Volatility Swap
- Swap between historical and implied volatility whereby:
* you can receive (pay) implied volatility and
* pay (receive) the realized vol
* during the covered period of time
- Implied Vol = "Fixed Rate", while Historical Vol = "Floating Rate"
- The realized Vol is figured out from an array of daily fixings. Fixings and formular are pre-agreed and described in the confirmation.
- The swap's notional is an "amount of vega"
- The contract is cash settled at expiry:
Cash Settlement = Swap notional x (Received -Paid) x 100

Varaince Swap
- Swap between actual and implied variance (Vol^2) whereby:
* you can receive (pay) implied variance and
* pay (receive) the realized variance
* during the covered period of time
- The actual variance is figured out from any array of daily fixings. Fixings and formula are pre-agreed and descibed in the confirmation.
- The swap's notional is an "amount of USD per variance".
- The contract is each settled at expiry:
Cash settlement = Swap notional x (Received - Paid) x 10,000

Contract Details:
With drift:
- The actual vol is calculated classically as (Ri representing daily log returns)
- The drift, materialized as the average of the log returns, makes this type of swaps difficult t hedge
Without drift:
- The actual vol is expressed slightly differently as: (Ri representing daily log returns)
- As easier to hedge, two-way price will be tighter. This is the most common form of swap found in the market
- Annualizing: most usually used are 250 or 252 days
- Fixing: anything good as long as it is occurring in a liquid center
- Fixing frequency: equity market is flexible (daily, weekly etc...) we only do daily at this stage

Applications:
- Expressing a volatility view
- Most common use
- Advantages are:
* allows taking pure vol view
* gamma management is defferred to the bank
* no premium outlay
- In the equity world, most often used to exploit the constant positive gap between implied and actual vol (received implied)
- Can be compared to straddle or strangle strategies, except Vega remains constant wherever spot moves.

Hedging:
- Asset Managers:
* Magnitude of portfolio rebalancing and thus transaction costs higher in volatile times
* May be used to circumvent regulatory constraints on options usuage

-Overlays
* Overlay managers with tight tracking error budgets need accurate currency vol forcasting tools
* Aim is to avoid large discrepancies between budgeted and actual TE.
* If asset allocation is run from implied vol/correlations, vol swap may help mitigate risk

- Currency Traders
* Empirically, profits rise with market vol
* Equates a long Vega position that might be unwanted
* Vol derivative seems more adequate to heldge a vol risk