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7/28/2019 d Bfx Vol Trades
1/24
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
7/28/2019 d Bfx Vol Trades
2/24
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
7/28/2019 d Bfx Vol Trades
3/24
7/28/2019 d Bfx Vol Trades
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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..
( ) ( )> L
S
L
LS
SG
TT
LST T log1
( )
+
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T dKKS
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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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N
i
N
iLS
i
iLS
N
i i
iLS
iii S
S
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S
1 1
2
2
11
2
2
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1log1log1Payoff
Corridor variance swap Timer
The corridor variance swap component is then handled according to the general theory, such that