Using Daily Range Data to Calibrate Volatility Diffusions and Extract
the Forward Integrated Variance
A. Ronald Gallant, Chien-Te Hsu, and George Tauchen
The Review of Economics and Statistics,
Vol. 84, No. 4., pp. 617-631.
A common 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/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 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.