FIXED DERIVATIVE MARKET IN INDIA

Fixed income derivatives for India
By Vijayan Subramani and Ananth Narayan G.
Introduction

Over the years, there have been significant reforms in the realm of interest rates in
India. Structural rigidities such as administered rates, mandated floors and caps on
deposit and lending rates, guaranteed high yields on government owned funds &
tax-free bonds are now increasingly things of the past. Additionally, the market for
Interest Rate Derivatives (IRD) in Indian Rupee has grown rapidly since it began in
June 1999, giving CFOs and Treasurers much more flexibility in managing their
interest rate exposures.

Flexible market determined interest rates and the tools to implement interest rate
views bring about new challenges to the Indian CFO. In the past, she would largely
be concerned with managing the liquidity risk of funding her company's operations.
Committed funding came in linked to practically static benchmarks such as bank
Prime Lending Rate (PLR). The ability of the CFO to reduce interest costs by
anticipating market movements or by astute funding and gapping was limited.

Today, besides managing the liquidity risk of funding the balance sheet, the Indian
CFO is increasingly accountable for actively managing the cost of such funding.
For this, she firstly has to clearly identify and monitor the holistic rate exposures
of her balance sheet, a process that requires robust metrics and systems. To
understand the opportunities at her disposal and to take cogent directional views, she
needs to be completely abreast of domestic and international fixed income, foreign
exchange and interest rate markets. She then has to choose an overall interest rate
strategy striking a balance between the risks she takes in relation to the actual benefits
she hopes to achieve. To support her operations, and to instill confidence amongst
stakeholders in her organization, she requires robust control, accounting and risk
management systems to be in place.

IRD in India has seen prolific growth over the past three years, both in terms of
volumes as well as the breadth of products. To an extent, this growth has almost
gone unnoticed: unlike the case of equity derivatives, where the growth has been
reasonably well tracked and documented. Even now, one hears of Finance Managers
and academicians lamenting the lack of depth in the IRD market, a comment that
would have been justified in 1999, but would be less than accurate today.

This paper first describes the various IRD products now available in India, from plain
vanilla inter-bank traded products, to some popular exotic structures. We will also
try and address frequently asked questions about this market: features of the Indian
market that puzzle domestic as well as foreign observers.
This paper is unapologetic about using basic mathematical expressions and formulae
wherever relevant. The author firmly believes that dealing any kind of derivatives is
not for the mathematically faint hearted. As a Finance Manager, unless one can price
and understand the hedging dynamics of derivatives, one could end up as easy prey for
zealous (and sadly, sometimes devious) traders.
Interest Rate Derivative Products in India

Interest rate swaps (IRS) and Forward rate agreements (FRA) in the rupee made
their entry in July 1999, following guidelines issued by the RBI (RBI circular MPD.BC.
187/07.01.279/1999-2000 dated July 7, 1999). The RBI does not as yet allow any
volatility (option) products on the rupee IRD side: thus caps/ floors/ barriers etc
cannot be structured on to any IRD. As readers would be aware, IRS and FRA are
derivatives that permit players to move between fixed interest rates and floating rates
linked to standard benchmarks.

In a typical example, a company issuing fixed rate long tenor bonds, but expecting
medium term softness of interest rates would receive a fixed rate against a floating
benchmark set at an appropriate frequency (say six months). The swap along with
the underlying bonds would effectively convert their fixed rate borrowing into floating
rate borrowings where the rates are reset every six months.

The RBI permits corporate customers to hedge interest rate risks on both the asset
and liability side, using rupee IRD. Customers need to identify and earmark genuine
exposures against each IRD, ensuring that the tenor and the notional of the hedge does
exceed that of the underlying. Banks dealing with customers must also satisfy
that the customer has genuine underlying exposures. Rupee IRD undertaken by customers
can be freely cancelled and rebooked.
In the Indian case, over the years, three basic benchmarks have dominated the
inter-bank market for swaps: those based on the overnight call rate benchmark
(Mumbai Inter-bank Offer Rate or MIBOR published by the NSE), those based on
the rupee rates implied in the US$/ INR foreign exchange (FX) market (Mumbai
Inter-bank Forward Offer Rate or MIFOR & Mumbai Inter-bank Tom Offer Rate or
MITOR) and those based on the Government of India (GOI) bond market. Other
benchmarks such as the 3-month commercial paper (CP) rate have also been used
in a few swaps, but no inter-bank market exists for such instruments.

