Filtering in asset pricing

Abstract

In the first chapter of this thesis, I propose a nonlinear filtering method to estimate latent processes based on the Taylor series approximations. The filter extends conventional methods such as the extended Kalman filter or the unscented Kalman filter and provides a tractable way to estimate filters of any order. I apply the filter to different models and demonstrate that this method is a good approach for the estimation of unobservable states as well as for parameter inference. I also find that filters with Taylor approximations can be as accurate as conventional Monte Carlo filters and computationally more efficient. Through this chapter I show that filters with Taylor approximations are a good approach for a number of problems in finance and economics that involve nonlinear dynamic modeling. In the second chapter, I investigate the recently documented, large time-series variation in the empirical market Sharpe ratio. I revisit the empirical evidence and ask whether estimates of Sharpe ratio volatility may be biased due to the limitations of the standard ordinary least squares (OLS) methods used in estimation. Based on simulated data from a standard calibration of the long-run risks model, I find that OLS methods used in prior literature produce Sharpe ratio volatility five times larger than its true variability. The difference arises due to measurement error. To address this issue, I propose the use of filtering techniques that account for the Sharpe ratio’s time variation. I find that these techniques produce Sharpe ratio volatility estimates of less than 15% on a quarterly basis, which match more closely the predictions of standard asset pricing models.