Transcription
Lecture 11:Quantitative Option StrategiesVolatility Statistical ArbitrageMarco AvellanedaG63.2936.001Spring Semester 2009
The theory
Weighted MC Approach Use a simple model for the dynamics of the single stock relative to itsETFModel the residual volatility as a fraction of the total implied (ATM) volof the stockdSit β iσ I ,atm dWt etf γ iσ i ,atm dZ tSSitγ i 1 Ri2 in the sense of regressionCalibrate this to all options on ETF and to the forward for the stock underconsideration, using Weighted Monte Carlo
Model Value vs. Market ValueCeur ( S , K , T ) e rT E WMC (max(ST K ,0))Solve for IVOLBSCall (S , T , K , r , d , σ imp (K , T )) Ceur ( S , K , T )Cmodel (S , K , T ) AmericanBSCall (S , T , K , r , d , σ imp (K , T ))Compare :Cmodel (S , K , T ), [ Cbid (S , K , T ), Coffer (S , K , T )]
A Brief History of Volatility 1990 – 2008:the CBOE VIX GW2TequilaEMVolatility decreases from 2003 to 2006-2007
S&P 500 Volatility 8/2006-4/2008Volatility Continuesto dropEquity mkt.Ignores financials;Volatility doubles inat the endLiquidity crunchRegime change in volatility
XLF (Financial S&P ETF) vs.VIXBear StearnsVolatility drops aresynchronous to Fed moves
Implementation of L/S Strategyin 2007 Few buy’’ signals in early 2007 Buying volatility gave poor results 2004-2006 Theta-neutral portfolios gave poor results in 2004-2006 Suggested selling volatility on strong signals in small amounts per name Hedging with ETFs (sector neutral) Hedging with SPY ( globally neutral’’) Synthetic insurance company: selling protection (Gamma) on many single names Hedging is the key to maintain market neutrality and get desired results(as we will see) In back-testing we use variance swaps instead of options for simplicity
Market-Neutrality matching different GreeksPortfolio profileVega RatioExposureVega NeutralVetf VstockTheta Neutralσ stockVetf Vstock σ etfnet long veganet long gammaGamma Neutralσ etfVetf Vstock σ stockcollect time decaynet long vegacollect time decaynet long gamma
utral Per Sector 2007Capital 1000 (all sectors)2007/02/15 1 %, drawdown 4%Bias: long etf gamma, collect decay (“etf light”)2007/01/03
11/022007/12/05Vega-Neutral 2006-2007Capital 1000 (all sectors)2006/06/12 13%, drawdown 8%Bias: long etf gamma, collect decay (“etf light”)2006/02/03
12/142007/12/27Vega-Neutral With SPY hedge2007/02/20VEGA-NEUTRAL HEDGE with SPYCAPITAL 1000Global vega hedging does not work: too much decay, imprecise2007/01/16
0720 /0107 /020 /01 307 /1920 /0207 /020 /02 507 /220 /03 107 /020 /03 807 /2320 /0407 /120 /04 007 /220 /05 507 /120 /05 007 /2520 /0607 /120 /06 207 /220 /07 707 /120 /07 307 /320 /08 007 /1420 /0807 /220 /09 907 /120 /10 407 /020 /10 107 /1620 /1007 /320 /11 107 /120 /12 507 /0/1 32/1820Gamma-Neutral/Sector 2007Capital 1000 4%, drawdown 5%1009080706050403020100Bias: collect decay, long vega
7/09/062007/10/052007/11/052007/12/05Gamma-Neutral 2006-2007Capital 10002006/05/05 8%, drawdown 7%Bias: collect decay, long vega2006/02/03
142007/06/262007/07/092007/07/192007/07/31Not enough collected decayand liquidity /11/212007/12/042007/12/14Theta-Neutral/Sector2007 Capital 10002007/03/26-4%, drawdown 6%Bias: long gamma, long vega2007/01/16
Quantitative Option Strategies Volatility Statistical Arbitrage Marco Avellaneda . Theta-Neutral/Sector 2007 Capital 1000 Bias: long gamma, long vega Not enough collected decay and liquidity crunch-50-40-30-20-10 0 10 20 30 2007/01/03 2007/01/16 2007/01/26 2007/02/07 2007/02/20 2007/03/02
