingale Kunita–Watanabe

Tools	Cameron–Martin formula Convergence of random variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal generator Itô integral Itô's lemma Kolmogorov continuity theorem Kolmogorov extension theorem Lévy–Prokhorov metric Malliavin calculus Martingale representation theorem Optional stopping theorem Prokhorov's theorem Quadratic variation Reflection principle Skorokhod integral Skorokhod's representation theorem Skorokhod space Snell envelope Stochastic differential equation Tanaka Stopping time Stratonovich integral Uniform integrability Usual hypotheses Wiener space Classical Abstract

Disciplines	Actuarial mathematics Econometrics Ergodic theory Extreme value theory (EVT) Large deviations theory Mathematical finance Mathematical statistics Probability theory Queueing theory Renewal theory Ruin theory Statistics Stochastic analysis Time series analysis Machine learning

List of topics Category

This article is issued from Wikipedia - version of the Wednesday, February 03, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.