Interest rate swap

Two parties owe interest on the same amount of money, one at a rate that is fixed and one at a rate that floats. They agree to pay each other's interest for a while. Nobody lends anybody anything; the principal is a reference figure and stays where it is.

That is an interest rate swap. Party A pays floating and receives fixed; Party B pays fixed and receives floating. On each payment date the two amounts are computed and only the net is paid.

A swap is, in effect, a strip of forward rate agreements — a series of forwards packaged as one contract, which is why the workbook groups swaps with forwards, futures and options as one of the four generic derivative products.

In India the Overnight Index Swap, written on Overnight MIBOR, is the successful one: the workbook describes the OTC interest rate swap market as having good volumes in OIS, in contrast to the exchange-traded contracts that took three attempts to establish.

The floating leg is the awkward one. In an OIS against Overnight MIBOR there is a new rate every business day, and the leg is accumulated with daily compounding over the swap period, weekends and holidays carrying the preceding day's rate for the number of calendar days involved.

The fixed leg is arithmetic: notional × fixed rate × days ÷ 365.

The net is settled, and it is a zero sum: whatever one party gains the other loses, exactly.

The workbook gives three reasons a swap is entered at all. It converts an exposure — a borrower paying floating who fears rising rates can pay fixed instead. It gains access to a rate otherwise unavailable, since the workbook lists "access to unavailable assets or markets" as an economic function and notes that a company may obtain a more favourable interest rate through a swap than by borrowing directly. And it expresses a view, because a swap is the cleanest way to be long or short a rate without touching a bond.

A bond swap is not a swap at all, and the workbook is careful about it: selling one bond and simultaneously buying another with the proceeds is two cash-market transactions, not a derivative contract.

Fixed leg    = Notional × Fixed rate × Days ÷ 365

Floating leg = Notional × [ Π (1 + rₜ × dₜ/365) − 1 ]     (daily compounded OIS)

Net settlement = Fixed leg − Floating leg, paid by whichever side is in deficit

The notional principal is never exchanged.

The workbook's one-month OIS. Notional Rs 100 crore, tenor one month, 32 days.

• A pays Overnight MIBOR, receives fixed 3.75%
• B pays fixed 3.75%, receives Overnight MIBOR

Overnight MIBOR fixes daily over the period — 3.70%, 3.73%, 3.70%, 3.65%, 3.69% and so on, drifting down to 3.45% by the fourth week — and the floating leg is accumulated with daily compounding:

Floating leg (A pays)     = Rs 0.315817 crore = Rs 31,58,169
Fixed leg (A receives)    = Rs 100 crore × 3.75% × 32/365
                          = Rs 32,87,671

Net pay-off to A          = Rs 1,29,503
Net pay-off to B          = (Rs 1,29,503)

Rs 100 crore of notional principal produced a settlement of Rs 1.29 lakh — thirteen basis points of the notional, over a month. That ratio is the point: the notional measures the exposure, not the cash flow.

A received fixed and MIBOR averaged below 3.75%, so A won. Had the RBI tightened mid-month and pushed the overnight rate to 4.20%, the floating leg would have come to roughly Rs 36.8 lakh and A would have paid about Rs 3.9 lakh instead.

Converting a borrowing. An NBFC has borrowed Rs 200 crore at Overnight MIBOR plus 120 bp and wants certainty for the next year. It enters a 1-year OIS paying fixed at 6.40% and receiving MIBOR:

Pays on the loan       : MIBOR + 1.20%
Pays on the swap       : 6.40%
Receives on the swap   : MIBOR
                         ─────────────
Effective cost         : 7.60% fixed

The MIBOR legs cancel. On Rs 200 crore that is Rs 15.2 crore a year, fixed, whatever the RBI does — and the loan itself was never renegotiated.

Chapter 2, section 2.2.4 (Swaps), defines the interest rate swap, works the Rs 100 crore Overnight MIBOR example in full with its daily fixings, and introduces the swaption. Section 2.5's summary table contrasts the interest rate swap with a bond swap, which is two cash transactions rather than a derivative. Section 2.1.1 lists access to otherwise unavailable rates among the economic functions of derivatives, and Chapter 3 notes that OTC interest rate swaps, particularly OIS, have been the successful segment in India.

Questions ask which generic derivative a described contract is, what is actually exchanged in a swap, and — computationally — the net settlement given a fixed rate, a notional and a period.

• The notional principal never moves. Only the net interest difference is settled; a Rs 100 crore swap settles in lakhs.
• Net the legs, do not pay both. Each party computes its own leg and one payment is made for the difference.
• A swap is not a loan. No money is advanced, no credit is extended on the principal, and there is no repayment at maturity.
• A bond swap is not an interest rate swap. Selling one bond to buy another is two underlying transactions, and the workbook says so explicitly.
• The OIS floating leg compounds daily. Averaging the daily MIBOR fixings and applying it once gives a different, wrong answer.
• Fixed-to-floating and floating-to-floating are both interest rate swaps. Fixed-to-fixed would exchange two known amounts and accomplish nothing.