Swaps

In this lesson, we learned about swaps

Swaps - contracts that transform one kind of cash flow into another.
      plain vanilla swap - fixed interest rate vs. floating interest rate
      commodity swaps - exchange floating price for a fixed price
      currency swaps - exchange floating currency rate for fixed currency rate



We then went through an example:

Company A can borrow at a fixed rate of 4% or a floating rate of LIBOR + 0.3%
Company B can borrow at a fixed rate of 5.2% or a floating rate of LIBOR + 1.0%
(LIBOR = London Interbank Interest Rate = base rate for floating interest rates)

In this case company A has the better deal in both the fixed rate and the floating rate.  But if both of the companies work together, they can be better off.

Company A borrows the fixed rate at 4%.
Company B borrows the floating rate at LIBOR + 1.0%

The companies then create the swap in which company A pays company B LIBOR rate and company B pays company A 3.95%.

In this case company A has outflows of 4% and LIBOR and inflows of 3.95% for a net rate of LIBOR + 0.05% (which is better than the floating rate they had originally).

In this case company B has outflows of LIBOR + 1.0% and 3.95% and inflows of LIBOR for a net rate of 4.95% (which is better than the fixed rate they had originally).

In actually, company A and company B would not engage directly in a swap.  Instead they would go through a financial intermediary in order to protect themselves from the risk of the other company defaulting.



The example with a financial intermediary:

Same conditions:
Company A can borrow at a fixed rate of 4% or a floating rate of LIBOR + 0.3%
Company B can borrow at a fixed rate of 5.2% or a floating rate of LIBOR + 1.0%

In this case:

Company A borrows the fixed rate at 4%.
Company B borrows the floating rate at LIBOR + 1.0%

Company A creates a swap with the financial intermediary- paying LIBOR and receiving 3.93% in return.
Company A creates a swap with the financial intermediary- paying 3.97% and receiving LIBOR in return.

The 0.04% difference (4 basis points) between 3.97% and 3.93% is the profit for the financial intermediary for providing this service AND taking on the risk of default from both companies (since the financial intermediary will be required to uphold a swap even if one company defaults).



We then priced an interest rate swap:

Let r(t) be the floating interest rate at time t.  This is unknown until period t.

The cash flows at time t=1...T are:
    Company A: receives Nr(t-1) and pays NX
    Company B: receives NX and pays Nr(t-1)
where N is the principal amount and r(t-1) is the rate in the previous period.

The value of the swap to company A is = (cash flow of floating rate bond) - (face value)
but we need to discount both these back to present value terms, so the value is:

We then set X so that V(A) = 0:

The value of the swap at time t=0 is set such that the company is indifferent to the fixed rate and the floating rate contracts.