I am valuing a series of asset swaps that are balance guaranteed swaps (BGS). This means that the owner of these swaps is hedged for prepayment risk, i.e. the owner would not have to rebalance the notional of the swap ?manually? but this is done automatically when a repayment takes place on the asset. Since in this case the swap fixes the interest payments on a pool of mortgages, the amortisation profile is driven by the actual underlying repayments/prepayments on the mortgage loans. The party that owns the mortgages and uses this swap to hedge these is long the options to increase/decrease the amortisation profile. This obviously has a value and needs to be priced in the swap. How should this option be priced? I am considering to price the value of the BGS 'option' via a cap/floor or bermudan swaption structure, since from the swap contains an implicit prepayment hedge and I understand that the cap/floor structure is a way to price this hedge. However, I have not been able to deduce for myself why this is the correct approach.Can anyone give my some theoretical background as to how this should be valued? Does anybody have any practical experience with pricing these type of swaps? How does the market do this (for instance in break-fee discussions, or for reporting purposes)?I hope my questions is written down clear enough, otherwise I can give more background!Regards,T

Interesting. This product, along with variations such as indexed amortizing swaps (where the amortization of swap notional is based on an actual function of some interest rate rather than on the prepayment behavior of a mortgage pool), blew up several trading desks twenty years ago, and I thought they had essentially disappeared. They are of historical interest, since they were arguably the main reason for a whole generation of quants to be hired in NY in the early 90's. The embedded optionality is arguably more swaption like than cap/floor like, and last time around there was much discussion about local volatility vs term volatility, normal vs lognormal, what parameters to make time dependent, etc.; but in this day and age I think the default approach would be to run a Monte Carlo simulation of a multi-factor interest rate model calibrated to interest rate option markets (ideally including Bermudan swawptions) along with your best estimate of the relevant prepayment function for the reference pool.

We describe their valuation in our book, section 19.5 onwardsVladimir

Thanks for you responses.So I am now trying to inventorise for what swaps that I have to value this adjustment is necessary. Conceptually, there are 2 types of amortisations:1) The swap's amortization schedule is set in advance, regardless of movements in interest rates2) The swap's amortization schedule is stochastic, but determined by events uncorrelated with interest rates (CPR)In what circumstances should I conclude that the amortization should be considered to be stochastic? I have done some empirical research, and I still find 'evidence' that there are people that base the amortization schedule of the swap based on the best estimate (or even the currently realized) CPR. What are your opinions on this? In what circumstances would that be appropriate?Thanks in advance!!Kr

QuoteOriginally posted by: TNLThanks for you responses.So I am now trying to inventorise for what swaps that I have to value this adjustment is necessary. Conceptually, there are 2 types of amortisations:1) The swap's amortization schedule is set in advance, regardless of movements in interest rates2) The swap's amortization schedule is stochastic, but determined by events uncorrelated with interest rates (CPR)In what circumstances should I conclude that the amortization should be considered to be stochastic? I have done some empirical research, and I still find 'evidence' that there are people that base the amortization schedule of the swap based on the best estimate (or even the currently realized) CPR. What are your opinions on this? In what circumstances would that be appropriate?Thanks in advance!!KrI think I am confused. In your original post you stated that you were looking to value balance guaranteed interest rate swaps referencing mortgage pools. Since the prepayment of mortgages is partially driven by changes in interest rates, the resulting covariance between the swap notional and the floating rate paid on the swap induces an "option like" valuation effect, even though there is no actual option embedded in the swap. The two conceptual types of amortization that you spell out above are both missing this feature. Case 1 can be directly valued through standard discounting and case 2 can typically be handled the same way based on the expected amortization schedule, at least as long as we can treat the stochastic amortization as diversifiable. But neither would be particularly helpful to your original question.

I think I understand why you are confused. The second type of contracts should read '2) The swap's amortization schedule is stochastic, but determined by events that are correlated with interest rates (for example, CPR)'.I am doing some research on the valuation methods applied to pre-crisis CDOs/CLOs and I have noticed that the amortization schedules of balance guaranteed swaps are considered to be deterministic. They are based on the best estimate of CPR, or on the historically realised. Unfortunately, I only have access to the valuation models applied for financial reporting purposes (which - compared to front office models - use a lot of short-cuts). I want to have a better feeling how the front office would price these swaps. I can not imagine that a trader would leave out the "option like" valuation effect (as you call it).Any thoughts?

There are models that price instruments called Inverse Interest Only Strips (IIO). The IIOs have an effective cap. A BGS is equivalent to an IIO without any cap. For example,an IIO might have a coupon of that is MAX(0,2.5%-LIBOR) -- hence an cap of 2.50%. The BGS has no cap.