Table 1 provides an overview of the IRS inter-bank market under these benchmarks. It provides estimated volumes, describes settlement conventions, the standard tenors
for which quotes are generally available, standard lot sizes and bid & ask spreads.
It also summarizes some of the other structured swaps that are popular in the market,
typically between authorized dealers and their customers.

When the RBI opened the IRD markets, it gave the participants freedom to choose
any floating rate benchmark from the rupee money and debt markets. Out of sheer lack
of any other credible money market benchmark, the overnight inter-bank call rate
was a natural first choice.

Thus the first rupee IRD was in the MIBOR Overnight Indexed Swap (OIS). In this swap, the floating rate is the daily compounded call rate (accrued over holidays). For short tenor swaps (up to 1-year), settlements occur on the maturity of the swap. In case of longer tenor swaps, settlements generally occur every six months. The net settlement would be computed by the following equation:



Here, N is the notional of the swap, mi is the MIBOR setting on the ith day, a is the
number of days for which mi is accrued, t is the tenor of the swap in days, and R is the fixed rate of the swap.
A few points about this product that would be relevant to mention at this stage:
(a) On October 18, 2002, the market for 1-year OIS closed at 5.80/5.85 (bid/ask). A customer looking to receive fixed against overnight MIBOR could therefore receive 5.80%. It is important to note that on account of the sleight of
compounding inherent in this product, the bet in this case is NOT that the average
MIBOR over the life of the swap would be at or lower than 5.80%. In fact, it can
be shown using equation 1 above that the bet is actually that the average call
would be at or lower than 5.64%. In this case, the daily compounding effect has
knocked off 16 basis points (bps) from the fixed rate to arrive at the average
expected MIBOR inherent in the price.

(b) The same sleight of compounding can also provide a very misleading picture
about the slope of the OIS yield curve. If on the same day, the 6-month OIS
closed at 5.75/5.80, seen against the 1-year quote of 5.80/5.85, the OIS
yield curve appears to be slightly upward sloping. In fact, the average
6-month MIBOR implied by a 6-month OIS rate of 5.75%
(again using equation 1) is actually 5.65%, slightly above the 5.64% implied
by the 1-year market. This implies that the market is fact imputing in a
lower average MIBOR rate in the latter half of the year, the hallmark of a
downward sloping yield curve.

(c) In the case of MIBOR OIS beyond 1-year tenor, since the swap is settled
every six months, the fixed rates are quoted on a semi-annual basis.
Periodic settlements help to reduce the credit exposure inherent in these
swaps.

(d) In the OECD world, the OIS for 1-year would typically quote at a rate lower
than the actual money market rate for the same tenor. In the US$ case, e.g.,
the US$ 1-year OIS (against overnight fed funds rate) would be lower than
the 1-year US$ LIBOR. Part of the reason for this basis spread lies on
the credit risk inherent in the cash US$ LIBOR curve. Being an actual
inter-bank cash market rate, the US$ LIBOR rate would include the credit
risk spread inherent in the exchange of the principal amount. The OIS on the
other hand, does not involve any exchange of the principal amount. In an
IRS, the principal is merely a notional amount used in the computation of
the fixed and floating cashflows that does not have to be exchanged upfront.

(e) OIS as a class of products are not very popular overseas: e.g., the volumes
in the US$ OIS would typically be a small fraction of volume of swaps using
3-month US$ LIBOR as the floating benchmark. In the case of the Indian
market, the popularity of the MIBOR OIS can be largely attributed to the
absence of a term money market, and therefore the absence of reliable term
money benchmarks. In the next section, however, we shall try and demonstrate
that the much maligned and misunderstood MIFOR benchmark performs remarkably
well as a surrogate term money benchmark.

(f) A frequently asked question relates to cancellation of existing contracts,
and the computation of the net settlement in such cases. This has been
addressed separately in the risk section, as a natural offshoot of the
building of the zero- curve for this product.

