Volatility Pairs Trading

New York Group 13

Gaurav Gandhi

Palash Kasodhan

David Lin

Michael Rehwinkel

Outline

• Overview

• Implied Volatility Time Series

• Proof of Concept

• Trading Implementation

• Results

• Conclusion

Overview

• Correlation of Implied Volatilities

• Reversion of correlated options

• Proof of Concept

• Implementation using straddles

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

Proof of Concept

• Pair most correlated for all 90 tickers

• Trade At-the-money implied volatility directly

• Top 10 correlated Pairs

Correlation/Trading Profit

0

0.2

0.4

0.6

0.8

1

1.2

0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95Correlation

Tra

din

g P

rofi

t

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

Cross Validation

Results

• Formation Period in 2007 H1 and trading in 2007 H2crit 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

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

Example Pair CNQ/DO (using cutoff =2)

Position PnL Distribution with Cutoff

cut-off = 1.5 cut-off = 2

Position PnL Distribution with Cutoff

cut-off = 2.5 cut-off = 3

Number of Days Position Open

• 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

Conclusions

• 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

Next Steps