Wednesday, December 5, 2012

Macro Views Series: 2013 Points To Ponder

Thoughts and observations for the coming year to ponder over, without any forecasts

Wednesday, October 10, 2012

The Big Short (Vol) Trade

Perhaps a (very bad) idea whose time has come, at least to give it a thought

Historically, selling far OTM options has been branded as a reck-less trade, especially in this post-Lehman markets obsessed with swans of the black variety in particular. But the chart below put things in a slightly different perspective

Assume a position where we sell a covered far OTM swaption payer (or receiver) spread. So we set aside an amount for the maximum loss arising out of the position. Such a position can be compared to a long bond position - we can imagine the sum set aside as an investment in the bonds and the premiums we receive as coupons. The event of the option spread getting exercised is similar to a default event. Assuming a standard 40% recovery, we can compute the yield of the equivalent bond position as 

yield = premium/(max loss/60%)

The above plot compares these yields on these imaginary bond-like positions (let's call them "Coins in Front of Road Rollers" bonds, or CFRR for short)  with bunds and BBB corps. Pre 2008 it was indeed a reck-less idea, the yields on these CFRR bonds are on an average much lower than the even the high quality bunds yield. But then something changed in 2008. With yield hitting the Zero Lower Bound (ZLB), the investors has chased down the yields on the so called High Yield (HY) bonds as well. The upside in bonds are limited with considerable downside. Not very much unlike a short vol trade. And these CFRR yield does not look so ugly now in the plot.

Fast monies and smart real monies chasing yield, and credit funds as well, should take a note of this fact. Putting money into HY to boost portfolio yield is not fundamentally very much different than selling OTM rates options. Given the current centrally administered markets with converging correlations, the default risk of a junk bond is marginally different than a massive move in rates (which will force many firms to default anyways)

On the flip side of this - those looking for BUYING far OTM options, an interesting area to look in to, I think, is far OTM 6 month LIBOR or 12 month LIBOR interest rates caps vs swaptions - less as a wedge trade and more to trade the regulatory risk of a reform of fixing submission method and consequent potential of much upward fixings for un-collateralized lending rates, if the current scenario persists

Friday, May 25, 2012

Volatility Smile in Rates | Understanding SABR Parameters

SABR is a standard skew model on the street for rates desk, but it's parameters and the part they play is often not very clear. Below is an approach for intuitive understanding of the parameters and how they affect pricing/calibration of collars and strangles

For strikes reasonably near the atm, we can have following approximation to good degree, for a normal bps vol and normal(horizontal when measured in bps vol) backbone

Skew = const1*correl*(volvol/atmvol)
Smile = const2*correl*(volvol/atmvol) + const3*(volvol/atmvol)^2

Here skew = (payer vol - rcvr vol)/atmvol, and smile = (payer vol + rcvr vol - 2*atmvol)/ atmvol

So the both the skew and smile depends on the relative strength of vol of vol to the ATM vol (or more precisely the local vol, but atmvol is a good proxy), i.e. on (volvol/atmvol). In case of skew this ratio acts through the correlation parameter. In case of smile, it is the square of the quantity that determines the wing vols. So as volvol/vol ratio goes down, the wings cheapen compared to ATM, and payers richen compared to receivers (given correlation is negative). And if correlation goes up, the skew steepen (on the payer side) given the ratio of volvol-to-vol is unchanged

Typically, this is a good approximation for reasonable strikes not too far away from the strikes

Also, for the smile, as the maturity goes up, the relative importance of the 2nd term (volvol to vol square) goes up compared to the 1st term, and so is the case as the width of the strangle goes up. So for wide long maturity stangle, (say 10y10y 200wide), the smile is practically determined by the 2nd part and correlation has practically zero impact. However, for short maturities they are of comparable importance and correlations and volvol gets entangled in both smile and skew. So a possible order of calibration can be first calibrating to the strangles followed by collars, recursively for long dated options and reverse for short dated options

To summarize the above, when looking at the sabr parameters, we should look at the correlations and volvol-to-vol ratio (relative strenght of volvol, NOT volvol itself)

In the recent rally that started March, we have seen a considerable richening of the payer skew. Upper-right, coming off from super-normal, upper left still sticking to log-normal

In the upper-right, in spite of a marked change in the realized correlation downwards, skew has moved up. At the same time, the volvol to vol ratio came down with increasing vol. So in effect, skew richened and the smile flattened out

With the Greece event risk in the near horizon, this cheapening of smile and receiver side skew represents an opportunity for play on the receiver sides with spreads/flies

I have left out another parameter of the SABR model from here, i.e. BETA. I will have another post to discuss that in details