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 Y t+1 =  t+1 +  t+1 where  t+1 ~ WN (0,  2 t+1 ) ARMA(1,1)  t+1 =  0 +  1 Y t +  t GARCH (1,1)  2 t+1 =  +  2 t +  2 t Conditional mean  t+1 = E [Y t+1  F t ] Conditional variance  2 t+1 = Var [Y t+1  F t ] F t as filtration Represents all information available at time t Generally exclusively by past returns consisted of sparse daily data i.e. opening and closing only F t = (y t, y t-1,  y 1 ) 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 F t RM =  (RM t, y t, RM t-1, y t-1,  y 1 ) ≠ F t,  2 t+1 = Var [Y t+1  F t ] ≠ Var [Y t+!  F t RM ] =  2 t+1 RM When Realized Measures (such as RV and BV are included),  becomes insignificant (   0,  > 0)  2 t+1 RM =  +  2 t +  2 t +  RV t Estimating a GARCH model with additional realized measures of volatility based on high-frequency data Now the F t RM includes 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 a single 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 to squared 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 u t ~ iid (0,  2 u ) and z t ~ iid(0,1) RM t =  +  h t +  (z t ) + u t Second volatility factor h t = var (y t  F t-1 ) F t-1 = (y t-1,RM t-1,y t-2,RM t-2.....)  (z t ): leverage condition Dependence between returns and future volatility Phenomenon is referred as leverage effect expected leverage is zero whenever z t has mean zero and unit variance  (z t ) =  1 a 1 (z t ) +  +  k a k (z t ) where Ea k (z t ) = 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 r t : return x t : realized measure of volatility z t ~ iid(0,1) u t ~ iid (0,  2 u ) h t = var (r t  F t-1 ) Where F t-1 = (r t-1,x t-1,r t-2,x t-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 h t Log-Linear GARCH (p, q) Automatically ensures positive variance Preserves the ARMA structure that characterizes some of the standard GARCH models Conditions z t = r t /h t 1/2 ~ iid(0,1) and u t ~ iid(0,  2 u ) Example: GARCH (1,1) h t-1 and r 2 t-1 Then log h t ~ AR(1) and log x t ~ 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 V t+1  t =  +  t  t-1 +  H t 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)