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e.g. average(C - O) 2

average( Z H + Z L ) has about five times the efficiency

One week high and low equivalent to daily data.

Also unbiased regardless of drift in BM.

Cumulative Variance

2001: US/CAD$ Exchange rate

US/CAD$ Exchange rate

Volatility 1995-2001

High vol begins Aug 27 вЂ˜98

Evident from graph of

exchange rate?

Moving average Volatility

Russian debt

crisis

Are ZH and ZL exponential

distributed? US/CAD$

exchange & Dow Jones

To transform from Geometric to Brownian Motion,

Z H = ln( H / O )( H / C )

Z L = ln( L / O ) ln( L / C )

In practice, measures of volatility

may differ. e.g. DJA

вЂў Intra-day volatility (High-Low estimator)>>inter-day vol

(open-close)

RISK MANAGEMENT

SURVIVORSHIP BIAS

вЂў E.g. Retrospective studies on performance

of mutual fund managers. Present market

value is conditional on low >0.

What happens to the mean of the

survivors as the variance

increases?

вЂў survivemovie

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