tradable volatility estimates - cmu · tradable volatility estimates bruno dupire head of...
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Tradable Volatility Estimates
Bruno DupireHead of Quantitative Research
Bloomberg L.P.
Conference in Honor of Steve ShreveCarnegie Mellon, June 3, 2015
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Outline
I. Trading Volatility Estimates
II. Tradable Estimates
III. A New Hi-Lo Based Tradable Estimate
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I. Trading Volatility Estimates
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Historical volatility tends to depend on the sampling frequency
SPX 2006 to 2011 Data
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Historical volatility tends to depend on the sampling frequency
SPX 2006 Data
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Historical volatility tends to depend on the sampling frequency
SPX 2007 Data
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Historical volatility tends to depend on the sampling frequency
SPX 2008 Data
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Historical volatility tends to depend on the sampling frequency
SPX 2009 Data
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Historical volatility tends to depend on the sampling frequency
SPX 2010 Data
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Historical volatility tends to depend on the sampling frequency
SPX 2011 Data
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Historical Vol / Historical Vol Arbitrage
If weekly historical vol < daily historical vol :
buy strip of T options, Δ-hedge daily
sell strip of T options, Δ-hedge weekly
Adding up :
do not buy or sell any option;
play intra-week mean reversion until T;
final P&L :
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Daily / Weekly Vol Arbitrage
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Intra week mean reversion strategy
Long
Short Short
Long
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1 day/1 week volatility tradeMore profitable when vol is high
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500 stocks cross section
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Daily – Weekly Vol Spread for S&P 500 constituents
Jan 2008 to Apr 2015
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Daily – Weekly Vol Spread for S&P 500 constituents
Jan 2008 to Apr 2015
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Covariation Trading
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Historical Cov / Historical Cov Arbitrage
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II. Tradable Estimates
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Some Definitions(Normal as opposed to Lognormal convention)
TradableUnbiased
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Discretized Quadratic Variation
Tradable unbiased estimate
Δ hedge of a parabola
Costless stock trading
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Classical Estimator
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Move-Based Estimator
For option pricing, a volatility estimate should reflect the cost of hedging
Hedge according to spot moves (move based) better than hedge at fixed times (time based)
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Move-Based Estimator
noise is smoothed out by phase averaging
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OHLC
Open
High
Low
Close
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Hi-Lo Estimates
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The Uncertainty of the Night
SPX Index GS US Equity
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But…
§ Hi-Lo Estimators are less useful than the classical one because they cannot be traded
§ Highs and Lows are always observed after the fact
§ However… we introduce a tradable Hi-Lo based estimator
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III. A New Hi-Lo Based Tradable Estimate
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Averaging Down
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A Side Note
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A New Estimator
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Trading Strategy
(Mid – Close)/Range
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Comparison of Estimators
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Conclusion
§ Most common volatility trade is historical vs implied
§ With tradable estimates: can trade historical vs historical, without any option market
§ Hi-Lo estimates are usually not tradable…
§ Not because they depend on Hi-Lo but because they do not depend on Close!
§ We introduce a new tradable estimate based on Hi-Lo (and Close!)
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Thank You