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

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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