Hi all,Could someone explain how the mortgage current coupon is calculated? preferably with a numerical example.I read that "current coupon is the semi-annual equivalent of the parity-price interpolated coupon" and "parity price is the price such that the coupon on the pass-through is the same as the bond equivalent yield". So say for example that we have FNMA 6.5% priced at 97.85 and FNMA 7.0% priced at 100.03, how can I calculate FNMA current coupon?

The general definition of "current coupon" in finance is the coupon rate that makes the instrument sell at par. In some cases that is interpreted as an interpoltion, in some cases as the closest coupon with liquid trading in the market (usually you use the coupon with the highest price less than or equal to par, rather than the closest coupon).If you are going to interpolate, there is no standard way to do it. You seem to have come across a specific definition, but not everyone would do it this way. Unfortunately, your particular definition requires prepayment assumptions about the securities, so I cannot answer the question without more information.A standard way to define the current coupon would be to use linear interpolation to find the coupon that makes the price par. In your case, that is (6.5% x 0.03 + 7.0% x 2.15)/2.18 = 6.9931%. Since your definition requires a conversion to bond-equivalent yield, that gives 7.0958%. A hypothetical FNMA with this coupon would sell for more than par, probably about 100.45. At that price, the yield might be 6.9931%, if the prepayments implied an average life of about 5 years. In that case, it would be the right answer. But if the prepayments impied a longer or shorter average life, the current coupon by your definition would be different.

Apologies for this late reply, I was trying to get more information about this before posting.I got the definition in my first post from http://www.servicing.com/MIAC/mims/MIMs ... per.pdfand the definition seems to be pretty standard in the industry. The parity price is like the "par" price for mortgages (usually slightly less than 100 due to I think delay in transferring the cashflows from the agencies), and at the parity price, the BEY = coupon and different prepayment assumptions do not affect the price. Some sort of search algorithm is used to find the price (i.e. the parity price) that satisfies the conditions above. The current coupon is then found by the interpolation of the coupons of 2 securities that are left and right of the parity price.I talked to someone from a MBS dealer about this and they were doing something very similar. On Bloomberg, MCCN <GO> lets you see the bloomberg values, but I don't know how bloomberg calculates those.

Why do you say "the definition appears to be pretty standard in the industry"?The paper's explanation is deeply garbled. Take it one step at a time:(1) "Parity price is the price such that the mortgage coupon equals the bond equivalent yield." Fine. Take the 7% coupon. A 7% BE yield corresponds to a 6.9% monthly yield. But the price of a 7% coupon mortgage at a 6.9% yield depends on the prepayment assumption. If we assume a newly issued, monthly level pay, 30 year mortgage, we get a parity price of $101.02. With average prepayments, the price falls to $100.62. With fast prepayments, to $100.32.(2) "If one linearly interpolates between the price of the 6.5% and the price of the 7.0% to the parity price. . ." What could the author be hoping to convey here? The parity price of the 6.5%, assuming zero prepayments, is $100.90, the parity price of the 7.0% is $101.02. The market prices are $97.55 and $100.01 respectively. What are we supposed to interpolate?The only thing that makes remote sense is to figure out the coupon at which the price equals the parity price, however we have to extrapolate for that. We should be using the 7.0% and the 7.5%. But if we do the extrapolation we find that a hypothetical 7.21% coupon mortgage should sell for its parity price of $101.07 and have a BE yield of 7.21%.If we assume average prepayments, we get 7.13%, with fast prepayments, 7.07%. If we assume prepayment speed varies with coupon (as it does) we get answers greater than 7.21%.(3) ". . .and applies this [presumably, the price computed in (2)] to the 6.5% and 7.0% coupons, one has the mortgage yield current coupon yield." This makes no sense at all. Why apply the price for a 7.21% mortgage to other coupons? We will get two difference yields if we do.The only sensible thing is to convert the 7.21% BE yield to a monthly yield, that gives 7.11%.Now let's take the entire exercise. The original stated goal was to find the hypothetical mortgage coupon such that yield did not depend on prepayment assumption. The author completely loses sight of that in the technicalities of converting monthly to bond equivalent, interpolating and converting back. While it's true that the definition of "yield" makes a difference here, the difference between the coupon for which the monthly and BE yields do not depend on prepayment assumption is insignificant.The monthly yield does not depend on prepayment assumption if (a) the price is $100 and (b) there is no delay. For BE yields or securities with delay, the price will always depend on prepayment assumption, the best you can do is find a price such that the derivative with respect to prepayment assumption is zero.This problem can be attacked is a robust way, using reasonable methods that give reliable results. The author does not show how to do that.