Valuation Commentary

Treating MBS settlement rigorously: AD&Co's OAS version 5.2
by Alex Levin

Recently we have been discussing ValueNet, our new backward induction system for MBS pricing. At the same time, AD&Co remains committed to further elevate the rigor of our "traditional" OAS application. Results of this work is version 5.2 that is still in a Beta-stage, but nevertheless has already become a better option than 5.1x.

Among several enhancements, the new version now supports settlement conditions with both "trading on balance" (TBA) and "trading on factor" (non-TBA). For the latter case, the system recognizes differences in delivery balances for various rate paths and includes "balance delivery" option into valuation. A rare system does this.

Balance delivery option

Balance delivery option results in an additional negative convexity for the dollar value of a non-TBA security arising due to the negative correlation between the percentage price and the balance being delivered.

Consider first a TBA delivery with a guaranteed balance. Suppose the risk-neutral world at delivery date contains 3 possible states, "up", "flat", and "down". The "up" state features high rates and low prices, let price of an MBS be 96. To reach the "down" state the rate must fall, so the price of the same MBS will become 101. For the "flat" world, the price is par. Let us further assume that all 3 states are equally likely.

Hence, the fair quoted price should be close to (1/3)*(96+100+101) = 99.

Consider now a specific security (not a TBA) typically traded "on factor". It means that the negotiated price at the trade date will apply to an unknown fraction of the balance remained after amortization between trade and settlement. Since there exists correlation between rates and prepayments we must assume that the remaining balance is likely to be higher in the "up" state than in the "down" state. Suppose that the original, trade-date, balance is $10M, which would drop to $9M at the up state, to $8M at the flat state, and to $7M at the down state. How would we value this forward transaction with an uncertain balance?

The market values should be added probabilistically without any hesitation:

(1/3)*(96*9M+100*8M+101*7M)/100 = $7.903M

However, the buyer won't pay $7.903M at delivery - he must pay a certain unit price for the actually delivered balance. How to compute this unit price? Let us first find the average balance as (1/3)*(9M+8M+7M)/100 = $8M, then relate $7.903M to that amount: (7.903/8.0)*100=98.79.

Why have we used the average balance as the denominator? Compare two settlement contracts:

Contract 1: pay random fair value at settlement. We checked above that it is worth $7.903M.
Contract 2: pay 98.79% for every dollar actually delivered. This is worth

(1/3)*(98.79*9+98.79*8+98.79*7)/100 = $7.903M too!

Hence, values of Contract 1 and Contract 2 are identical to one another, which ends the proof.

In particular, we learned that a non-TBA forward contract is worth 21 basis points (6-7 ticks) less than a TBA forward contract, which constitutes the value of the balance delivery option, in our example. The option would be almost worthless for the next-month delivery because there exists little (if any) correlation between future rates and the next-month balance (recall the prepay lag). The option matters for remote settlements (2 and more months), especially for CMOs. Indeed, many CMO classes may amortize quickly before settlement. If, for the same price profile as in the above example, the balances had been $9M, $7M, and $5M (instead of 9, 8, and 7), the value loss would have been nearly half-point.

The ultimate forward settlement formula

Suppose the PV% denotes the expected present value of an MBS' cashflow; it is measured in percentage points off the trade-date balance. Note that an MBS investor is not entitled to receive any proceeds until the first month after the settlement. Similarly FP% is the forward price measured off an unknown settle-date principal. Denote DF as the discount factor between trade and settlement known from the trade-date market. Finally, denote AF as the mathematical expectation of amortization factor between trade and settlement. This is the measure fully discussed above. Then,

Where Accrued% stay for the settle-date accrued interest in percents. If security does not amortize (AF = 1), we get the usual forward settlement rule.

In version 5.2, the settlement date can be entered for up to 12 months forward with every position having it's own entry.

Other improvements

The list of other highlights and improvements found in version 5.2 OAS is fairly significant:

· All needed rates are now interpolated intra-month so that passing the month-end does not result in a price jump.

· We included an option to "fudge" short rates to static instruments. This option provides exact valuation of option-free instruments (hence, the discount factors) even with a limited Monte Carlo or Quasi-Monte-Carlo sample.

· Monte-Carlo pricing accuracy is displayed so there will be less need to ask about recommended number of paths.

· Intex's "as of" date is shown for CMOs/ABS. This date (and the deal structure) will change with the trade date. In particular, one can re-run for past dates to verify or replicate the past runs.

· Expected balance settlement factor is shown for all instruments; CMOs is a particularly important case.

"Day 1" adjustment

While model upgrades are typically free to our clients, many proved hesitant in accepting any changes. Experience shows that practitioners associate a model change with the trouble of revising and re-running past analysis often worth 1-2-3 years of history.

There is absolutely no need to re-run past marks and risk measurements! Instead, users should make a "Day 1" adjustment. Suppose the long series of marks is based on a constant OAS assumption. Then, preserving the last price, re-compute the new OAS using an upgraded version and stick to it going forward.