Econ 201
by David Kim3.2.11
Measuring & Forecasting
• Measuring and forecasting latent volatility is important in regards to:– Asset allocation– Option pricing– Risk management
Brownlees and Gallo (2009)
• Looks at different volatility measures improve out-of-sample forecasting ability of standard methods
• Looks into issue of forcasting Value-at-Risk (VaR) by looking at various volatility measures– Realized volatility– Bipower volatility– Two-scales realized volatility– Realized kernel– Daily range
VaR Modeling
• Assumes
– ht – conditional variance of daily return
– nt – i.i.d. unit variance from an appropriate cumulative distribution F
– One-day-ahead VaR is defined as maximum one-day-ahead loss
Volatility Measures
• Realized volatility
• Bipower realized volatility
Volatility Measures (cont’d)
• Two-scales realized volatility
– Let– Define:
– This estimator combines information from both slow and fast time scales
Volatility Measures (cont’d)
• Realized kernel
– Yh(pt) =– k( ) = appropriate weight function
• as the sample frequency increases, realized kernel can get the fastest convergence rate
·
Volatility Measures (cont’d)
• Daily Range
– phigh,t – largest log-price
– plow,t – lowest log-price– Affected by a much lower measurement error• It is as precise as realized volatility if using a sample of
low frequency data and certain conditions
Companies
• HJ Heinz Company (HNZ) and Kraft Foods Inc. (KFT)– Consumer goods sector within the food industry– Both diversified companies
HNZ: Price
HNZ: Returns
HNZ: Relative Contribution of Jumps
HNZ: RV Volatility Signature
HNZ: BV Volatility Signature
KFT: Price
KFT: Returns
KFT: Relative Contribution of Jumps
KFT: RV Volatility Signature
KFT: BV Volatility Signature
HNZ: RV
HNZ: BV
KFT: RV
KFT: BV
• Look further into all volatility measures • If an appropriate area for research, include
more stocks• Other potential areas of interest:– How presence of jumps has information relevant
to forecasting volatility• HAR modelling frame