Sunday, October 15, 2006

Actually... swap contracts are set to zero because

I am ignorant/stupid. But this sunday afternoon I have seen the light! Thank ya jesus, thank ya lord.

A swap contract is not meant to create an NPV zero exchange throughout the life of the SWAP (otherwise why would anyone ever enter into a swap). It's guided by the principle of expected return, not no-arbitrage spreads. The only time no-arbitrage spreads come into play is the initial pricing of the swap contract, which is determined by the value of a floating rate bond (initially worth par), and the fixed rate set to make the stream of payments worth par, otherwise, the long swap position would profit risklessly 6-months from now with a coupon determined completely above par. The fixed rate paid must equal a coupon rate that makes the stream of payments worth par using rates determined by the yield curve today... and that's actualy determined by ZERO rates, NOT implied forwards.

Movements in the rates are free to go where they please, and the swap contract is not worth zero anymore after time progresses and rates shift. What was I thinking? Swap contracts worth an initial NPV zero and not no-arbitrage zero... HA!

That's alot of "X"es on my Problem Set #3 :(

Debt instruments kicks my ass.

Sunday, October 08, 2006

Why should swap contracts ever be set to zero?

It's strange... when two parties enter into a swap contract, the initial agreement is worth zero, and the fixed rate payment recieved by the party long the swap is determined based on implied forward rates that would make the value of the floating contract equal to that of the fixed to create an NPV zero exchange.

However, implied forward rate movements almost always exceed that of the actual future spot rate as a function of the averaging effect of the increase or decrease. Does it make sense that swap contracts should be zero at the initial signing? If so, doesn't that mean that the party that long the swap contract almost always receive a fixed rate that is slightly higher than what should be received (provided that the six-month coupon implied by the forward rate overshoots that of the actual coupon paid in an increasing rate environment, and the long swap receives fixed payments higher than what is deserved) or receive a fixed rate that is slightly lower than what should be received (provided that the six-month coupon implied by the forward rate undershoots the actual coupon paid in an decreasing rate environment).

The floater that is implied in both scenarios derive its value from implied forward derived from zero rates. Unless the yield curve is a straight line, the value of the floater in the swap contract value equation seems almost always over/understated.