A swaption can be regarded as an option to exchange a fixed rate bond for the principal amount of the swap. If the swaption gives the holder the right to pay fixed and receive floating, it is a put option on a fixed rate bond with a strike price equal to the principal. If the right is to receive fixed and pay floating, it is a call option on a similar bond. This is what the course notes say. But the expressions that follow seem to be the other way round. it says later Thus, if the swaption gives the holder the right to receive a fixed rate RX – ie the payments are the opposite way around to previously – the value of the swaption is and the expression that follows looks like a put payoff! Pls help!
Yes, this sounded contradictory to me as well. In addition, I could not understand put-call parity of interest rate cap and floor price: cap price = floor price + value of swap. how does the value of swap make this parity? Can someone elaborate.
Hi r_v.s The paragraph of rationale you mention is on page 15 of Chapter 12 of the Course Notes and the expressions you refer to are on page 17. Note that on page 16, there is a line of ActEd text which says we don’t use this particular option related argument to value the swaptions! Instead, we use the concept of swap rates. Remember that the swap rate is the fixed interest rate that would be exchanged for LIBOR in a new swap – it would be the fixed interest rate that makes the value of the swap equal to zero. Imagine a swaption that gives us the right to pay fixed and receive floating – this is equivalent to having a put option on a fixed rate bond with strike equal to the principal (100). So, when we take out the swaption, the swap rate would be set so that the value of the fixed interest payments would be equal to the value of the floating rate payments. Let’s say this swap rate is Rx. Let’s also say that after we take out the swaption, floating rates fall. Intuitively this is bad news – we have an option to make fixed payments and receive floating, but the floating payments are lower than we originally expected. So we won’t exercise. Thinking about this in terms of a put option on a bond – we had the right to sell a bond and receive the principal (100) – but the discounted value of those fixed coupon payments and final redemption payments has now risen and is worth more than 100 (because the variable rates have fallen) – so we won’t want to sell the bond now if we are only going to get 100. So we won’t exercise. Finally, thinking about this in terms of swap rates: When we get to the exercise date of the swaption, if we were to recalculate the swap rate based on the new lower floating rates, the swap rate would be lower. Let’s say this swap rate is R. So under the swap we would pay away Rx, but the ‘fair rate’ to pay now would be lower - only R. So we won’t exercise. More formally, the payoffs from a swaption are: L/m max(R-Rx, 0) This is the expression we see at the top of page 17. The text notes that this is a call option on R, with a strike price of Rx and we can go on to value it appropriately. Does that help? Gresham
One way of thinking about this is to imagine a situation where we bought caplets and sold floorlets, each with a strike of 5%. So if interest rates were above 5% we would exercise the caplets and receive a payoff. If interest rates fell below 5% someone else would exercise the floorlets and we would need to pay out money. Essentially the cashflows would be the same as if we had taken out a swap where we receive floating and pay fixed 5% Does that help? Gresham
