## Variance Risk Premium Dynamics: The Impact of Asset Price Jumps on Variance Risk Premia

**By Jackson Pfeiffer**

This paper utilizes the high-frequency stock price data and the corresponding daily option price data of several highly capitalized corporations in order to investigate the impact that asset price jumps of individual equities have on the equities’ respective variance risk premia. The findings of this paper describe many characteristics of the variance risk premia of individual equities, supporting some expectations of the characteristics, and refuting others. In the process of investigating these characteristics, this paper proposes a simple estimator for the market price of the variance risk of an individual equity.

**Advisor:** George Tauchen |** JEL Codes:** G1, G19, G11 |** Tagged: **Variance Risk, Variance Swaps, Price Jumps

## Cross-Stock Comparisons of the Relative Contribution of Jumps to Total Price Variance

**By Vivek Bhattacharya**

This paper uses high-frequency price data to study the relative contribution of jumps to the total volatility of an equity. In particular, it systematically compares the relative contribution of jumps across a panel of stocks from three different industries by computing the cross-correlation of this statistic for pairs of stocks. We identify a number of empirical regularities in this cross-correlation and compare these observations to predictions from a standard jump-diffusion model for the joint price process of two stocks. A main finding of this paper is that this jump-diffusion model, when calibrated to particular pairs of stocks in the data, cannot replicate some of the empirical patterns observed. The model predictions differ from the empirical observations systematically: predictions for pairs of stocks from the same industry are on the whole much less accurate than predictions for pairs of stocks from different industries. Some possible explanations for this discrepancy are discussed.

**Advisor:** George Tauchen |** JEL Codes:** C5, C52, C58 |** Tagged: **Econometric Modeling, Financial Econometrics, High-Fequency Data, Jumps

## Empirical Analysis on the Effects of Jumps on Realized Beta and the Disentanglement of Jump Beta1

**By Hao Sun**

This paper constructs jump-robust estimators for the beta in Capital Asset Pricing Model (CAPM) in order to test the robustness of the recently developed Realized Beta in the presence of large discontinuous movements, or jumps, in stock prices. To complete the analysis on effect of jump on Realized Beta, this paper also disentangles jump beta and diffusive beta from the Realized Beta measurement in order to examine whether stocks react differently to jumps under the CAPM. Then, the results are compared to recent literatures tackling the same problem from different approaches.

**Advisor: **George Tauchen

## Simultaneous Occurrence of Price Jumps and Changes in Diffusive Price Volatility

**By Shunting Wei**

This paper uses high frequency financial data to study the changes in diffusive stock price volatility when price jumps are likely to have occurred. In particular, we study this effect on two levels. Firstly, we compare diffusive volatility on jump and non-jump days. Secondly, we study the change in diffusive volatility in local windows before and after 5-minute intervals on which price jumps are likely to have occurred. We find evidence that market price jumps occur simultaneously with a change in diffusive volatility with negative dependence in the direction of the jump and the volatility change. However, a similar relationship is not detectable in individual stock price data.

**Advisor:** George Tauchen |** JEL Codes:** C22, G1, G19 |** Tagged: **Diffusive Volatility, Jump Tests, Realized Volatility, Stock Price Jumps

## Examination of Time-Variant Asset Correlations Using High- Frequency Data

**By Mingwei Lei**

Drawing motivation from the 2007-2009 global financial crises, this paper looks to further examine the potential time-variant nature of asset correlations. Specifically, high frequency price data and its accompanying tools are utilized to examine the relationship between asset correlations and market volatility. Through further analyses of this relationship using linear regressions, this paper presents some significant results that provide striking evidence for the time-variability of asset correlations. These findings have crucial implications for portfolio managers as well as risk management professionals alike, especially in the contest of diversification.

