List the four possible ways this swaption could be exercised?

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h21

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Question 9 on exercise of reading 50 asks us to list the four possible ways this swaption could be exercised, and indicate the relevant cash flows in each case.

The answer doesnt make sense to me at all, anyone help me understand why are there 4 different ways?

for example, this is the answer
The annualized fixed payment per $1 of notional principal is 0.0312(360/180) = 0.0624. Based on a notional principal of $50,000,000, the four possible ways to exercise this swaption are:
  1. Exercise the swaption, entering into a receive-fixed, pay-floating swap. The fixed receipt is (based on the exercise rate of 7 percent) $50,000,000(0.07 × 180/360) $1,750,000.
    The first floating payment is (based on the 180-day rate of 4.20 percent in effect at the time the swap is initiated) $50,000,000(0.0420 × 180/360) = $1,050,000.
  2. Exercise the swaption, entering into a receive-fixed, pay-floating swap and entering into a pay-fixed, receive-floating swap at the market rate.
    The fixed receipt is (based on the exercise rate of 7 percent) $1,750,000.
    The fixed payment is (based on the rate of 6.24 percent) $50,000,000 (0.0624 × 180/360) = $1,560,000.
    The first floating payment and receipt of $1,050,000 offset each other
  3. Exercise the swaption with offsetting swap netted.
    The holder would receive a net payment stream of $1,750,000 − $1,560,000 = $190,000.
  4. The holder can choose to receive an up-front cash payment now of $190,000 (0.9794 + 0.9547 + 0.9246 + 0.8832) = $710,961.
I really dont understand the second part, where on earth is this coming from? Why would you want to do a reversed version of the original swap to start with?
 
It’s just one of the ways to capture the gain, which is what the question asked. You enter a reverse swap to cancel out the floating side of the two swaps and isolate the fixed swaps to capture the gain. In this case, at swaption expiration, the fixed rate on the swaption contract is higher than the market rate at expiration, which is a gain to a receiver swaption. Receive a higher fixed rate than you will be paying.
Whether this would happen in reality however depends on the settlement terms of the swaption contract determined at initiation. Cash settlement (option iv.) is the most common.
 
First, you have to remember a swaption is actually an opswap. It is not a swap of options. It is rather an option to enter into a swap. Very important. LOL
Now. The question says to consider a European receiver swaption. Think about it. A European receiver swaption. You buy a European call option to have the right to enter into a swap agreement whereby you will be the receive-fixed side. This means you will be the pay-float side. That immediately demonstrates one way to exercise the option and answers i).
ii) This is an arbitrage setup. Since the interest rates have changed in your favor (decreased) you can enter into your receive fixed at 7%, pay float agreement as in i) but also enter into an opposite swap to receive float pay fixed 6.24% using a current maket swap. You should appreciate the fact that the two floating attributes cancel each other but the fixed attributes do not: So you lock in a profit of 0.76%. This is guaranteed small profit. In i) your profit was bigger but was subject to floating rate fluctuation that could during the next couple of years go against you.
 
iii) and iV) are extensions of ii)
iii) says that in the setup seen in ii) instead of making 4 cash transactions, in which 2 cash flows are exactly the same (floating payments), why not just net them 4 together and pay the difference of 190,000? (Note this is 0.76% of 50,000,000 paid semiannually).
iV) takes it even further in saying that since you are entitled to 4 payments worth 190,000 each, why not pay you the PV of all payments and shred the contracts and do not call me or contact me ever again…?
 
maybe i am confused about the idea of floating rate, but if it is a floating rate, shouldnt each floating rate have different rate? thus not every payment is the same? what did i miss here?
 
There is only one floating rate - today’s rate! Floating rate simply means the rate will change together with the market. You don’t fix anything.
 
krokodilizm wrote:
There is only one floating rate - today’s rate! Floating rate simply means the rate will change together with the market. You don’t fix anything.
Click to expand...
but then how do you know every future cash flow is the same amount
 
h21 wrote:
krokodilizm wrote:
There is only one floating rate - today’s rate! Floating rate simply means the rate will change together with the market. You don’t fix anything.
Click to expand...
but then how do you know every future cash flow is the same amount
Click to expand...
You don’t! Not for the floating side anyways. You only know the first floating cash flow at initiation. But, if you are in two swaps with the same maturity and based on the same rates, one as a floating payer and one as a floating receiver, it doesn’t matter to you how the floating rate may change. Whatever the rate reset to, you will both pay and receive that rate, effectively cancelling the floating payment out. Thus the only difference now is the fixed rate. In the case of a swaption, you can enter the option to engage in a swap at a pre-determined fixed rate. If you are the fixed rate receiver, and if rates have fallen at contract expiration, you can excersise the option to receive a higher rate than the market rate at the time.
Section 6.3 of R50 does a pretty good job illustrating swaption payoffs.
 
h21 wrote:
krokodilizm wrote:There is only one floating rate - today’s rate! Floating rate simply means the rate will change together with the market. You don’t fix anything.
Click to expand...
but then how do you know every future cash flow is the same amount
Click to expand...
The fixed rate on a swap is just that: fixed.
If you exercise a swaption to offset an existing swap, then you’re paying one fixed rate and receiving another fixed rate, one based on the original swap, the other the market rate at the time the swaption is exercised.
 
got it
ah derivatives….notes only scratch a tiny surface
 
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