3 June 2011

Trading VIX

For professional investors only

Philippe COMBESCOT

Global Structuring Group

Equity & Commodity Derivatives

3 June 2011 2

Reminder : What is VIX

� The VIX measures the market’s expectation of the S&P 500 volatility over the next 30 days implied by listed option prices.

Source: Bloomberg, as of Jun 1, 2011

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VIX

90% percentile : 29.6

50% percentile : 18.7

10% percentile : 12.1

3 June 2011 3

VIX Index main characteristics

� The VIX Index is mean reverting.

� The VIX Index is negatively correlated to the SPX.

� Large spikes in falling equity markets

� Slower transition from high to low volatility regimes

� The VIX Index is on average higher than the realized volatility over the following 30 days.

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VIX

SPX (lhs)

VIX Index (rhs)

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0d

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VIX

VIX - rlz vol (lhs)

VIX (rhs)

3 June 2011 4

VIX Index is not directly investable

� The VIX Index is the result of a mathematical formula based on options prices.

� The replicating portfolio of options will give the value of VIX2, not the VIX

� An option portfolio worth the VIX today will have to be rebalanced to match the VIX tomorrow. It will suffer time decay and rebalancing costs.

There is no portfolio of assets/derivatives worth the VIX Index every day.

You cannot buy the VIX.

� How can investors get exposure to the VIX Index?

� VIX Futures

� VIX Options

3 June 2011 5

Trading the VIX using Futures

Source: Bloomberg, as of February 23rd, 2010

3 June 2011 6

VIX Futures’ Description

For illustrative purpose only

Today Jan-10 21 Sep-11 + 30 days

= Oct-11 SPX option expiry

Expectation of VIX value

Expectation of 30-day volatility

VIX

21 Sep11Today

Sep-11 VIX Future

Illustration of Sep-11 VIX Future

Source: Bloomberg, as of February 23trd, 2010

Sep-11 VIX Future’s value is today’s expectation of what the VIX will be worth on the 21 Sep-11, as it will be implied on that day by the Oct-11 SPX option.

� Since the VIX is not investable, there is no cash and carry strategy to link the VIX spot and VIX future prices.

� The settlement value is a Special Opening Quotation of VIX (Bloomberg: VRO Index) computed using a specific auction on the listed options of the replicating portfolio. So you can print the cash settlement of the future.

3 June 2011 7

VIX Futures’ characteristics

� There are usually 8 listed maturities for VIX futures, one for each of the first eight following months.

� The future contract lot size is $1,000.

� VIX futures have become the most liquid volatility instruments for up to 3 month maturity. It is as large as the vega exposure traded on the SPX options listed market. On average, $30 million notional trades every day on the first 3 contracts.

� A typical market would be for 250 contracts and 0.25 wide. Market on the screen would be for 25 contract and 0.1 wide.

3 June 2011 8

VIX futures term structure

Example of VIX Futures’ Term Structures

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VIX Month 1 Month 2 Month 3 Month 4 Month 5 Month 6

31-May-11

27-Oct-08

21-Nov-06

30-Apr-09

3 June 2011 9

Common strategies using VIX Futures

� Long VIX future to hedge a long equity portfolio (beware of the roll cost !)

� Short VIX future on volatility spikes.

� Long VIX future to protect a short realized volatility strategy.

� Term structure arbitrage : Short front month future / Long long term future.

� Relative value arbitrage :

� VIX futures vs OTC variance swaps

� VIX futures vs listed options

The roll cost

Futures term structure in contango Futures term structure in backwardation

The cost of rolling into a

new contract is higher for

the period 1 than for the

period 2

1m 2m 3m 4m Maturity

Price

Cost

Roll

1m 2m 3m 4m Maturity

Price

Profit

Roll

The profit of rolling into a

new contract is higher for

the period 1 than for the

period 2

1

2 1

2

1

2

1

2

� Finding the right balance between short-term volatility and long-term volatility

� Front month futures are very reactive, but the rolling costs are generally more expensive due to a steeper contango on the front. Moreover the high volatility makes entry and exit timing more difficult.

� Longer term futures are cheaper to roll but display lesser reactivity

� The performance of rolling a long future position can be broken down into

� Spot return : Price return of one future over one roll period

� Roll return : Impact of switching from one future to the next

3 June 2011 11

Trading the VIX using Options

3 June 2011 12

VIX Options characteristics

� VIX options are european options cash settled.

� There are usually 6 listed maturities for VIX options, one for each of the first six following months.

� VIX options expire on the same dates as VIX Futures and with the same settlement value.

� Strikes range from 10 to 75.

� Lot size is $100.

� Delta hedging can be done through VIX futures.

� Good liquidity on the first 3 expiries.

� Market is generally 0.15 wide and standard size is $ 250,000 notional.

3 June 2011 13

Implied Volatility of VIX Options

VIX Volatility Term Structure

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Month 1 Month 2 Month 3 Month 4 Month 5 Month 6

Maturity

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lati

lity

VIX Volatility Implied Skew

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VIX

Vo

lati

lity

ATM Vol of VIX OptionsImplied volatility of VIX options is high compared to other assets.

The shorter the maturity the higher the implied volatility.

The implied volatility skew of VIX is “inverted”. The higher the strike, the higher the implied volatility.

3 June 2011 14

Common strategies using VIX Options

� Buying out of the money calls to protect a long equity portfolio against a market crash.

� Selling at the money calls to monetize high implied volatility levels

� Buying long dated out of the money puts to monetize a steep contango

� Selling at the money straddle to monetize the high level of vol of vol.

Disclaimer

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The information contained herein is provided to the client by BNP Paribas on a strictly confidential basis. It may not be reproduced (in whole or in part) or delivered to any other person without the prior written permission of BNP Paribas. Although the information in this document has been obtained from sources which BNP Paribas believes to be reliable, BNP Paribas does not represent or warrant its accuracy and such information may be incomplete or condensed. Information in this publication is intended as a general outline of the subjects covered and should not be regarded as comprehensive or sufficient for making decisions, nor should it be used in place of professional advice. Any prices or examples of possible transactions contained in this document are set out for illustrative purposes only and do not constitute any form of offer from BNP Paribas to trade on such terms or constitute an indication that it is possible to trade on those precise terms. All estimates and opinions included in this document constitute the judgement of BNP Paribas as of the date of the document and may be subject to change without notice. BNP Paribas does not accept responsibility for any loss arising from any action taken by anyone using this material. BNP Paribas and its affiliates may, from time to time, effect or have effected an own account transaction in, or make a market or deal as principal in or for, the instruments mentioned herein, or in options, futures and other derivative instruments based thereon and may, to the extent permitted by law, have acted upon or used the information herein contained, or the analysis upon which it is based. This document is prepared for professional investors and is not intended for private customers and should not be passed on to any such persons.

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