We have seen that an interest rate swap is a contractual agreement entered into between two counterparties under which each agrees to make periodic payment to the other for an agreed period of time based upon a notional amount of principal. The principal amount is notional because there is no need to exchange actual amounts of principal in a single currency transaction: there is no foreign exchange component to be taken account of. Equally, however, a notional amount of principal is required in order to compute the actual cash amounts that will be periodically exchanged.

We have seen the prodct. But what fixing the price, that is rational and acceptable to the seller and buyer?

On the face of it, this may appear to a complex task for the layman, as it will be difficult to foresee future trends in interest volatalities and calculate a premium on rational basis. Over past experience people in the trade have learned to encapsulate the complexities and seek the guidance of a specific reference-rates like MIBOR, MIFOR to be used as tools to rationally assess the future trends and arrive at a reasonable acceptable premium rate. The Jaspal Bindra Committee appointed by RBI has given considerable attention to this question. Before we consider their recommendations, it will be useful to consider the standard internatinal practice in this respect, as quoted hereundedr from the website of Green Interest Rate Swap Management.

"If we consider the generic fixed-to-floating interest rate swap, the most obvious difficulty to be overcome in pricing such a swap would seem to be the fact that the future stream of floating rate payments to be made by one counterparty is unknown at the time the swap is being priced. This must be literally true: no one can know with absolute certainty what the 6 month US dollar Libor rate will be in 12 months time or 18 months time. However, if the capital markets do not possess an infallible crystal ball in which the precise trend of future interest rates can be observed, the markets do possess a considerable body of information about the relationship between interest rates and future periods of time.

"In many countries, for example, there is a deep and liquid market in interest bearing securities issued by the government. These securities pay interest on a periodic basis, they are issued with a wide range of maturities, principal is repaid only at maturity and at any given point in time the market values these securities to yield whatever rate of interest is necessary to make the securities trade at their par value.

"It is possible, therefore, to plot a graph of the yields of such securities having regard to their varying maturities. This graph is known generally as a yield curve -- i.e.: the relationship between future interest rates and time -- and a graph showing the yield of securities displaying the same characteristics as government securities is known as the par coupon yield curve. The classic example of a par coupon yield curve is the US Treasury yield curve. A different kind of security to a government security or similar interest bearing note is the zero-coupon bond. The zero-coupon bond does not pay interest at periodic intervals. Instead it is issued at a discount from its par or face value but is redeemed at par, the accumulated discount which is then repaid representing compounded or "rolled-up" interest. A graph of the internal rate of return (IRR) of zero-coupon bonds over a range of maturities is known as the zero-coupon yield curve.

"Finally, at any time the market is prepared to quote an investor forward interest rates. If, for example, an investor wishes to place a sum of money on deposit for six months and then reinvest that deposit once it has matured for a further six months, then the market will quote today a rate at which the investor can re-invest his deposit in six months time. This is not an exercise in "crystal ball gazing" by the market. On the contrary, the six month forward deposit rate is a mathematically derived rate which reflects an arbitrage relationship between current (or spot) interest rates and forward interest rates. In other words, the six month forward interest rate will always be the precise rate of interest which eliminates any arbitrage profit. The forward interest rate will leave the investor indifferent as to whether he invests for six months and then re-invests for a further six months at the six month forward interest rate or whether he invests for a twelve month period at today's twelve month deposit rate.

"The graphical relationship of forward interest rates is known as the forward yield curve. One must conclude, therefore, that even if -- literally -- future interest rates cannot be known in advance, the market does possess a great deal of information concerning the yield generated by existing instruments over future periods of time and it does have the ability to calculate forward interest rates which will always be at such a level as to eliminate any arbitrage profit with spot interest rates. Future floating rates of interest can be calculated, therefore, using the forward yield curve but this in itself is not sufficient to let us calculate the fixed rate payments due under the swap. A further piece of the puzzle is missing and this relates to the fact that the net present value of the aggregate set of cashflows due under any swap is -- at inception -- zero. The truth of this statement will become clear if we reflect on the fact that the net present value of any fixed rate or floating rate loan must be zero when that loan is granted, provided, of course, that the loan has been priced according to prevailing market terms. This must be true, since otherwise it would be possible to make money simply by borrowing money, a nonsensical result However, we have already seen that a fixed to floating interest rate swap is no more than the combination of a fixed rate loan and a floating rate loan without the initial borrowing and subsequent repayment of a principal amount. The net present value of both the fixed rate stream of payments and the floating rate stream of payments in a fixed to floating interest rate swap is zero, therefore, and the net present value of the complete swap must be zero, since it involves the exchange of one zero net present value stream of payments for a second net present value stream of payments.

