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DB Best Structured

FX Linked Products

House 2006

Strictly Private and Confidential

Volatility TradesVariance, Volatili ty and Conditional Variance Swaps

Volatility Swaptions,

Forward Vol Agreements and Knockout Forward Vol Agreements

March 2008

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Summary

The traditional vol trades are volatility swaps, variance swaps and FVAs

These are covered in detail in preparation for the introduction of

Conditional variance swaps with 1 specific trade idea

Volatility swaptions - with 2 specific trade ideas

Knockout FVAs - with a specific trade idea

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Variance Swaps Pricing and Hedging

There is a static hedgefor variance swaps in terms of vanilla options (see quant box). This means thatvariance swap pricing is model independent. In other words two traders who agree on the prices of vanillaoptions will necessarily agree on the book open price of the variance swap this is not the case for vol swaps

Quant Box

Hedging (and pricing) Variance Swaps

The variance swap is replicated (see Mathematics of

realised variance tradesslides for details) by setting up astatic options portfolio of the form

A potentially significant practical consequence of this is thatclients with systems which can handle vanilla options

should be able to easily extend their systems to handle

variance swaps whereas volatility swaps will requiresophisticated modelling in their own right.

As hedging variance swaps involves buying out of the moneyoptions they trade over the at-the-moneys (delta-neutrals) invol terms

Choice of fixing can be important..

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S

L

LS

SG

TT

LST T log1

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In combination with a static cash position and a dynamic delta hedging strategy which involves holding

at each time i for which is above the level and 0 below. The timer component is handled using a strip of digitals.

LST >1 iS

iS

where is the ratio of the annualisation factor andN orN-1 and is 1 if is aboveL and zero otherwise, so the upside conditionalvariance swap is replicated as a static portfolio of vanilla options represented mathematically as

= =

>

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=

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=

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N

i

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iLS

i

iLS

N

i i

iLS

iii S

S

S

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1 1

2

2

11

2

2

1

1log1log1Payoff

Corridor variance swap Timer

The corridor variance swap component is then handled according to the general theory, such that