**Advisor:** George Tauchen |** JEL Codes:** G, G1, G10, G11, G14 |** Tagged: **Asset correlations, Diversification, Financial Crisis, High-Frequency Data, Market Volatility, Time-Variant Correlations, Time-Variant Volatility

## Relative Contribution of Common Jumps in Realized Correlation

**By Kyu Won Choi**

This paper studies common intraday jumps and relative contribution of these common jumps

in realized correlation between individual stocks and market index, using high-frequency price

data. We find that the common jumps significantly contribute in realized correlation at different

threshold cut-offs and both common jumps and realized correlation are relatively consistent across

time period including financial crisis. We also find a weak, positive relationship between relative

contribution of common jumps and realized correlation, when we further sample high-frequency

data into a year. We also observe that the volatility index and market index reveal the strongest

relationship.

**Advisor:** Geourge Tauchen, Tim Bollerslev |** JEL Codes:** C40, C58, G10 |** Tagged: ** Diffusive Covariation, Realized Correlation, Relative Contribution of Common Jumps

## Beta Estimation Using High Frequency Data

**By Angela Ryu**

Using high frequency stock price data in estimating nancial measures often causes serious distortion. It is due to the existence of the market microstructure noise, the lag of the observed price to the underlying value due to market friction. The adverse eect of the noise can be avoided by choosing an appropriate sampling frequency. In this study, using mean square error as the measure of accuracy in beta estimation, the optimal pair of sampling frequency and the trailing window was empirically found to be as short as 1 minute and 1 week, respectively. This surprising result may be due to the low market noise resulting from its high liquidity and the econometric properties of the errors-in-variables model. Moreover, the realized beta obtained from the optimal pair outperformed the constant beta from the CAPM when overnight returns were excluded. The comparison further strengthens the argument that the underlying beta is time-varying.

**Advisor:** George Tauchen |** JEL Codes:** C51, C58, G17 |** Tagged: **Beta estimation, Beta Trailing Window, High-Frequency Data, Market Microstructure Noise, Optimal Sampling Interval, Realized Beta

## Time-Varying Beta: The Heterogeneous Autoregressive Beta Model

**By Kunal Jain**

Conventional models of volatility estimation do not capture the persistence in high-frequency market data and are not able to limit the impact of market micro-structure noise present at very finely sampled intervals. In an attempt to incorporate these two elements, we use the beta-metric as a proxy for equity-specific volatility and use finely sampled time-varying conditional forecasts estimated using the Heterogeneous Auto-regressive framework to form a predictive beta model. The findings suggest that this predictive beta is better able to capture persistence in financial data and limit the effect of micro-structure noise in high frequency data when compared to the existing benchmarks.

**Advisor: **George Tauchen |** JEL Codes: **C01, C13, C22, C29, C58 | **Tagged: **Beta, Financial Markets, Heterogeneous Autoregressive, Persistence

## Extreme Value Theory with High-Frequency Financial Data

**By Abhinay Sawant**

Extreme Value Theory (EVT) is one of the most commonly applied models in financial risk management for estimating the Value at Risk of a portfolio. However, the EVT model is practical for estimation only when data is independent and identically distributed, which usually does not characterize financial returns data. This paper aims to modify this model by using high-frequency data to standardize financial returns by their realized volatility and then tests the modified model with recent equity data. The results from the paper show an improvement in the EVT model when forward volatility can be properly forecasted.

**Advisor: **George Tauchen

## Spurious Jump Detection and Intraday Changes in Volatility

**By Matthew Roqnile**

We investigate the properties of several nonparametric tests for jumps in financial markets. We derive a theoretical property of these tests not observed in any of the previous literature: when they are applied to finitely sampled data, they are generally biased toward finding too many jumps. This results from bias in finite-sample estimation of several important test components. The severity of the bias corresponds to the magnitude of change in volatility over the course of a day. We use data on

an intraday volatility pattern in several US equities, which results in quantitatively significant changes in the level of volatility during the day, to undertake Monte Carlo simulations of a price process without jumps. Applying several jump tests to the simulated data, we detect one-half to two-thirds as many jumps as in the observed data, suggesting that many jumps currently detected in empirical applications of these tests are spurious. We also present several possible modifications to jump tests that limit the effect of intraday patterns in volatility, all of which produce dramatically lower estimates of the frequency and importance of jumps.

**Advisor:** George Tauchen