"The pricing picture is now complete. Since the floating rate payments due under the swap can be calculated as explained above, the fixed rate payments will be of such an amount that when they are deducted from the floating rate payments and the net cash flow for each period is discounted at the appropriate rate given by the zero coupon yield curve, the net present value of the swap will be zero. It might also be noted that the actual fixed rate produced by the above calculation represents the par coupon rate payable for that maturity if the stream of fixed rate payments due under the swap are viewed as being a hypothetical fixed rate security. This could be proved by using standard fixed rate bond valuation techniques".
[Source - Website of "Green Interest Rate Swap Management]

The Group in its report states:-

After prolonged deliberations and assessing the present state of underlying debt market and OTC derivative market, the Group narrowed down its focus on four contracts viz., a) Short-term MIBOR Futures Contracts, b) MIFOR Futures Contract, c) Bond Futures Contract and d) Long-term Bond Index Futures Contract.

The derivative contracts short-listed by the Group for trading on the stock exchanges at the initial stage are described briefly as under :

1. Short-term MIBOR Futures Contract

   This would be a futures contract based on the FIMMDA-NSE Overnight Daily MIBOR. There would be 12 variants of this futures contract depending on contract tenor, viz., a 1-month contract, a 2-month contract, and so on up to a 12-month contract. Contract price would be quoted on a 100 minus MIBOR basis. A contract would expire on the last business day of the expiration month. Daily settlement will take place at the closing price of the Futures contract where closing price would be the last 30 minutes' weighted average prices of the deals reported on the system. If it is not traded during last half an hour, then the last traded price should be considered as closing price. The final settlement will take place in cash on the expiration day based on the simple average MIBOR fixations for the tenor of the contract. The fixation for the day prior to a holiday would be considered as the MIBOR fixation for the holiday for a contract.

2. MIFOR Futures Contract

   This would be futures contract based on the 6-month LIBOR and Rupee-Dollar 6-month forward rate provided by FEDAI for the expiration date. These contracts would be quarterly contracts and will follow the March-June-September-December expiration cycle. Contract price would be quoted on a 100 minus MIFOR basis. A contract would expire on the last business day of the expiration month. Daily settlement will take place at the closing price of the Futures contract where closing price would be the last 30 minutes' weighted average prices of the deals reported on the system. If it is not traded during last half an hour, then the last traded price should be considered as closing price. The final settlement will take place in cash on the contract expiration day based on the MIFOR computed for the day by the stock exchange after the close of market hours taking into account the relevant LIBOR rate as well as the Rupee-US$ Forward premia computed by FEDAI (currently 6-month).

3. Bond Futures Contract

   This would be a futures contract based on specific underlying Central Government bonds. There would be four variants of this futures contract depending on contract tenor, viz., a 3-month contract, a 6-month contract, a 9-month contract, and a 12-month contract. The specific bond(s) will be as identified by the stock exchange from time to time based on broad parameters like liquidity, outstanding issue size, etc. These futures would be valued on quoted clean price. On expiration day, the final cash settlement would be on the basis of closing price of the day.

4. Long-term Bond Index Futures Contract

   This futures contract would be based on an index derived from liquid securities in the long term maturity bucket, such as 8-12 years. The market capitalisation for the purpose of this index will be based on actual weighted average trade prices. There would be four variants of this futures contract depending on contract tenor, viz., a 3-month contract, a 6-month contract, a 9-month contract and a 12-month contract. The price quote shall be clean composite price. Daily settlement would be done at the closing price of the day

The valuation of interest rate options is a complex issue which has been the subject of intense academic debate. Because option valuation requires future interest rates as well as volatilities, it becomes important to model the evolution of interest rates going forward. Several models are available for pricing and valuing interest rate options. Illustratively:

• Closed Form Model: Black's Model

• Single Factor Models: Vasicek and Cox, Ingersoll and Ross Model

• Multi-Factor Models: Heath Jarrow and Merton, Longstaff and Schwartz

• Markov Models: Ho and Lee, Hull and White

Black's model is the most widely used model for pricing simple interest rate options whereas Heath, Jarrow and Morton model is employed for pricing complex options. The Group recommends that derivative dealers can choose the pricing and valuation model for interest rate options according to their opinion on the suitability of the models keeping in view certain parameters illustrated in Annex V.6. (of the report).

The most commonly followed approach in the international context for the implementation of interest rate models for option pricing is to use traded prices of caps and floors in the market to calibrate the model. This eliminates the need to get explicit volatilities because the implied volatilities in traded options give information about the term structure of volatility, as long as there exist sufficiently traded options across the spectrum for which the model has to be implemented. This model can then be used for the valuation of other options. In view of this, the Group recommends that FIMMDA should publish the prices to be used by banks/PDs/FIs for valuation after polling sufficient number of market participants who are quoting the prices. Moreover, it should also publish the volatilities using a suitable model. Banks are free to use the volatilities or the prices as per their requirement. The broad policies regarding calibration of model parameters and other features like stress-testing and back-testing should follow the internationally accepted best practices as laid down by BIS.

Annx.V.6. of the Report referred above is reproduced in the next article

MIBOR - Mumbai Inter Bank Offer Rate
MIFOR - Mumbai Inter-Bank Forward Offered Rate
MIOCS - Mumbai Inter-Bank Offered Currency Swaps
MIOIS - Mumbai Inter-Bank Overnight Index Swaps
FEDAI - Foreign Exchange Dealers Association of India
FIMMDA - Fixed Income Money Market & Derivatives Association of India