**Off-market swap**

In this type of swap, a premium is built into the swap price to fund the purchase of options or to allow for the restructuring of a hedge portfolio. Off-market swaps are generally used to restructure or cancel old swap/hedge deals: essentially, they simulate a refinancing pack-age (Source: Risk Publications)

- The swap value reflects the difference between the swap price and the interest rate that would make the swap have zero value

– As soon as market interest rates change after a swap is entered, the swap has value

- An off-market swap is one in which the fixed rate is such that the fixed rate and floating rate sides of the swap do not have equal value

– Thus, the swap has value to one of the counterparties

- If the fixed rate in our at-the-market swap example was 5.75% instead of 5.62%

– The value of the floating rate side would not change

– The value of the fixed rate side would be lower than the floating rate side

– The swap has value to the floating rate payer

**Off-Market Pricing**

The off-market pricing problem arises when, for one reason or another a client of the swap dealer requires a swap coupon that is different from that quoted for par swaps. Most often, a need for off-market pricing arises when the client has an existing commitment that it cannot perfectly offset at the par coupon.

Adjustments to swap pricing to reflect the off-market requirements of a counterparty can be handled in three ways. These are all based on equating present values and they are equivalent in a present value sense. The first method is to determine the present value differential between the at-market swap and the required off-market swap. The counterparty receiving the greater present value would then pay that identical sum to the other counterparty. If the off-market swap has a swap coupon below that for at-market swaps, the payment is called a **buy down.** If the off-market swap has a swap coupon above that for at-market swaps, the payment is called a **buy up.**

Suppose that a counterparty wants to be the fixed-rate payer on a five year swap. At-market pricing requires a swap coupon of 9.52 percent. The client, however, would like a swap with a coupon of only 9.30 percent. The notional principal is $20 million. The differential is 0.22 percent (22 bps) per year or 11 basis points per six month period. Since this same differential will be exchanged each period, we can view it as an annuity. The problem is then to determine the present value of 11 basis points on $20 million (0.0011 * $20 million = $22,000) for ten periods (5 years * 2 periods per year) using a semiannual discount rate of 9.52 percent. The present value annuity formula, given by equation below is used for this purpose. The calculation follows immediately.

PVA = PMT * [ (1 - (1 + y/m)-nm ) / (y/m)] where,

PVA = Present value of the annuity

PMT = Annuity payment (per period)

y = yield or discount rate (annual)

m = Periods per year

n = Number of years (tenor)

PVA = 22000 * (1 – (1 + 0.0952/2) -10 ) / (0.0952/2) = $171,875.65.

We conclude that the off-market swap required by the client has a present value of $ 171,875.65 in favor of the client. Thus, to obtain a lower rate that the current swap coupon for at-market swaps, the client will have to pay the dealer an up-front fee of $ 171,875.65. Because the client is looking for a coupon below the current market rate, this constitutes a **buy down.**

The second method for adjusting the present values is to require a payment upon the termination of the swap. Since we know the present value from the previous calculation, we can easily project the terminal value (TV) using the same rate. This calculation appears below:

TV = PVA * (1 + 0.0952/2)10 = $ 171,875.65 * 1.59204 = $ 273, 633.49.

Terminal value adjustments are rarely, if ever, used to adjust the pricing on off-market swaps.

The final method and one that is often used is to adjust the floating rate side of the swap to maintain the present value equality of the two legs of the swap. In this particular case, we know that the client wants a swap coupon that is 22 basis points less than the at-market swap coupon. This 22 basis point differential is, of course, quoted bond basis. Before adjusting the floating-rate side of the swap, we will need to determine the money market basis equivalent. This adjustment has been is illustrated below.

Floating leg adjustment = (-22 bps) * 360/365 = -12.7 bps.

The swap would then have a swap coupon of 9.30 percent and a floating rate of 6-M LIBOR minus 21.7 bps. The buy down and floating leg off-market adjustments are shown below.

Method 1:

Buy Down

Firm -> 9.30 percent + $ 0.171 million front end --> Swap Dealer --> 6M LIBOR -> Firm

Method 2:

Floating leg

adjustment

Firm -> 9.30 percent --> Swap Dealer --> 6M LIBOR - 21.7 bps -——> Firm

Source: Understanding Swaps by John F. Marshall, Kenneth R. Kapner)