Possible Research Interests

1. Possible Research Interests Kyu Won Choi Econ 201FS February 16, 2011

2. GARCH model + Realized Variation Measures • Combining realized variation measures based on high-frequency data with more traditional GARCH type models • Some Examples • Realized GARCH Models • HEAVY models • Multiplicative Error Model • HYBRID GARCH Models • Generalized Expected RV (GERV) models • HARG-RV models • Other multi-period forecasts joint models

3. High Frequency Data • Realized Measures based on high frequency data • Valuable predictors of future volatility • Realized Variance (most commonly used) • Bi-power Variance • Realized Kernel • High frequency data is crucial • Volatility is highly persistent • The more accurate measure of a current volatility, the better able to forecast volatility • Evaluation of volatility forecast models • accurate proxy when comparing volatility models • Close analysis of announcements and the effects

4. Standard GARCH Model • Yt+1 = t+1+ t+1 where t+1 ~ WN (0, 2t+1) • ARMA(1,1) t+1 = 0 + 1Yt+t • GARCH (1,1) 2t+1=  + 2t+ 2t • Conditional mean t+1= E [Yt+1 Ft] • Conditional variance 2t+1 = Var [Yt+1 Ft] • Ftas filtration • Represents all information available at time t • Generally exclusively by past returnsconsisted of sparse daily data • i.e. opening and closing only • Ft = (yt, yt-1,  y1) • Consisting of high frequency information is useful • such as 30-min intraday transaction prices, bid/ask quotes, etc

5. Adding Realized Measures of Volatility: GARCH-X Model • Since Ft RM = (RMt, yt, RM t-1, yt-1,  y1)≠ Ft, 2t+1 = Var [Yt+1 Ft] ≠ Var [Yt+! FtRM] = 2t+1RM • When Realized Measures (such as RV and BV are included),  becomes insignificant ( 0,  > 0) • 2t+1RM =  + 2t+ 2t+ RVt • Estimating a GARCH model with additional realized measures of volatility based on high-frequency data • Now the Ft RMincludes greater set of data • Including variable that adds predictive power • Realized measures can improve the empirical fit

6. GRAPH illustrated in the class • GARCH model is sensitive to rapid volatility change (jump) • Slow at “catching up”:longer time periods (around 3 months) to reach the new volatility • GARCH-X model within a few days

7. GARCH-X Model • Two different methods • depending on the number of latent volatility variables • Parallel GARCH structure • For each realized measure, additional GARCH-type model (latent volatility process) is introduced • Multiplicative Error Model (MEM) • High-frequency based Volatility Model (HEAVY) • Realized Measures • Similar to the traditional GARCH • Realized GARCH model with asingle latent volatility factor • Connected to conditional variance of returns

8. Parallel GARCH Structure • MEM and HEAVY models digress from the traditional GARCH • Which uses only a single latent volatility factor • HEAVY model by Shephard and Sheppard (2010) • Realized kernel (RK) • Multiplicative Error Model (MEM) by Engel (2002) • In addition tosquared returns, • Two realized measures • Intraday range (high minus low) • Realized variance

9. Realized GARCH • Measurement equation that ties the realized measure to the conditional variance of returns • where ut ~ iid (0, 2u) and zt~ iid(0,1) RMt =  + ht + (zt) + ut • Second volatility factorht = var (yt Ft-1) • Ft-1 = (yt-1,RMt-1,yt-2,RMt-2.....) • (zt):leverage condition • Dependence between returns and future volatility • Phenomenon is referred as leverage effect • expected leverage is zero whenever zt has mean zero and unit variance • (zt) = 1a1(zt) +  + kak(zt) where Eak(zt) = 0 for k • News impact curve: how positive and negative shocks to the price affect future volatility

10. Linear Realized GARCH (1,1) model • Simplest GARCH (1,1) equation • rt : return • xt :realized measure of volatility • zt~ iid(0,1) ut ~ iid (0, 2u) • ht= var (rt Ft-1) • Where Ft-1= (rt-1,xt-1,rt-2,xt-2.....) • Last equation relates observed realized measure to the latent volatility:measurement equation • Leverage function

11. Log-Linear Realized GARCH • Key variable of interest: conditional variance ht • Log-Linear GARCH (p, q) • Automatically ensures positive variance • Preserves the ARMA structure that characterizes some of the standard GARCH models • Conditions zt = rt/ht1/2 ~ iid(0,1) and ut~ iid(0, 2u) • Example: GARCH (1,1) ht-1 and r2t-1 • Then log ht~ AR(1) and log xt ~ ARMA(1,1)

12. Key Models (Hansen, Huang, Shek, 2011)

13. HYBRID GARCH • High Frequency Data-Based Projection-Driven GARCH • Volatility driven by HYBRID processes Vt+1t =  + tt-1 + Ht where Ht is HYBRID process • Volatility process need not be defined to be conditional variance of returns • Tomorrow’s expected volatility using intra-daily returns • Next three days volatility forecasting with past daily data • Three broad classes of HYBRID processes • Parameter-free process purely data driven • Structural HYBRIDS assuming an underlying high frequency data structure • HYBRID filter processes

14. The Practical Application • Out-of-sample forecasting • Risk Measurement & Management • Asset Pricing • Portfolio Allocation • Option Pricing

15. Work To Do & Further Interests • Use the data and compare various GARCH +RM • Observe the positive and negative sides of each • Multivariate GARCH models & Realized GARCH framework: multi-factor structure (multi-period forecasting) • m realized measures and k latent volatility variables • Presence of jumps in the price process • Information about forecasting volatility • Inclusion of a jump robust realized measure • Extent to which microstructure effects are relevant for the forecasting problem • using realized measures that are robust to microstructure effects

16. References • Realized GARCH: A Joint Model for Returns and Realized Measures of Volatility (Hansen, Huang, Shek, 2010) • Forecasting Volatility using High Frequency Data (Hansen, Lunde, 2011) • The Class of HYBRID-GARCH Models (Chen, Ghysels,Wang, 2011) • Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian (Torben G. Andersen, Bollerslev, Diebold, Labys, 2000)