USD swaption skew

Skew in 2010


2010 year dollar fixed income markets weathered various events ranging from hopes in recovery of housing market, Euro currency crisis, Federal reserve’s unconventional methods to handle the crisis of 2008 and geo political events. USD yield curve responds to these events accordingly and rises up when inflation talk takes precedence and falls when safe haven mentality seeps in. Changes in swaption skew reflect these scenarios.

Spot Yield curve is broken down into short dated, 2y, intermediate 5y, medium term long dated 10y and long dated 30y.

Skew is broken down into structures trading 1y and less as short dated, more than 1y and less than 5y medium term and 5y and beyond is long dated.

Players in swaption markets trade options on interest rate swaps to express views on swap rates. In this market Payer swaption and Receiver swaption are akin to call and put on Libor interest rates. Treasury yield curve along with swap spreads will represent the Swap curve on which options are traded. Implied volatility is a measure of dispersion of swap rates at some point in future. High Implied volatility suggests higher dispersion and higher cost of options. Swaption market volatility is depicted more aptly by Normalized volatility. Forward rate times Log normal implied volatility is equal to Normalized volatility.

Normal Volatility = Forward Rate X Log Implied Volatility

Rising Normalized volatility suggests bid for volatility and converse is true for falling normalized volatility.

Interest rates are correlated to Normalized vols. This correlation varies from 1 to -1. In general rising rates will have falling Normalized vols and vice versa. This means a positive correlation. But other factors can weigh in to amplify and depress the correlations. For instance normalized vols for 30y tails are at -0.3.

These factors give a framework of measure to estimate the value in an ATM option.

1) Correlation with rates

2) Volatility ranking

3) Volatility Roll down

4) Carry

5) Implied and realized volatility ratio

6) Implied and realized premium

Skew: Market players attach volatility different from at the money options to Out of the money options. This difference in implied volatility is called skew. Existence of skew is due to demand and supply factors, view of players on the speed of rise and fall in interest rates. Skew dynamics can be abstracted into different kinds of shapes. These shapes are termed as Normal, lognormal, square root, quarter power, super normal and super lognormal skews. These skew shapes are not arbitrary but capture the underlying rates distribution phenomenon.

Log normal skew: level of Interest rates is directly proportional to normalized volatilities. When interest rates are closer to zero, due to zero lower bound rate changes will be lognormal distributed. In this skew, we tend to see, higher normalized volatilities for Out of the money payer swaptions proportional to interest rate level.

Normal skew: level of Interest rates is independent of normalized volatilities. When interest rates are away from zero rate changes will be normal distributed. In this skew, we tend to see, higher flat to similar normalized volatilities for Out of the money payer swaptions and at the money options.

Interest rates move up and down so do normalized volatilities. Swaption skew moves can be traced to moves from one skew level to another skew level. This can be termed as skew migration. Log normal skew can become super lognormal skew that is normalized vols rise fast as interest rates are rising. Similarly, skew can lower to Square root and quarter power. In these two regimes, Normalized volatilities don’t rise as fast as they rise in lognormal regime. After quarter power regime we can think of normal skew level where normalized vols are independent of rate moves. Finally beyond normal skew regime we can think of normalized vols falling when rates are rising.

Spot and forward yield curves tell us about what market is thinking today with current set of information. Volatility players take one step further by trying to guess the range of the yield curve moves with current set of information. This guessing game involves attaching equal probabilities to various rate changes. But reality is far different from ideal state. Some players think rates will go up, others think go down and another group think rates will remain range bound. Markets do what they want and winners and losers are declared accordingly. Due to this kind of market environment, its not accurate to attach equal probabilities when thinking of range of outcomes centered away from the forward curve. Systematic way of attaching higher and lower probabilities to distributions centered on rates other than forward curve is called skew.

Skew arising due to change in market sentiment towards rise or fall of rates can be captured by risk reversal transactions. Risk reversal is defined as buying and selling OTM call and put with same moneyness. For instance, buy ATM + 25 call and sell ATM - 25 put will translate to buying a risk reversal. This strategy is employed to sell rich put skew and buy cheaper call skew and position for rise in rates. This risk reversal price can be compared against price for a normal, log normal skew to identify traded skew.

Skew also arises due to demand and supply in the markets. This factor can be traced by comparing current skew level to historical skew and rate moves and sentiment in the market. Normally flow traders are privy to this kind of information but in no time this information will become public.

Another factor that plays into skew development is when rates move up and down without any particular direction. In other words if high realized volatility persists out of the money option should have higher value than what they normally have. This price can be captured by Butterfly quotes or straddle and strangle swaps. Straddle provides market level for ATM volatility. Strangle will provide indication of Out of the money options. These two quotes combined provide value of the skew for out of the money options.

Demand & supply, Risk reversals and Butterfly quotes together measure the shape of the skew. Indirectly describing how investors expect the volatility to rise. This view is captured by normalized volatility thus resulting in various skew shapes.

SABR Model interpretation of swaption skew.

Skew can be analyzed using SABR model. For detailed discussion of SABR model I will refer to a presentation I put together. SABR model has Rho and nu parameters to capture the Smile and skew of the swaption skews. I looked at NU and Rho parameter for 10y tails from Totem monthly data. Interestingly Vol of vol remained very stable. Month over month yield curve changes had minute effect across most of the maturities. This suggests very low levels of realized volatility in the market. Rho parameter showed changes by becoming positive when rates are rising and negative in falling yield curve scenario. This doesn’t give any predictability to market vols direction but describes the dynamics reasonably.

Short dated skew for 10y tails for different option expiries, 1m, 3m, 6m and 1y expiries manifest skew that is Lognormal to less log normal. As of November month end skew levels are more lognormal.

Does understanding of these skew shapes give us any understanding of how to trade swaptions markets? I think it does. When we clearly understand what has happened we can predict the future outcome with a reasonable confidence. This requires proper description of past and current states and future expected states of market levels.



Short dated skew

1y 10y, 1y 5y, 1y 2y

1y 10y

In January, 10y Rates at 3.74 and 2s 10s at 261 bps. By end of November, 10y swaps are trading at 2.95. 2s10s at 220 bps.

As Spread between 2s 10s widens spread between spot and forward rate increases.

ATM straddles were trading at 830 bps. From here market premium has fallen down to 742 bps by end of November.

Normal vols have fallen down from 126 to 108.

Skew shape remained more or less log normal. 200 low receivers are trading at 56 and 200 high payers are trading at 175 normal vols.



1y 5y

In January, 5y Rates at 2.66 and 2s 10s at 261 bps. By end of November, 5y swaps are trading at 1.74. 2s10s at 220 bps.

ATM straddles were trading at 471 bps. From here market premium has fallen down to 392 bps by end of November.

Normal vols have fallen down from 129 to 104.

Skew shape remained more or less log normal. 200 low receivers are trading at 47 and 200 high payers are trading at 197 normal vols.

1y 30y

In January, 30y Rates at 4.41 and 2s 10s at 261 bps. By end of November, 30y swaps are trading at 3.81 2s10s at 220 bps.

ATM straddles were trading at 1448 bps. From here market premium has fallen down to 1429 bps by end of November.

Normal vols have fallen down from 111 to 101.

Skew shape remained less log normal and more square root. 200 low receivers are trading at 70 and 200 high payers are trading at 142 normal vols.