An Eigenfunction Approach for Volatility Modeling

In this paper, we introduce a new approach for volatility modeling in discrete and continuous time.

[1]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

[2]  P. Clark.  A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices , 1973 .

[3]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[4]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[5]  L. Hansen.  A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators , 1985 .

[6]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[7]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[8]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[9]  James B. Wiggins.  Option values under stochastic volatility: Theory and empirical estimates , 1987 .

[10]  G. Schwert.  Why Does Stock Market Volatility Change Over Time? , 1988 .

[11]  A. Gallant,et al.  Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications , 1989 .

[12]  S. Turnbull,et al.  Pricing foreign currency options with stochastic volatility , 1990 .

[13]  Daniel B. Nelson.  ARCH models as diffusion approximations , 1990 .

[14]  Daniel B. Nelson.  Stationarity and Persistence in the GARCH(1,1) Model , 1990, Econometric Theory.

[15]  D. Duffie,et al.  Simulated Moments Estimation of Markov Models of Asset Prices , 1990 .

[16]  E. Stein,et al.  Stock Price Distributions with Stochastic Volatility: An Analytic Approach , 1991 .

[17]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[18]  G. Constantinides.  A Theory of the Nominal Term Structure of Interest Rates , 1992 .

[19]  S. Heston.  A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[20]  T. Nijman,et al.  Temporal Aggregation of GARCH Processes. , 1993 .

[21]  L. Hansen,et al.  Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes , 1993 .

[22]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[23]  Tim Bollerslev,et al.  COMMON PERSISTENCE IN CONDITIONAL VARIANCES , 1993 .

[24]  Peter E. Rossi,et al.  Nonlinear dynamic structures , 1993 .

[25]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models , 1994 .

[26]  Dean P. Foster,et al.  Asypmtotic Filtering Theory for Univariate Arch Models , 1994 .

[27]  N. Shephard,et al.  Multivariate stochastic variance models , 1994 .

[28]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[29]  A. Gallant,et al.  Which Moments to Match? , 1995, Econometric Theory.

[30]  L. Hansen,et al.  Efficient Estimation of Linear Asset Pricing Models with Moving-Average Errors , 1997 .

[31]  Bent E. Sørensen,et al.  GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study , 1996 .

[32]  D. Duffie,et al.  A YIELD-FACTOR MODEL OF INTEREST RATES , 1996 .

[33]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

[34]  Bent E. Sørensen,et al.  A Continuous-Time Arbitrage-Pricing Model With Stochastic Volatility and Jumps , 1996 .

[35]  Daniel B. Nelson.  A Note on the Normalized Errors in ARCH and Stochastic Volatility Models , 1996, Econometric Theory.

[36]  A. Harvey,et al.  5 Stochastic volatility , 1996 .

[37]  Timothy G. Conley,et al.  BOOTSTRAPPING THE LONG RUN , 1997, Macroeconomic Dynamics.

[38]  Timothy G. Conley,et al.  Short-term interest rates as subordinated diffusions , 1997 .

[39]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[40]  N. Touzi,et al.  TESTING FOR EMBEDDABILITY BY STATIONARY REVERSIBLE CONTINUOUS-TIME MARKOV PROCESSES , 1998, Econometric Theory.

[41]  L. Hansen,et al.  Spectral methods for identifying scalar diffusions , 1998 .

[42]  Paolo Zaffaroni,et al.  Nonlinear time series with long memory: a model for stochastic volatility , 1998 .

[43]  É. Renault,et al.  Aggregations and Marginalization of Garch and Stochastic Volatility Models , 1998 .

[44]  Enrique Sentana,et al.  Conditional means of time series processes and time series processes for conditional means , 1998 .

[45]  Peter E. Rossi,et al.  Stochastic Volatility: Univariate and Multivariate Extensions , 1999 .

[46]  A. Ronald Gallant,et al.  The relative efficiency of method of moments estimators , 1999 .

[47]  Bent E. Sørensen,et al.  Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study , 1999 .

[48]  D. Duffie,et al.  Transform Analysis and Asset Pricing for Affine Jump-Diffusions , 1999 .

[49]  A. Gallant,et al.  A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation , 1999 .

[50]  George Tauchen,et al.  Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance , 1999 .

[51]  R. Leipus,et al.  STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM , 2000, Econometric Theory.

[52]  Robert F. Dittmar,et al.  Quadratic Term Structure Models: Theory and Evidence , 2000 .

[53]  N. Shephard,et al.  Non-Gaussian OU based models and some of their uses in financial economics , 2000 .

[54]  P. Robinson,et al.  The memory of stochastic volatility models , 2001 .

[55]  Luca Benzoni,et al.  An Empirical Investigation of Continuous-Time Equity Return Models , 2001 .

[56]  René Garcia,et al.  Asymmetric Smiles, Leverage Effects and Structural Parameters , 2001 .

[57]  Yacine Aït-Sahalia.  Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed‐form Approximation Approach , 2002 .

[58]  N. Shephard,et al.  Markov chain Monte Carlo methods for stochastic volatility models , 2002 .

[59]  Liuren Wu,et al.  Asset Pricing under the Quadratic Class , 2002, Journal of Financial and Quantitative Analysis.

[60]  A. Gallant,et al.  Purebred or hybrid?: Reproducing the volatility in term structure dynamics , 2003 .

[61]  A. Gallant,et al.  Alternative models for stock price dynamics , 2003 .