# Modelling a prepayment loan via an swap and swaptions

I heard there is a possibility to model a loan contract including a prepayment option with the help of a swap including a swaption? I know that it is possbile to construct a prepayment loan as a callable bond in a binomial tree, but I'm not sure if this relation is somehow related to a swap.

Honestly I did not get the intuition how loans can be modelled as swaps.

K.S.

The idea is that as provider of the loan, you are recieving a fixed amount from the client. When he decides to prepay the loan, you will recieve the money and invest it at a market rate, a floating one, for the next periods until the loan is over in order to cancel the cashflows from the loan. In both cases, the swaption and the callable bond are the same at prepayment date, someone is entering a swap in floating rate and fixed rate.

• In "The concepts and practice of mathematical finance" of M. Joshi at chapter 13 you can find a good explanation. Oct 18, 2016 at 22:24
• So does this mean that as a borrower: Oct 25, 2016 at 12:38
• So does this mean that as a borrower, I have a short Position in a payer swaption? Oct 25, 2016 at 12:39

They are basically the same thing. For example , if you own the callable loan, it is worth 100pct of principal amount + value of a callable swap where you receive fixed versus libor and you are short a receiver option on the call date.

• why do i receive "fixed vs libor"? I'm receiving "fixed interest" (since the credit is ammortizied ist more like floating) but there is only one short CF in the beginning of the contract? Oct 17, 2016 at 7:32
• A loan (unlike a mortgage) is usually not amortized, you make fixed interest payments each quarter and refund the full loan amount only at the end. Oct 17, 2016 at 11:51

So to sum up:

a loan/mortgage with a prepayment Option is from the Position of the Lender: - Long in a Receiver swap - Short in a Receiver Swaption?

or equivalently from the Position of the borrower: - Short in a Bond - Long in a Call Option on that bond --> Long in a Receiver Swaption