Econ 201 by David Kim

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 – h t – conditional variance of daily return – n t – 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 – Y h (p t ) = – k( ) = appropriate weight function as the sample frequency increases, realized kernel can get the fastest convergence rate ·

Volatility Measures (cont’d) Daily Range – p high,t – largest log-price – p low,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