The MITOR/ MIFOR swap market
When RBI first allowed INR swaps and FRA, the participants were given the freedom to choose any mutually acceptable benchmark from the INR debt and money markets. As
discussed earlier, there still is no rupee term money market to speak of in India, and therefore benchmarks linked to the money markets were necessarily linked to the
overnight call rate. However, banks, institutions and corporate entities have for some time now accessed a surrogate inter-bank term money market for INR, using the US$/ INR forwards market.

The US$/ INR forwards market is fairly liquid up to the 1-year segment, with estimated daily volumes ranging between US$ 1.5 to 2.5 Billion. It is usually assumed that the bulk of these volumes would be on account of foreign exchange hedging activities: say by exporters and importers crystallizing their future foreign currency cashflows. In fact, a large proportion of the volumes are actually from money market players looking to either raise or deploy their rupee liabilities using this route.

Foreign banks with a large NRI deposit base frequently use the US$ /INR swap market to switch their FCNR(B) based US$ funds into INR, to fund their rupee assets. INR surplus banks unable to raise adequate INR assets of acceptable credit quality, swap their INR funds into US$ using the forwards market and invest the US$ locally or overseas.
Clearly, seen holistically, the INR surplus banks have simply lent the INR funds in a surrogate INR term money market, using the US$/INR swap market as a via media.

There was a time when the RBI frowned upon this use of the US$/INR swap market as a surrogate INR term money market. In January 1998, for instance, when the RBI had to
intervene to protect a rapidly depreciating rupee, they actually spoke of clamping down on 'arbitrage' between the FX and money markets: presumably commenting on the
already prevalent practice of banks deploying INR in the FX markets, and thereby
reducing the forward premium to be paid by importers of US$. Arguably, by denying interest rate parity, the RBI was at that time trying to keep a lid on actual domestic interest rates, while at the same time protecting the rupee from excessive depreciation by keeping the US$/INR forward premia high. The high premia would in turn deter buyers of US$, provide an incentive to sellers of US$ and keep the cost of banks and corporate entities holding speculative long US$/ short INR positions high.

When the first RBI IRS/ FRA circular was issued in June 1999, there was actually a
report of two banks concluding a deal between themselves using a 'money market'
benchmark that was the derived from the US$/INR swap market. The RBI was at that
time quick to disallow this benchmark, thereby clarifying that it did not consider the FX and money markets to be completely integrated. However, in the credit policy statement of April 27, 2000, the RBI Governor indicated that " with a view to providing more flexibility for pricing of rupee interest rate derivatives and to facilitate some integration between the money and foreign exchange markets, the use of interest rates implied in the foreign exchange forward market as a benchmark would be permitted in addition to the existing domestic money and debt rates".

This was the genesis of the Reuters (term) MIFOR and (overnight) MITOR benchmarks, and the market for swaps based on them. The computation of this rate draws on the
classical interest rate parity formula:


Here F is the forward rate of 1 US$ in INR terms, S is the current spot US$/ INR rate, r is the implied rupee interest rate, d is the US$ LIBOR rate for the tenor and t is the relevant time period.

With our foreign currency reserves swelling since then, and further liberalization by the RBI on borrowing and lending of foreign currency by authorized dealers, the integration between the money and FX markets is far more comprehensive today. This leads us to believe that in the absence of true term MIBOR benchmarks (though MIOIS swaps labeled in table 1 stake a claim), the long tenor MIFOR benchmarks act as an adequate surrogate. Entities looking for a rupee equivalent of the 3-month US$ LIBOR
benchmark would do little wrong in selecting the 3-month MIFOR as the closest answer.

Since a MIBOR OIS market already existed, the participants quickly found a counterpart for this product with an FX based benchmark: the MITOR based INR OIS. The product closely mirrors the MIBOR OIS market, with the same net settlement formula (equation 1), with the exception that mi would now be the daily MITOR setting as opposed to the MIBOR setting. Note that there is a MIBOR setting on Saturdays, with the rupee call money market operating on that day. With the FX markets being closed however, no MITOR setting occurs on Saturdays.

