## Wednesday, March 20, 2013

### The Correct Way to Spot Relative Value in Volatility Surface

While looking at the swaption grid of at-the-money volatility, and comparing them for relative richness, failure to take in to account the current yield curve and volatility surface term structure can be very mis-leading. This is especially true given the current steep slopes, where this simple ommission can be disastrous. For example if 3m2y options look very cheap compared to 3m10y, it does not mean buying the former and selling the later is profitable, even if the market does not move against us. The 3m options will become 2m options in 1 months time. And if 2m2y is even more cheaper to 2m10y, compared to the cheapness of 3m2y to 3m10y, then this position can bleed very seriously. Also as the time decays, the strike of the options changes from ATMF and slides along the skew, and this may also distort the trade dynamics. Therefore to compare apple to apple, it is utmost important to convert the ATM vol numbers to an equivalent number taking in account this time decay and skew slide. Below is a robust method for that

The concept of the method is quite stratight forward: that the total PnL loss from a long straddle position arising out of time decay in the real world (chaging volatility term structure and yield curve term structure) should be equivalent to the pure time decay loss in a world where volatility and yield curve term structure are flat. This method then converts each point to a equivalent number in a locally flat vol and curve scenario, which can then be compared directly - bps to bps - to any other point.

One way to get the equivalent volatility is by setting variance loss on both this scenario equal, as below

The same can be obtained from the basic options equation. Consider the PnL for a delta-hedged equation, ignoring cross-greeks. Then the pnl from a equivalent vol position should be equal to the same on the surface
Expressing all the greeks in terms of Gamma, assuming low enough cost of carry
Substituting, that gives
Which is exactly the expression above

## Thursday, March 14, 2013

### US Short End Rates Mis-pricing

Below shows the unemployment rate in US vs the priced in change in rates forwards (q-o-q changes). The dotted blue line extrapolates the current trends in unemployment.

This suggest by late 2014, the Fed will hit its target of 6.5% unemployment rate, from where we can see active tightening. With a large QE portfolio, the tightening may be not in terms of QE exits but rates hikes. There is all chance Fed will sit on at least a part of its QE portfolio through maturities. This suggests the market pricing in the rate hikes considerably later that the official target is reached. This presents a very good opportunities to go short in the short term rates vs euro. The best points are 3m (caps). This can be structured in caps with positive carry. The risk being a flare up of crisis in euro leading to a funding crunch in the region and a spike in short term rates. This should be mitigated to some extent by transmitted funding pressure across the Atlantic, as well as a very large drop in euro exchange rate

The underlying economic theme in US remains unchanged, as per the latest Fed Flow of Funds reports. The consumer credit going strong (along with corporate credits) where as de-leveraging continues in financial sector as well as in home mortgages - the key this year therefore, I think, is not the unemployment numbers, but rather housing recovery. That will determine the performance of this trade

Happy Pi day

## Friday, March 8, 2013

### Equity/ Commodity Decoupling

Charts above captures a broad-based decoupling of baseline equity growth vs commodities. Which is doubly strange as in a zero interest world, the commodities carry costs are minimal and has lot more capacity to absorb downward price pressure. A genuine decoupling setting the stage for a correction? or a advancement of technology where commodities are less relevant to global growth?

Hard to argue for a sudden great leap in technology where "best minds of the generations are thinking about how to make people click ads"

## Tuesday, March 5, 2013

### Payers (Swaption) Vs CDS Relative Value

Payers and CDS have some equivalence in extreme sovereign events - both can be structured as effective hedges against a sov bonds portfolios. In case of a sov default, the CDS is a straight forward hedge, and the payers benifits from the resulting selloffs. It is interesting to take a rough-cut look at the relative value between them I compute the strikes of a 100bps wide payer spread which is equivalent to a cds hedge (cost same upfront and have same max payouts in the event of default) - under different assumptions - 1) standard: 40% recovery and no deppreciation in FX, 2) moderate: 40% recovery and a 25% deppreciation in FX w.r.t USD, 3) severe: 20% recovery and a 25% decline in FX. The charts below shows the payers strikes (from current ATMF in bps) in Y-axis vs CDS spread in X-axis. Any point below the RED line indicates payers are trading cheaper to CDS, and similarly any points above it indicate payers are relatively trading richer. The instruments considered are 5y CDSs vs 5y10y payer spreads