Volatility Pairs Trading New York Group 13 Gaurav Gandhi Palash Kasodhan David Lin

1. Volatility Pairs Trading New York Group 13 Gaurav Gandhi Palash Kasodhan David Lin Michael Rehwinkel

2. Outline • Overview • Implied Volatility Time Series • Proof of Concept • Trading Implementation • Results • Conclusion

3. Overview Correlation of Implied Volatilities Reversion of correlated options Proof of Concept Implementation using straddles

4. Implied Volatility Time Series Goal: Time series of implied volatility of At-the-money options for chosen names Dataset Oil Industry: SIC 13 CRSP for equity prices OptionMetrics for option prices Time series creation Java Application Only 90 of 214 tickers remained due to missing data Interpolation for up to 5 days of missing data

5. Proof of Concept Pair most correlated for all 90 tickers Trade At-the-money implied volatility directly Top 10 correlated Pairs

6. Trading Implementation At-the-money Straddles No Greek hedging Normalize data to calculate simple ratio Parameters/Thresholds: For entering position For exiting position (for profit/bailout & forced exercise) Tailing days for moving average Client exercising

7. Cross Validation

8. Results Formation Period in 2007 H1 and trading in 2007 H2 crit 0.3 bail 0.5 extrigger 0.33 ttexp 60 norm.days 30 c Total PNL 1.5 5.08536568 2 7.434366373 2.5 3.669043944 3 1.260628469

9. Example Pair CNQ/DO (using cutoff =2) OpenDate CloseDate x.position x.strike x.expiry x.openVal x.closeVal x.pnl y.strike 20070709 20070719 1 70 20070922 1 1.337179487 0.337179487 105 20070802 20070815 1 70 20071222 1 1.163492063 0.163492063 100 20070824 20070904 -1 65 20071222 1 1.093137255 -0.093137255 100 20070921 20071029 -1 75 20071222 1 1.108910891 -0.108910891 115 20071102 20071114 1 80 20080119 1 1.202654867 0.202654867 110 20071120 20071130 -1 70 20080119 1 0.925531915 0.074468085 110 20071210 20071221 -1 65 20080322 1 1.068181818 -0.068181818 125 20071226 20071231 1 70 20080322 1 0.961904762 -0.038095238 140 y.Expiry y.openVal y.closeVal y.pnl position.pnl days.open no.data.close f.exercise bail reached.crit.pnl 20070922 1 0.945736434 0.054263566 0.391443053 10 0 0 0 1 20071222 1 0.778801843 0.221198157 0.38469022 13 0 0 0 1 20071222 1 1.462416107 0.462416107 0.369278852 11 0 0 0 1 20071222 1 0.873333333 -0.126666667 -0.235577558 38 0 1 0 0 20080119 1 0.872222222 0.127777778 0.330432645 12.04166667 0 0 0 1 20080119 1 1.096710526 0.096710526 0.171178611 10 0 1 0 0 20080322 1 1.702487562 0.702487562 0.634305744 11 0 0 0 1 20080322 1 1.014218009 -0.014218009 -0.052313248 5 0 0 0 0

10. Example Pair CNQ/DO (using cutoff =2)

11. Position PnL Distribution with Cutoff cut-off = 1.5 cut-off = 2

12. Position PnL Distribution with Cutoff cut-off = 2.5 cut-off = 3

13. Number of Days Position Open

14. Conclusions • Volatility Pairs Trading can be profitable, as the results indicate • The cut off parameter has the maximum influence on PnL • We need a high bailout to account for 4 option positions • Bid – Ask Spreads eat into potential profits. Other transaction costs not even considered. • Not hedged perfectly (unlike trading IV directly) as the following risk remains • Residual delta risk • Net Theta decay as the long and short straddle wont cancel theta completely

15. Next Steps • Greek Hedging - Delta  & Theta • Synthesize Variance Swaps using Listed Options • Dynamic Hedging vs Static Hedging • Dispersion Trading: for e.g. buying the volatility of an index and selling the volatility of its constituents • Use Street Events Feed – To identify when the volatility pattern could be broken by extra-ordinary news