The standard MIFOR swap is for 2,3,5,7 and 10-year tenors, with the 6-month MIFOR as the benchmark, settled semi-annually on an act/ 365 basis.
A few points about the MITOR/ MIFOR swaps:
(a) The benchmarks are what we like to call reverse interest rate parity
benchmarks. In the G7 world, the underlying term money markets would be
deep, and the FX forward rate would simply flow out of the term money rates,
under the interest rate parity theorem. In the Indian case, however, the FX
market is far more liquid than the INR term money market is. In a sense,
currently, the FX forward and the US$ LIBOR rate determine where the
appropriate INR term money rate stands at.

(b) Note the basis difference between US$ LIBOR (act/360) and INR (act/365),
which introduces a critical factor in the MIFOR/ MITOR computation.

(c) The MIFOR swap rate would also indicate where cross currency swaps involving
INR should quote. If the current 5-year MIFOR rate is 6.70/6.80, then it
would be reasonable to expect that a corporate looking to swap from INR to
US$ or US$ to INR against flat US$ LIBOR (floating) would expect to see a
price of 6.70/6.80. A word of caution though. Even in the US$/ JPY markets,
there is a basis swap between US$ LIBOR and JPY LIBOR. This means that flat
US$ LIBOR can be swapped not into flat JPY LIBOR, but into a spread over JPY
LIBOR. This is a function of the demand/ supply mismatch in the underlying
currency swap markets, and the fact that cross currency swaps usually
involve exchange of principals, and therefore impact liquidity. A similar
phenomenon was observed in the Indian markets, say in end May 2002. The 5-
year MIFOR was then quoting at 8.80/9.00, whereas US$/INR currency swaps for
the same tenor were quoting at 8.90/9.10 against floating US$ LIBOR for the
same tenor.
(d) A frequently asked question is, what is the basis on which dealers quote
term
MIFOR swap rates?
The easiest (and correct) answer is that there is a reasonably
liquid inter-bank market that deals on a two-way price. Through price discovery
and supply & demand, this market rate has been determined, and is the best hedge for a quoted price. However, the following events contribute to movements in the
MIFOR rates:

- Movement in US$ swap rates. A large number of Indian entities have in
the past raised US$ (and other foreign currency liabilities) through the
external commercial borrowing (ECB) route. Some of them sold these
funds outright in the spot FX market, and have yet to completely hedge
the US$ interest and principal payable in the future. If US$ swap rates
were to harden, with little or no change in the MIFOR swap rates, the
implied cost of purchasing their forward US$ would reduce considerably.
In other words, the POS rate (see table 1) would reduce considerablyEntities taking advantage of this would bring paying pressure into the
MIFOR market, through the US$/ INR currency swap or outright forward route.

- On the converse side, current regulations also permit domestic entities to
swap their INR liabilities into US$ liabilities. Exporters with expected
future streams of foreign currency flows watch the spread between long
tenor US$ swap rates and the MIFOR rates. If the spread was to widen on
account of a dip in US$ swap rates, the POS rate could imply a
depreciation of the rupee to an extent greater than that expected by the
exporter. This would ultimately lead to receiving pressure on the MIFOR
rate through the long tenor currency swap/ outright forward premia route.
- As an interesting offshoot of the discussions above, several astute
corporate entities have in the past managed to raise US$ funds at
extremely competitive rates through a combination of rupee borrowing
and an INR to US$ currency swap. Even today, if a company can raise 5-
year rupee funds at 7.00% (semi) through a bond issuance, it can choose
to swap it into US$ (through a currency swap) to approximately US$
LIBOR + 25 bps. If the same corporate had dealt in June 2002, using the
same route, it would have raised US$ funds at US$ LIBOR - 30 bps. This
is clearly a far more competitive rate than most local corporate bodies can
command if they were to raise funds through the ECB route. In addition,
ECB also has added hidden costs on account of withholding tax.
Therefore, corporate spread is a factor that determines where the MIFOR
swaps deal.

