The following issues were discussed with regard to the valuation of options:

1. Likely Benchmarks

2. Information about spot rates and forward rates and its sources.

3. Information about the term structure of volatilities

4. The interest rate model to be used

The benchmarks, which will be used for interest rate options such as caps and floors, will depend on where the activity takes place in the market. As such the following types of benchmarks are available in the Indian context

1. The Government Securities curve, notably the one-year T-bill yield

2. Interest rate curve derived from currency forwards and their corresponding long term swap rates, notably Mumbai Inter-Bank Forward Offer Rate (MIFOR) and Mumbai Inter-Bank Offered Currency Swaps (MIOCS).

3. Overnight rates and the OIS curve.
   Each of these types have different behavioral characteristics and these curves will require their own interest rate models. Information about forward rates can be determined from the corresponding swap rate curve.

The sources of these curves will be as follows:

1. The GOI-Sec curve used will be the FIMMDA-PDAI-Bloomberg yield curve. There are some conceptual difficulties with the implementation of an interest rate model based on this curve. These arise because of jumps in forward rates determined from this curve. These will be addressed subsequently in the section on volatility.

2. The MIFOR and MIOCS curves used will be the FIMMDA-Reuters MIFOR and MIOCS benchmarks.

3. The overnight benchmark used will be the FIMMDA-NSE MIBOR and the FIMMDA-Reuters MIOIS curve will be the benchmark for overnight swap curve.

There are several ways of getting information about the term structure of volatilities.

1. Historical Volatilities

   Historical volatilities of forward rates can be determined from a database of historical forward rate curves. Some kind of a weighing scheme such as the Exponentially Weighted Moving Average method can be used to give greater weight to recent changes in the underlying rate. However, this approach is flawed for three reasons: What drives option valuation is not the volatility that the market has experienced but volatility that the market is expecting in future. In this sense, using historical volatilities is conceptually unsound. Time dependence of the volatility of the forward rate cannot be explicitly modeled using information about historical vols.

   Most of the benchmarks that are used in the Indian Market are "Fitted" curves. Forward rates determined from these tend to jump a lot because of large kinks in the underlying zero coupon curve. Many forward rates are not accessible because a forward market does not exist. Because of this, using these rate to determine volatilities is likely to significantly overestimate the volatilities.

2. Polling of Volatilities

   An alternative to historical volatilities is polling the term structure of volatilities for each of these individual benchmarks. The time-dependence of forward rate volatilities can be explicitly modeled or fitted in this case and this information can be used in the implementation of an interest rate model.

3. Polling prices of standard caps and floors

   FIMMDA would publish the prices to be used by the Banks/PD for the valuation. Moreover it will also publish the volatilities using a suitable model. Banks are free to use the volatilities or the prices as per their requirement.

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 the 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.

If a polling process is followed, FIMMDA will ensure that there are sufficient number of market participants who are quoting the pricing. As in the case of other polling process, the outliers will be discarded at the time of arriving at the average.

Crucial to this approach is the presence of a market. However, in the absence of a market, it should be possible to poll prices of certain standard options and use this information. This only requires that a sufficient number of market participants be present. The advantage of this method is that it can be used even after the market develops fully. Its robustness increases as the market develops and as the polled prices converge with actual traded prices.

Since the Indian market is not likely to involve exotic options at inception, it is suggested that a model similar to the LIBOR Market Model (LMM) suggested by Brace, Gaterek and Musiela (1997) be used, with day-count conventions appropriate to the benchmark for which it is being implemented. The model makes several assumptions which include the presence of a complete forwards market and log-normality in forward rates. While most of these assumptions hold true in developed liquid markets and while market practice in developed markets has been to use the valuation formulae of this model (which are the same as the formulae given by the Black model developed in 1975), it has not yet been tested whether many of these are applicable in the Indian market. In view of the popularity and conceptual soundness of the LMM model, FIMMDA suggested using it for calculation of implied volatilities.

On estimation of volatilities for pricing and valuation, it was seen that OTC interest rate derivatives will be mostly customised products. Thus, pricing of these will require market makers to have sufficient expertise to estimate volatilities to be used for pricing these products. For some standard maturities and standard benchmarks, market makers can quote volatility estimates. Gradually the growth in the volumes will see products becoming standardised. As OTC markets develop, the extent to which market participants engage in large numbers of transactions with similar terms increases, because certain instruments serve the risk-management needs of a large number of market participants. At this stage of development, for valuation or marking to market purpose an independent agency like FIMMDA could publish on a regular basis, the volatility matrix for different maturities for different benchmarks with the different strikes based on the market poll.

The market participants will be free to use any model for marking to market / model of their option portfolio, provided the regulatory guidelines (for market risk management) in respect of management and internal controls of models are adhered to.

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