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# Hull Chapter 7 Swaps

#### Jupiter3

##### New Member
Hello,

I have some question to some exercises of the Hull's book about Derivatives.

1. Let's look at some question like 7.1:
"Companies A and B have been offered the following rates per annum on a \$20 million five-year loan: Fixed Rate Company A Floating Rate 5.0% Company B LIBOR+0.1% 6.4% LIBOR+0.6% Company A requires a floating-rate loan; company B requires a fixed-rate loan. Design a swap that will net a bank, acting as intermediary, 0.1% per annum and that will appear equally attractive to both companies."

There is no unique solution/unique values of cashflows for this problem. We only have to note for an appropriate solution that the earnings for the Financial intermediary (0.1%), for company A (LIBOR-0.3 %) and company B (6.0%) are satisfied. Am I right?

2.
Let's compare question 7.1 with question 7.9. For the solution of question 7.9 why are the arrows of the cashflows vice versa as in question 7.1. i.e. why do the companies earn something from the outside (by bonds) not like in question 7.1 pay something to the outside? In which cases do I have to "make arrows to the outside, in which cases "to the inside"?

Thank you!

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@Jupiter3 Hull 7.1 imagines companies that seek to borrow ("Company A requires a floating-rate loan; company B requires a fixed-rate loan.") but Hull 7.9 images companies that seek to invest ("Company X requires a fixed-rate investment; company Y requires a floating-rate investment."). The arrows represent not the initial inflow/outflow but instead the interest "coupon" payments. So, in 7.1, Company A initially borrows (this is an inflow which is NOT displayed!) and then makes a series of interest rate payments, hence the arrows pointing out. In Hull 7.9, the initial outflow (investments) are not displayed, but instead the received interest "coupon" payments. In short, the principal is not displayed in these, only the interest payments.

Re: the unique solution (this is discussed in our examples more deeply), you are correct that normally there are an infinite number of solutions. In Hull 7.1, the total gain of 0.90% can be shared many ways. But the key given assumption is "that will appear equally attractive to both companies." which tells us to solve for the swap that splits this gain into 0.45% for each company. Given this "constraint," there is only the one solution. I hope that's helpful,

#### Jupiter3

##### New Member
Thank you I understand the first point but I'm not quite sure about the the "unique solution".
For example in question 7.9 the sample solution is
.

But my solution is (changes are marked in red colour)
.
In both solutions the cash flows of company X resp. Y are equal. But it's still another solution.
Is my solution wrong?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Jupiter3 Your solution is not wrong (it's right!). However, notice that it isn't quite "rationalized" (what is the best word .... maybe "simplified"). Imagine you are the Company Y and I am the Bank. In your solution, our agreement is you pay me 8.8% fixed in exchange for receiving LIBOR + 0.3%. It totally works! ... However, we can "streamline" our agreement by "permanently" netting the extra 0.3% which, albeit this is just paperwork, is mathematically redundant. We might as well simplify our numbers to: you pay 8.5% and receive LIBOR. There is no difference really. But I think it's safe to say that these probably usually eliminate such redundancies, or put another way, seek such semi-obvious simplifications (otherwise, there truly are an infinite number of solutions). I hope that helps!