- Finally, like corporate spreads, the swap market also measures itself as a
spread over the underlying sovereign curve, in our case, the GOI Bond
market. It can be argued that this swap spread has a measure of the risk of
dealing in the inter-bank market, as opposed to dealing in the risk-free
Treasuries for the same tenor. It must be noted, however, that unlike
corporate bonds, interest rate swaps do not involve risk on the principal
amount. True, the underlying 6-month MIFOR or US$ LIBOR are cash
curve measures that incorporate inter-bank credit risk, but the 5-year
MIFOR or US$ LIBOR swap does not by itself involve any principal
exchange. At any rate, MIFOR based swaps offer excellent price risk
hedging tools for banks, institutions and other corporate entities alike.
Like in the US$ and other G7 swap markets, increasingly, MIFOR swaps
are seen as pure INR term interest price risk hedging and speculating
tools, which brings about flows far more than those arising on account of
foreign exchange underlying exposures.
The GOI swap market

The last of the inter-bank benchmarks is the Government of India bond market (GOI) rates. The broad parameters of swaps on the GOI are summarized in table 1. A few points to note about the GOI swap markets:
(a) Since shorting of GOI bonds is not allowed in India, offering FRA quotes or
hedging GOI swaps in the cash market can be tricky. Invariably, authorized
dealers are left with some portion of the risk from these swaps that cannot be
hedged completely.

(b) As will be discussed in the section on pricing and valuation, GOI swaps present
some unique mathematical issues in creation of the zero curves and estimating the
value of future floating rates. Invariably, GOI based swaps will not be valued
correctly by most systems and algorithms, and adequate care has to be taken to
reserve for these differences. Most systems assume the bonds are par bonds (i.e.,
with a price of 100 today, with coupon cashflows equal to the current YTM), and
are also unable to adjust for the fact that the coupon dates do not coincide for
different benchmark bonds.

(c) The GOI swap market quotes at a spread over (or under) the cash GOI curve, For
instance, while the benchmark 5-year GOI bond may be at 6.35% (annualized),
the 5-year swap (floating 1-year GOI) can quote at 6.30/6.50 (T-5/T+15). When
this market first began in August 2000, the first set of deals were actually dealt at T-15, while in May/ June 2002, this spread actually climbed to T+30/T+50.
Paying the fixed rate on this swap provides banks with an oblique way of actually
shorting the GOI bond, something otherwise disallowed by regulations. In a
sense, the spread over the cash curve is a measure of what banks are willing to
pay to be able to, in a sense, short the GOI bond.
Making sense of it all
Given that pictures say a thousand words, lets take a look at some interesting graphs
(a) Graph 1 traces the 1-year GOI, MIBOR OIS and MIFOR rates since 1999.
Notice that the spread between the three rates tend to wax and wane.
(b) Graph 2, 3, 4 trace the MIFOR and GOI rates for the 2, 3 and 5-year tenors over
time.
(c) Graph 5 traces the 5-year MIFOR and AAA corporate rate over time.
(d) Graph 6 traces the spread between 1-year MIFOR and 5-year MIFOR, as also
the spread between the 1-year GOI and the 5-year GOI
(e) Graph 7 traces the State Bank of India PLR against the 1-year MIFOR, over a
period of time. Would you say the PLR is a truly floating rate?

The spread graphs have been included to indicate that it simply might not be enough to have the right directional view of the markets. To maximize gains (and minimize losses should the view be wrong), it is exceedingly important that the correct benchmark be chosen to implement directional views. Also, given the wide fluctuations in the spreads between any two curves, several trading opportunities exist on spread trades alone.
Building pricing and valuation systemsHaving touched upon the various basic building blocks of rupee IRD, a few points on their valuation and pricing of non-standard derivatives.

The building block to any valuation system is the building of the tenor wise zero discount factors (zdf) for each curve. Zero discount factors are simply the factor by which a cashflow occurring sometime in the future needs to be multiplied by, to arrive at its net present value. For tenors up to 1 year, MIFOR zdf can be easily determined using the logic used above. However, for the longer tenors, where swap rates quote on semi-annual settlement basis, the matter becomes a little more involved. The easiest way to proceed is to follow the concept of bootstrapping, where starting from the nearest quoted tenors, we build all the way up to the farthest tenor, each time solving for one unknown variable. If we had the 18 month (semi-annual) MIFOR quote as r18, for instance, we could solve for the unknown 18-month zdf z18, using our prior knowledge of the 6-month and 12-month zdf (z6 & z12 respectively) solving the equation:

The y6, y12, y18 represent the fraction of the year for the period in question using the appropriate basis (act/ 365 in the case of rupee swaps).

