Suppose I have a portfolio of mortgages and package them as a bond in one currency (e.g. USD).I want to issue the bond as a EUR denominated bond and hence I would need to invlove cross currency swap.However, there is a risk for both pre payments and defaults in the underlying portfolio.How can I be able to price a swap (e.g. cross currency swap) with a notional than can vary over time?Is there anything published on this, anything done by banks? Anything that could start me would be of great interest.Many thanks...

The problem sounds new and interesting even from theoretical point of view. If you wish to make something yourself then probably it is better to start with no default case then later make an adjustment. First, it makes sense to write the solution a single currency. Then, the notional of the payments convert in foreign currency by using forward rate contract data. This is close to PV pricing. Next, you can adjust valuation formula for no default or 0-coupon issues. Note that bond defaults is an event related to US T-bond though LGD would be expressed eu currency. Default on currency can be considered itself because it can be considered as independent on mortgage portfolio bonds at least in the first order approximation. It also depends on a size of the mortgage portfolio. Though one can see that everything doing here beginning with PV pricing is sufficient for the quite a stable economy. For the current state of economy PV pricing lost too much. Indeed, using couple years observations one can come to the conclusion that primary players in mortgage market failed with their pricing methodologies. It is clear that using historical data we can discover that over the lifetime of a mortgage the PV of the face value ( which can be determine as immediate investment of the mortgage premium up to the mortgage expiration ) does not equal to the original PV. This fact represents the market risk which does not represent in PV pricing formulas.

Try googling "balance guaranteed swaps". This family of products goes back to the 80's, albeit primarily in the form of balance guaranteed interest rate swaps. They were a direct precursor to index amortizing swaps, which arguably were the main driver of quants being hired to develop interest rate models (at least in the US) in the early 90's. The primary problem with valuing/hedging balance guaranteed swaps that refers to a mortgage portfolio is that you have the full prepayment and default model to worry about + the correlation (loosely speaking) between these events and the rate underlying your swap. Many a swap desk blew themselves up on these products in the mid 90's. And I have no idea what list said.

I've never seen this for cross-currency, but many years ago people used to use index-amortized swaps in an attempt to hedge the interest rate risk on MBSs. The concept is that there would be a fixed table of percentages and that on each swap fixing you would use an index to look up in the table and reduce the notional by the corresponding table percentage. They could be priced pretty easily via Monte Carlo. The problem with them was that they were very illiquid (i.e., if you sold off the MBS it was hard to unwind), prepays were more of a function of the whole term structure (rather than a single index) and all of the stuff which happens between swap fixings, and it was hard to construct a good table up front (at swap inception).Anyway, a Google search on these ought to get you started. Oops. Cross posted with bearish.

Thank for replies Jim & Bearish,Talked to my trading desk and apparently it was no problem pricing these structure but rather a question about monitoring the risk and hedging the positions due to lack of underlying market. Thanks bearish for correct name.

QuoteOriginally posted by: difflab2000Thank for replies Jim & Bearish,Talked to my trading desk and apparently it was no problem pricing these structure but rather a question about monitoring the risk and hedging the positions due to lack of underlying market. Thanks bearish for correct name.Surprised as I would have thought there was a big market for non dom hedging of MBS

Always worry when there is no problem pricing a derivative but no way to hedge it.

QuoteOriginally posted by: bearishTry googling "balance guaranteed swaps". This family of products goes back to the 80's, albeit primarily in the form of balance guaranteed interest rate swaps. They were a direct precursor to index amortizing swaps, which arguably were the main driver of quants being hired to develop interest rate models (at least in the US) in the early 90's. The primary problem with valuing/hedging balance guaranteed swaps that refers to a mortgage portfolio is that you have the full prepayment and default model to worry about + the correlation (loosely speaking) between these events and the rate underlying your swap. Many a swap desk blew themselves up on these products in the mid 90's. IIRC, UBS was the culprit for destroying the IAS market. One guy there had a crappy model written in APL that underpriced them so UBS got all the business. I interviewed for a job in that group. When the guy running it told me they were pricing using 80 paths my jaw dropped. At BT we were using a minimum of 6,000 and 30,000 for the more complicated ones. When I asked him how that was possible, he just said 'variance reduction' and quickly changed the subject. Needless to say, I didn't get that job. Who wants a quant that asks pesky questions?QuoteAnd I have no idea what list said.Moi aussi.