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

MBS and Interest Rate Relationship

Risk Factor for MBS:
1. Interest Rate Risks: Level of rates (duration, convexity); slope of rate curve (partial duration); interest rate volatility (vega)
2. Other Risk Factors: Principal prepayment, spread risk

MBS Duration & Convexity:
* Homeowner has a prepay option similar to a receiver/call option.
* Higher coupons have a higher refinance incentive, thus lower duration.
* Duration of the index is diretional with mortgage rates.
* Negative convexity, compared with a straight bond, is because of prepay option
* MBS gains less in a rally than do Treasuries/swaps
* 4.5% and 5% coupons most negatively convex, because:
1) convexity is similar to an option gamma, hightest ATM
2) 4.5% and 5% coupons are closest to ATM (cc 4.2%) after refinance costs

MBS Vega
* MBS declines in value for increased in implied volatility
* Across the MBS coupon stack, two factors pull vega in opposite direction
1) Cash-flows are more uncertain for par than premium MBS => par MBS have greater vega
2) More uncertainty => higher mortgage rate => premium MBS lose less => premium MBS have lesser vega

Hedges for MBS Interest Rate Risk
* Duration / partial duration: hedged using different points on tsy/swap curve
* Negative convexity: hedged using short-dated swaption (3m*10y or 3m*5y)
* Vega: hedged using long-dated swaption (5y*5y)

Impact of MBS Hedging on Spreads
* The MBS universe is large
* The changes in MBS duration are hedged by paying/receiving in 5y, 10y swaps
* This causes positive directionality between swap spread and MBS rates/durations
* MBS flows large in 3m*10y swaption notional terms
* Convexity risk related to rate^2 and not rates - effect exacerbated in large moves
* Most of the convexity risk hedged with short-dated options on intermediate (5y and 10y) tails
* Large moves in MBS rates, particularly close to "strike", cause a demand for short-dated options on intermediate tails

MBS Hedgers and Their Strategies
* The GSEs buy MBS and hedge most interest rate risk
1) Using agency debt, swaps, and short- and long-dated options
2) Have a disproportionate impact on longer-dated options
* Mortgage originators hedge their loan pipeline
1) Using the TBA market, as well as swaps and short-dated options
2) Especially active in a sell-off that follows a refinancing wave
* Mortgage servicers hedge their MSRs using TBA collateral
1) Increases their negative convexity exposure
2) active in swaps and short-dated options

The GSEs (FNM & FRE) - The levered entities
* The GSEs maintain a portfolio of roughly $1.5 trillion, likely to grow
* The GSEs hedge most interest rate risk
* The greater leverage (1:30) means they actively hedge the vega risk

Originator's Pipeline Risk
* The fall-out risk: associated with mortgage originators whereby the borrower can walk-away from the quoted rate
* When interest rates are stable, originators can estimate fall-out well
* But when rates change rapidly... most risk during a refi-wave, like in 2003 and 2009!

Mortgage Servicers Interest Rate Risk
* Mortgage Servicing Right (MSR) is like an IO... negative duration, negative convexity
* When rates rise, the asset extends and so servicers need to shed duration, and vice versa
* Servicers hedge:
1) Negative duration: using the TBA market, which makes the more negatively convex
2) Negative convexity: buy short-dated options