The above method would be carried forward to the 2-year point and so on, using the previously calculated zdf rates and the next swap rate, to obtain the next unknown zdf. For dates between the standard quoted tenor points (say the 2.3 year date from today), some assumptions have to be made on the interpolation methodology to be followed. There is a large array of such methods available: simple linear interpolation of zeroyields, linear interpolation of the zdf, exponential interpolation of zero-yields, cubicspline etc. to name a few. Often, there is no 'right' answer as to which method is best suited for which curve. Practitioners will need to choose the methodology that they feel best captures the way in which the particular market operates.

Once the zdf factors for each market curve have been determined, valuation of swaps and their cashflows is relatively simple. Floating rates are simply those implied by the underlying curve. Care must be taken to ensure that the floating rates are estimated on the correct side: e.g. MIFOR resets are on the offer rate, whereas MIOIS resets are on the mid, depending on market convention for settlement. Knowing the 6-month and 1-year discount factors, one can calculate the 6-month floating rate at the end of 6 months (i.e., the 6X12 FRA as follows)

Where y 6 x 12 is again the fraction of the year appropriate to the period 6 months over 12 months, using the calculation basis (act/ 365 in the case of MIFOR).
Once all the floating rates have been estimated, any swap simply becomes a series of net cashflows occurring at discrete points of time. Usually, this series would simply be
present valued on the same curve using its discount factors.

Where the markets operate on large bid/ask spreads, adequate care needs to be taken to ensure the correct side rates have been taken into account for computation of the zdf, and in the valuation process itself. For banks running a large portfolio of swaps, valuation can be done on the mid-curve, with an additional portfolio level cost to close reserve, arising on account of the bid/ask spreads that need to be crossed in closing out the gaps.
Curves such as the GOI bond curve present a separate unique set of problems.
(a) Firstly, shorting of actual GOI bonds is not allowed in the market. The basic
assumption in building the zdf and FRA rates would be that shorting is permitted. One way to get around this problem is to assume that long bond positions arising from GOI swaps would be liquidated in the swap market itself. In making such assumptions, however, one needs to bear in mind the large bid/ask spreads of the GOI swap market, which would then need to be crossed.

(b) (The GOI benchmark bonds are not par bonds (i.e., their price today is different
from the face value), and benchmark on-the-run bonds across different tenors
have different coupon dates. However, most zero-curves built for this product
class, assume that the bonds are par bonds, and that the coupon flows for all
bonds happen on the same set of dates. This produces anomalies in the GOI zero
curve. The easiest test for this would be to introduce a set of cashflows that
mimic the actual cashflow of a long tenor bond, with the same coupons, cashflow
dates and principal repayment. If the curve was accurate, the present value of
these cashflows ought to be the correct market price of the bond. Invariably, there
is a difference that crops up, that is sometimes seriously significant. Involved
software is available, that minimizes differences of this nature. In the absence of
such software, however, manual corrections and reserves may need to be
introduced to provide for the differences.
(c) As mentioned earlier, it is important to note that the GOI based swaps quote at a spread over (or under) the cash curve. Several banks continue to value their GOI
swaps portfolio on the cash GOI curve itself. Such a valuation needs to be
adjusted for this swap spread, with appropriate portfolio level adjustments on the
impact of the large bid/ask spreads inherent in the market.

(d) The floating rate for GOI swaps is the YTM of the benchmark bond on the reset
date. Most valuation systems calculate the underlying as a zero-rate (as in the
case of equation 4 above). If the reset benchmark is a long tenor bond (e.g. a 5-
year underlying), this can make a very significant difference.

Exotic Interest Rate Derivative Products in India
'Exotic' interest rate derivative structures, worldwide, generally have their origins in the following:
(a) Unusual slope of yield curves
(b) Unusual volatilities implied on interest rate options (c) Unusual spreads between different yield curves

In India, (b) cannot apply, since swaptions, caps, floors etc. are not permitted in IRD. (a) and (c) have however, spurred a few structures with a twist.
Setting variations: advance/ arrears/ average
Swaps in the inter-bank are dealt on an advance-reset basis. In such cases, reset dates lag the actual cashflow dates by a settlement period. Thus in the case of a 5-year MIFOR (semi-annual), resets would be decided 6 months prior to the actual exchange of the cashflow. In the case of inter-bank FRA deals, the cash-flow occurs immediately after the start date, so that the reset date and the cashflow date almost coincide. But in a FRA, the settlement is actually deemed to happen at the end of the FRA period, and the net settlement that happens close to the start period is actually calculated by present valuing this deemed cashflow. To that extent, even inter-bank FRA deals are essentially on an advance reset basis.

