High-Frequency Financial Volatility and the Pricing of Volatility Risk

The idea that integrates parts of this dissertation is that high-frequency data allow for more precise and robust methods for forecasting financial volatility and elucidating the role of volatility in forming asset prices. Thus, the first two chapters compare the performance of model-free forecasts specifically designed to employ high-frequency data with the performance of "classical" forecasts developed for daily data. The final chapter of the dissertation incorporates high-frequency data to verify the predictions of asset pricing models about the risk-return relationships at the very shortest horizons. The results are arranged in the following order. Chapter 1 presents the analytical comparison of feasible reduced-form forecasts designed to employ high-frequency data and model-based forecasts updated to use high-frequency data. The prediction errors of both forecast groups are calculated using the ESV-representation of Meddahi (2003), which allows one to generalize the statements from this analysis to a wider class of volatility processes. The results show that reduced-form forecasts outperform model-based forecasts at longer horizons and perform just as well for day-ahead forecasts. Chapter 2 expands the conclusions from Chapter 1 to economic measures of forecast performance. These performance measures are constructed within a microeconomic framework that mimics the decision making process of a variance trader who uses volatility forecasts to predict the future profitability of a trade. The results support the theoretical predictions of Chapter 1. Chapter 3 is co-authored with Professor Tim Bollerslev and Professor George Tauchen. It extends the "long-run risk" model of Bansal and Yaron(2004) to consistently price volatility risks and to be applicable to high-frequency data. The hypothesis at the outset is that while financial volatility is a long-memory process (it exhibits long-range dependence), its own variance (volatility-of-volatility) is a short memory one. Then the presented model implies that the volatility premium (the measure of the difference between option-implied and expected variances) should be short-memory as well. This insight is confirmed by studying cross correlations of returns and volatility measures. Horizons at which cross correlations are considered are unique for the literature; they start at intra-day values, as short as five minutes.