Yang Liu‎ > ‎


The following are the abstracts of the research papers that will be included in my Ph.D. dissertation.

Factor Premia in Variance Risk
with X. Xiao

We propose a two-factor variance model that extracts the common dynamics in stock variances by imposing factor structures directly on the variance series. The two factors can be identified independently as a market variance (MV) factor and a variance residual (VR) factor, respectively governing the short-term and long-term dynamics of individual stock variances. We show that the MV factor resembles the shape of the index variances and carries a positive premium, which has an excess spillover effect on individual stock variances. On the contrary, the VR factor serves to compensate the excess spillover by having a negative premium. The differences in the factor premia and memories suggest that an option portfolio with long positions on long-term individual stock straddles and short positions on short-term index straddles generates significant positive returns. The strategy can be further enhanced by choosing straddles according to their model predicted variance risk premia. The advantage of the model-based strategy is demonstrated in both in- and out-of-sample analysis.

We propose a new approach to correlation structure modeling by assuming intraday dynamics of the conditional correlations. We derive the link between the correlations of different frequencies followed by a temporal aggregation procedure that successfully accommodates the intraday dynamics into a daily recurrence equation. The validity of the aggregation process and the superiority of the resulting HFGAS model are supported by several Monte Carlo simulations. Empirical application on the intraday currency returns of GBP/USD and EUR/USD shows a good in-sample performance of the HFGAS model. The advantage of using the HFGAS model is further illustrated by an application on portfolio strategies.

We develop a class of multivariate volatility models with common factors in the volatility series. We discuss the identification of the models and compare the properties to those of the class of the factor GARCH models. Next, we study the properties of the maximum likelihood coefficient estimators and the likelihood ratio tests for the number of common factors. The accuracy of these asymptotic approximation is studied in a number of Monte Carlo experiments. The methods are applied in several empirical examples including VaR coverage rates and market beta estimations.

Ongoing Research:

Factor Models on Time-varying Market Betas
I show that the volatility-factor model can be adapted perfectly in a conditional CAPM formulation. 

Closed-Form Solutions for Option Pricing in Continuous-time Volatility-Factor Models
I derive the continuous-time version of the volatility-factor model and corresponding option pricing formulas in closed-form.


The market variance factor resembles the index variance, thus having a positive factor premium. The variance residual factor only exists on individual stocks and offsets the market variance risk premium spillover. 

The intraday correlation dynamics simply cannot be ignored, as shown by the grey line, which is the hourly correlation between GBP/USD and EUR/USD.

Volatility factors display different patterns in a portfolio with IBM, DD and BA. Those factors are statistically independent.

There are numerous ways to calculate time-varying betas, yet I go back to the classics and follow the CAPM.