An adaptive model for security prices driven by latent values: parameter estimation and option pricing effects

Abstract

We develop a model where the log of stock price is regressive to latent intrinsic value. The model is similar to an Ornstein–Uhlenbeck model but differs in that log price reverts to stochastic intrinsic value. Since intrinsic value is latent, we use a Kalman filter to estimate parameters. The model generates autocorrelated residuals and the Kalman filter yields volatility estimates that are considerably different from those that assume log price differences are independent. We price calls using both the standard estimators and those derived from the Kalman filter to demonstrate the impact of inappropriate estimation techniques. We estimate parameters for selected stocks and test delta hedging performance versus alternative models.