Steep yield curve slopes can imply FRA rates that rapidly accelerate as one moves along the yield curve. Corporate customers looking for additional 'carry' therefore, may prefer to set on an arrears or average basis. This year, e.g., several customers dealt in 1-year
INR/US$ coupon swaps, where the floating rate was the 1-year US$ LIBOR, set in
arrears. In doing this, the customers were betting that the actual 1-year US$ LIBOR at the end of 1-year from the trade date, would be lower than that implied by the 12X24 FRA on the trade date.
These trades carry a convexity risk. This means that the swap cannot be hedged
completely at inception: as the market moves, the hedge itself would need to be adjusted. This is best explained through an example. Take the case of a bank which has done a 1 year US$ swap with a customer, where it agrees to pay a fixed rate I, and will in turn receive US$ 1-year LIBOR set in arrears. To hedge the US$ side, assume it enters into a FRA with another bank. Note that the FRA will be settled on an implicit advance basis, since the net settlement in the FRA will be computed on NPV-ed terms. The cashflow of the deal and the hedge, from the bank's perspective, therefore looks as follows:

Here, X is the total cashflow for the bank at the end of 1 year, N is the notional of the customer swap, Nf is the notional of the hedge FRA, i is the US$ 1-year LIBOR at the end of 1 year. This is assuming that the same I rate has been passed on tot the customer: however, any difference in the rates can also be easily accommodated in the analysis that follows. It can now be shown that the delta of the cashflow, with respect to small changes in the 12X24 US$ LIBOR is as follows:



Notice that the hedge FRA notional is not constant, but varies with changes in the 12X24 rates itself. In essence, as i increases, the FRA notional must increase, and as i drops, the notional decreases. Clearly, under this rule, as the LIBOR FRA moves up and down, the bank eventually ends with a positive P&L impact. The converse is the case with the customer: if the implied US$ LIBOR for the reset period were to show large volatility, from a hedge sense, the customer would actually be losing out.

To quantify the convexity benefit (or cost), therefore, one would need to take a view on the volatility of the underlying US$ LIBOR curve. Statistically, it is possible to estimate this element, by making a few assumptions about US$ LIBOR time series. The derivation of this formula would be beyond the scope of this material.
Constant Maturity Treasury Swaps (CMT)
The first set of 'different' swaps began with a flurry of CMT swaps during 2001. Please refer to table 1 for a brief description of this structure.

The most popular CMT was a 5X5: i.e. a 5-year swap, with annual/ semi-annual resets, where the benchmark was the floating 5-year GOI YTM from INBMK. In addition, 3,7 and 10-year bonds have also been used as benchmarks.
The swap owed its popularity to the steep slope of the GOI curve at that time. Graph 8
traces the GOI yield curve during October 2001. The spread between the 5-year GOI and 10-year GOI was then close to 150 bps. While the 5-year bonds was at 7.5% and the 10-year bond was at 9.00%, the yield curve implied that the 5-year bond YTM at the end of 5 years (or the 5-year over 10-year FRA) was in excess of 12%. Customers who thought that this was well above their expectations of where the market for 5-year at the end of 5 years would actually settle, received the fixed CMT against the floating 5-year INBMK benchmark.
To an extent at least, the subsequent narrowing of the 5X10 GOI spreads can be
attributed to banks and their corporate customers receiving fixed rates on the CMT products. From a closing peak of 161 bps seen towards the end of October 2001, the

spread narrowed to as low as 37 bps in July 2002. It currently is at close to its historical average at about 85 bps.

Like in the case of arrears/ average structures, it must be borne in mind that this product has convexity and volatility embedded in it. The payer of the fixed rate would be long convexity/ volatility, whereas the receiver of the fixed rate would be short convexity volatility. The analysis of this would be very similar to those of equation 5(a), (b), (c), with a small difference arising on account of the bond element in CMT.

