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Edmund Li , VP
Financial Engineering
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Wednesday, July 07th, 2010.
In the past decade, CMM products (constant maturity mortgage forward and constant maturity mortgage swap) have emerged in the mortgage market as very effective hedging instruments, especially in the servicing hedging area. The mortgage market has two distinguishing characteristics: (a) first, the mortgage products have negative convexity; (b) secondly, the valuation of mortgage products (WL, MSR, and TBA) is all dependent on certain prepayment models. This results in pricing values of mortgage assets from different firms often being difficult to compare. The purpose of the CMM rate (index) is to build a term structure of mortgage rate that is a market universal mortgage rate structure independent of prepayment models and without negative convexity. Furthermore, this rate structure can be compared not only across different firms but with other (Treasury, LIBOR/Swap) markets as well. An example of a CMM forward rate structure usually appears as follows:
Obs Date CMM Forward Spread to spot
Spot 05/22/09 4.203 0.0
1M 06/22/09 4.213 1.0
2M 07/22/09 4.233 3.0
3M 08/24/09 4.243 4.0
The emergence of CMM derivatives has changed the traditional way servicers hedge the mortgage rate risk. In this short essay, we briefly go through the CMM index calculation (both spot and forward) and discuss some application of CMM products in the mortgage markets.
1. Spot CMM rate calculation.
The spot CMM rate calculation has been standardized in the mortgage community. It is the direct result of the 30-day forward current coupon, straddled by the discount and premium coupon of two TBA prices, that produces the par TBA price. The standardization of CMM rates has universalized the current coupon calculation in the mortgage community and is now a benchmark
where the price Pprem and Pdisc have been adjusted for cash flow delay. The spot CMM rate from the above formula will be translated in a BEY format. The spot CMM rate lays the foundation for the forward CMM rate calculation.
2. Forward CMM rate calculation.
The forward CMM rate is a little complicated compared with the spot CMM rate. There are two consecutive steps for constructing forward breakeven CMM rates. First, since TBA is negative convexity, the TBA price has to incorporate the adjustment of this convexity. The adjustment takes the form:
where P0CMM is the rate after the convexity adjustment. In the above expression, the ideal candidate of volatility is the one taken from the mortgage option market. In practice, it is sufficient to take a benchmark swaption volatility from the swap market, and one usually uses a scaling factor to rescale the volatility to get the actual volatility for this correction.
Secondly, the forward CMM rate is the weighted average of the scenario CMM rate, the distribution of which is dependent on the forward distribution of TBA prices. The TBA price distribution is assumed to be relied on the probability distribution of the benchmark swap rate. The forward TBA can thus be calculated based on the following formula,
where dX is a shock (or shift) to the benchmark swap curve and Ddura is the duration for the corresponding coupon stack. The distribution of swap rate is needed to build a scenario forward TBA price distribution; usually a normal distribution of a swap rate is assumed. From the construction of the CMM rate, we can see that the CMM rate has eliminated the negative convexity of the TBA price. Thus, the CMM rate has duration almost to one and shows almost no convexity.
3. Long term CMM rate calculation.
The problem with the long term CMM rate construction comes from the fact that the TBA market is now available for only a few months, and thus, even for a short term forward CMM rate, some interpolation techniques should be used to get the forward TBA price. For further long term CMM rates, there is no good solution for constructing this CMM rate. The long term CMM rate has not standardized so far and the market has no consensus on the comparability of long term CMM rate. The prevailing methodology is to use a current coupon model based on some benchmark swap rates and some volatility factors, and these model are usually then regressed through historical pricing using some prepayment model. So far, the majority of CMM market is dominated by CMM forwards.
4. Application of CMM product in servicing hedging.
The growth of CMM products in servicing hedging comes from their advantages over traditional hedging tools. Traditionally, servicers use swap and TBA to hedge the mortgage rate risk. However, hedging with swaps introduces basis risk and hedging with TBAs brings more negative convexity into the overall portfolio. Although the aggravated convexity can be hedged again using swaptions, the new swaptions in the position will bring extra basis risk between the mortgage option volatility and swaption volatility. The traditional hedging approach also requires frequent rebalancing of the position and higher transaction cost. We can see from the above analysis, that the CMM rate does not show negative convexity compared with hedging with TBA, and also eliminates basis risk compared with hedging with swaps. Thus, using CMM products as hedging instruments, changes in a servicing portfolio due to a change of mortgage rates will be offset by changes in CMM forwards. In current hedging practice, instead of using TBAs and swaps as hedge tools, it becomes more popular for the servicers to use CMM products as hedging tools. Hedging with CMM products will neither incur extra negative convexity nor extra basis risk. Hedging with CMM products also saves transaction costs. Other applications of CMMs include their use in mortgage basis trades and carry trades.
In MIAC’s new release of the SP3 ALM tool, we have built our CMM forward calculator. The forward CMM rates are calculated using convexity adjustment and scenario rate distribution of TBA coupon stack. MIAC’s CMM calculator has been verified against results of other dealers and shows an excellent match.
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