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Swap Pricing

To price a swap, we need to determine the present value of cash flows of each leg of the transaction. In an interest rate swap, the fixed leg is fairly straightforward since the cash flows are specified by the coupon rate set at the time of the agreement. Pricing the floating leg is more complex since, by definition, the cash flows change with future changes in the interest rates. The pricing both legs of the swap is examined in detail below.

Fixed Leg of a Swap

Fixed leg of a swp formula

where

Pfix = present value of cash flows for the fixed leg,
N = notional principal amount,
R = fixed coupon rate,
n = number of coupons payable between value date and maturity date,
αi- 1,i = accrual factor between dates i - 1 and i based on the specified accrual method, and
Di = discount factor on cash flow date i.

Floating Leg of a swap

Floating leg of a swap formula

and

where

Pfit = present values of cash flows for floating leg,
N = notional principal amount,
Fi-1, i = (implied) forward rate from date i - 1 to date i,
αi- 1,i = accrual factor from date i - 1 to date i based on the specified accrual method, and
n = number of cash flows from settlement date to the maturity date, and
Di = discount factor on cash flow date i.

Interest Rate Swap

A swap is a contractual agreement to exchange net cash flows for a specified pay leg and receive leg, each of which may be either fixed or floating. The present value of cash flows of the swap is the difference between the values of the two streams of cash flows. In other words,

pay floating, receive fixed

Pswap = Pfix - Pflt,

pay fixed, receive floating

Pswap = Pflt - Pfix.

Swap Risk Statistics

Several risk statistics are calculated for interest rate swaps including modified duration, convexity, and basis point value. These swap risk statistics are based on the risk statistics for the individual legs of the swap, as described below.

For the individual fixed and floating legs of the swap, the modified duration, convexity and basis point value are calculated numerically by bumping the accruing and discounting curves. The rates in the accruing and discounting curves are bumped up by a small amount Δ, and down by Δ. These bumped curves are then used to obtain the bumped up and bumped down fair value PΔ and P, respectively.

Example: Vanilla Fixed for Floating Interest Rate Swap

From a counterparty's perspective, a swap can be viewed as two series of cash flows: outflows are known as the "pay leg" and inflows are known as the "receive leg". Suppose the following situation exists:

Company A Company B
'AA' credit rating 'A' credit rating
can issue fixed debt at 7% can issue fixed debt at 7.65%
can borrow floating at LIBOR + 10 bps can borrow floating at LIBOR + 30 bps
believes rates will be stable or falling, wants floating wants secure funding - fixed debt

The current swap rate is 7.2% vs. LIBOR flat. Both companies will find it advantageous to enter into the swap, as illustrated by the following diagram:

swap pricing diagram

The net funding cost for each company can be represented as follows:

Company A Company B
Pay: 7% fixed Pay: LIBOR + 30bps
Receive: 7.2% fixed Receive: LIBOR floating
Pay: LIBOR floating Pay: 7.2% fixed
Net: LIBOR - 20bps Net: 7.5% fixed

Company A effectively borrows floating at LIBOR - 20bps for a net savings of 30bps compared to funding by way of LIBOR directly.

Company B effectively borrows fixed at 7.5%, a 15bps discount compared to issuing fixed debt at 7.65%.

Related articles:

FINCAD interest rate swap functions can be used for the following:

  • Generic interest rate swaps, allows custom structure (variable notional, variable fixed leg coupon)
  • Cross-currency and basis swaps
  • % LIBOR swaps
  • Non-generic interest rate swaps
  • Fixed legs
  • Floating Rate Notes

To evaluate the FINCAD solutions to value various interest rate swaps, contact a FINCAD Representative.