Assume a simple CMT for 1-year tenor, on a notional N, where a bank pays a customer a fixed rate, and receives a floating 5-year INBMK YTM set in arrears (i.e. at the end of 1 year). Assume that as a hedge, the bank purchases a 6-year bond today, for settlement 1-year in advance (clearly not permitted today, but this would be the ideal hedge). In that case, the total payoff X for the bank, set to occur one year down the road will be:


Here, Dm is the forward modified duration of the bond. Clearly, as yields change, this forward modified duration will change, and the hedge will need to be rebalanced. As the bond's forward YTM increases, the duration will decrease, as will the current price of the bond. Therefore, as yields increase, the bank will need to purchase successively more bonds. Conversely, it can be shown that as the yields drop, the bank will need to sell its holding stock. This is clearly a win-win situation for the bank; i.e. a long convexity position. How much it actually makes from this convexity clearly depends on the volatility of the YTM movement: the more volatile the curve is, the more it stands to gain. This is clearly a long volatility position for the bank.

On the other hand, for the customer who has received the rupee fixed rate, this represents a short convexity and short volatility position.

The benefit from the long volatility position, in the absence of a proper volatility market, is relatively marginal for the bank, given the huge transaction costs & bid/ask spreads involved in all rupee swaps. To achieve the theoretical gain from the convexity, the bank must cross these spreads. On the other hand, the cost being borne by the receiver of the fixed rate is for real, and is a factor that must be taken into account should the customer desire to unwind or cancel his swap.
Quanto products
This is a rupee IRD with a twist: while the notional principal currency is in rupees, the floating benchmark is not a rupee benchmark, but that of another currency. The only quanto swaps reported in the market have a US$ LIBOR underlying. In a sense, the payoff is similar to a rupee coupon swap, which customers generally use to move from an INR rate to a US$ interest rate. However, a plain coupon swap carries a US$/INR FX risk, since the customer needs to pay the interest in US$. For customers looking to assume US$ LIBOR risk without the attendant FX risk, Quanto is the ideal product.

From a regulatory angle, one could argue as to whether this is strictly allowed, since the RBI has only allowed rupee benchmarks to be used as floating resets. However, banks have argued that if coupon swaps can be permitted, then quantos, which have the same interest rate risks, without the attendant FX rate risk, should also be permitted. Also,since MIFOR is an accepted rupee benchmark that is computed as a function of the US$ LIBOR and the US$/INR forward FX points, in a sense, a quanto is a MIFOR swap with the premia points fixed beforehand.

Hedging a quanto poses issues for banks. In essence, the basic hedge on a rupee quanto where the bank has paid a fixed rate is for the bank to receive a fixed rate in the US$ LIBOR swap market for the same tenor. However, the notional of this hedge US$ swap will change as the USD/INR outright forward rate changes. It can be shown that if the US$/INR outright forward rate increases, the bank will need to reduce its US$ swap hedge. In the interim, if the US$ swap rate has increased, the bank will stand to lose money on its hedge. If however, the US$ swap rates have declines, the bank makes money on its delta rebalancing. The converse will be true if the US$/INR forward ratedeclines.

This phenomenon is expressed in terms of a cross-convexity (or cross-gamma), where the correlation coefficient between the US$/INR outright forward rate and the US$ swap curve becomes critical. As the previous passage shows, if this correlation were to be positive, the bank (having paid the fixed rate on the quanto) would tend to lose money in its process of delta rebalancing.
To price in the quanto element (arising from the cross gamma, which has a monetary impact depending on the volatility of the underlying US$/INR forward curve and the US$ swap curve), the floating cashflows of the quanto need to be adjusted by the
following factor:


Conclusion

This paper merely provides a snapshot of a growing traded market of INR Interest Rate Derivatives. It has been silent on the following critical issues:

(a) The risk management of derivatives in the Indian context: covering market,
credit, legal, systems and accounting risks.
(b) Synthesizing an objective approach to managing balance sheet risk: correctly
identifying the risks, developing the 'correct' risk management strategy and using derivatives to implement it.
These are sadly, beyond the scope of this paper. However, the importance of the above cannot be overemphasized. Before we take the next leap forward and introduce trading in interest rate volatilities & options, it might be in order to take stock of these issues and ensure that Indian entities do not fall prey to some of the derivatives based scandals that have hit the headlines over the past two decades in the developed markets.