Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance

Acommon model for security price dynamics is the continuous-time stochastic volatility model. For this model, Hull and White (1987) show that the price of a derivative claim is the conditional expectation of the Black-Scholes price with the forward integrated variance replacing the Black-Scholes variance. Implementing the Hull and White characterization requires both estimates of the price dynamics and the conditional distribution of the forward integrated variance given observed variables. Using daily data on close-to-close price movement and the daily range, we find that standard models do not fit the data very well and that a more general three-factor model does better, as it mimics the long-memory feature of financial volatility. We develop techniques for estimating the conditional distribution of the forward integrated variance given observed variables.

[1]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[2]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[3]  M. Parkinson.  The Extreme Value Method for Estimating the Variance of the Rate of Return , 1980 .

[4]  M. J. Klass,et al.  On the Estimation of Security Price Volatilities from Historical Data , 1980 .

[5]  S. Beckers,et al.  Variances of Security Price Returns Based on High , 1983 .

[6]  K. French,et al.  Expected stock returns and volatility , 1987 .

[7]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[8]  A. Lo.  Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data , 1986, Econometric Theory.

[9]  Robert Fildes,et al.  Journal of business and economic statistics 5: Garcia-Ferrer, A. et al., Macroeconomic forecasting using pooled international data, (1987), 53-67 , 1988 .

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

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

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

[13]  Bong-Soo Lee,et al.  Simulation estimation of time-series models☆ , 1991 .

[14]  David Hsieh.  Chaos and Nonlinear Dynamics: Application to Financial Markets , 1991 .

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

[16]  Daniel B. Nelson,et al.  Filtering and Forecasting with Misspecified Arch Models Ii: Making the Right Forecast with the Wrong Model , 1992 .

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

[18]  R. Engle,et al.  A Permanent and Transitory Component Model of Stock Return Volatility , 1993 .

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

[20]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[21]  A. Gallant,et al.  A NONPARAMETRIC APPROACH TO NONLINEAR TIME SERIES ANALYSIS: ESTIMATION AND SIMULATION* , 1993 .

[22]  Dongcheol Kim,et al.  Alternative Models for the Conditional Heteroscedasticity of Stock Returns , 1994 .

[23]  A. Gallant,et al.  Specification Analysis of Continuous Time Models in Finance , 1995 .

[24]  Yacine Ait-Sahalia.  Testing Continuous-Time Models of the Spot Interest Rate , 1995 .

[25]  B. Werker,et al.  Closing the GARCH gap: Continuous time GARCH modeling , 1996 .

[26]  T. Bollerslev,et al.  MODELING AND PRICING LONG- MEMORY IN STOCK MARKET VOLATILITY , 1996 .

[27]  Ming Liu,et al.  Volume, Volatility, and Leverage: A Dynamic Analysis , 1995 .

[28]  A. Ronald Gallant,et al.  Qualitative and asymptotic performance of SNP density estimators , 1996 .

[29]  C. Granger,et al.  Modeling volatility persistence of speculative returns: A new approach , 1996 .

[30]  George Tauchen.  New Minimum Chi-Square Methods in Empirical Finance , 1996 .

[31]  T. Andersen,et al.  Estimating continuous-time stochastic volatility models of the short-term interest rate , 1997 .

[32]  Rómulo A. Chumacero,et al.  Finite Sample Properties of the Efficient Method of Moments , 1997 .

[33]  A. Gallant,et al.  Estimating stochastic differential equations efficiently by minimum chi-squared , 1997 .

[34]  Trading Volume and the Short and Long-run Components of Volatility , 1997 .

[35]  A. Gallant,et al.  Estimation of Stochastic Volatility Models with Diagnostics , 1995 .

[36]  G. Denk,et al.  Numerical solution of stochastic di erential-algebraic equations with applications to transient nois , 1998 .

[37]  George Tauchen,et al.  The Objective Function of Simulation Estimators Near the Boundary of the Unstable Region of the Parameter Space , 1998, Review of Economics and Statistics.

[38]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[39]  A. Gallant,et al.  Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions , 1998 .

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

[41]  F. Diebold,et al.  The Distribution of Exchange Rate Volatility , 1999 .

[42]  P. Phillips.  BOOTSTRAPPING I(1) DATA BY PETER C. B. PHILLIPS COWLES FOUNDATION PAPER NO. 1310 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS , 2010 .