Master Chapter Two

Interest Rate Derivatives

I’ll share the practical workings of interest rate swaps, cross currency swaps, cross currency basis and related variations. The content would build on the foundations discussed in the section on Time Value of Money and cash products.
    • Interest Rate Swap (IRS) – is an exchange of the same currency interest rate payments between two parties interested to either express an interest rate view and or hedge interest rate risk. The more commonly referred convention is the exchange of fixed vs floating rate payments. Risk on an IRS therefore can be decomposed as being a long (short) floating rate bond and short (long) fixed rate bond. Other salient features below:
          • Counterparties that trade par interest rate swaps enter into a swap with 0 Present Value adjusted of course for bid-offer slippage i.e. execution mid denotes that the PV of projected floating rate cash flows is equal to PV of fixed rate cash flows through the tenor of the swap.
          • Markets also trade swaps with a fixed strike (usually different from the par swap level) if one is trading the same currency for the same dates so as to minimise the number of line items on the risk blotter. For instance a 3.5% September IMM 5y KRW IRS can be initiated by trading the bid or the offer side of the par swap quote with an exchange of fee between the two counterparties offsetting the present value on the swap.
          • Paying a fixed rate swap = short rates or selling a bond, receiving a fixed rate swap = long rates or buying a bond
          • There is no principal notional exchange as in the same currency IRS the fixed and the floating payments net off. Only net cash flows at the time of reset/unwind/maturity are exchanged.
          • Pricing of a swap – fixed rate can be thought of as the IRR of the expected floating rate for the underlying swap tenor. In other words the fixed rate of a swap for a tenor T is the implied average floating rate for that tenor such that the PV of the expected floating rate payments is equal to the PV of the fixed rate payments.
PV of fixed rate cash flows= C × D F 1  + C × D F 2  + ... + C × D F n
PV of floating rate cash flows = FL R 1  × D F 1  + FL R 2  × D F 2  + ... + FL R n  × D F n

Where C is the par fixed swap trading in the market,

DFn is the discount factor for the nth time period

FLRn is the expected or projected floating rate for the nth time period

Mathematically then the observed par fixed swap rate C can also be derived by equating the two notations above and plugging in the expected floating rates in progressive time periods.

Importantly,

D F n  =  1 ( 1 + FL R n ) n

Assuming for the sake of simplicity the cash flows are funded at the floating rate. We discuss a more nuanced concept of the discount curve being different from the projected floating rate curve later in the section.

          • Duration and DV01 of a swap – worth repeating here that if you think of duration as the time taken to receive the promised cash flows then the concept is incongruous for a swap with 0 PV (when it’s initiated). To assess the interest rate sensitivity for a portfolio of bonds and swaps we end up using the modified duration of just the fixed leg of the swap (same as that for a fixed rate bond with same fixed leg cash flows) as the duration of the swap; rate sensitivity of the floating leg is much smaller as discussed in the duration of a floating rate bond. Dollar value of a basis point (DV01) for swap is a more astute measure for assessing the interest rate sensitivity (and the more widely followed duration metric) of a swap.
          • DV01 of a swap is the sum of the DV01 of the fixed and floating legs (remember that DV01 captures the direction of risk to assess the portfolio’s pnl swings with movement in rates) of the swap or is the sum of the DV01 of a long (short) fixed rate vs short (long) floating rate bond being exchanged as implied in the swap cash flows. DV01 of the floating leg is a function of the swap reset frequency. Also until the first reset – the interest rate sensitivity of the floating rate bond doesn’t come into play i.e. the DV01 of the swap for a tenor T is equal to that of a fixed rate bond for the same tenor. After the first reset however the floating leg would acquire a finite DV01 albeit small, equivalent to that of a bond with a tenor of the floating rate period.
          • If you recall the Bond DV01 for a Bond’s dollar duration notation below where B is the bond price:
DV01 = − Modified duration × M arket value of the Bond notional × 0.01% 

The same for a swap would be denoted as

DV01 = − Mod duration of  the fixed leg × ( 1 + P V fixed leg ) −  {− Mod duration of  latest reset × ( 1​ + P V reset  leg )}
DV01 = − Mod duration of  the fixed leg × ( 1 + P V fixed leg ) 
 −  {− Mod duration of  latest reset × ( 1​ + P V reset  leg )}
          • The positive convexity of being long a bond in the same manner would also apply on a long swap (received rates) position.
          • Breaking down risk buckets in a swap – risk in a swap is crucially dependent on the way the curve is constructed. Usually market traded tenors are used to construct (bootstrap) the curve, hence risk of any tenor of a swap would be deemed sensitive to the movement in swap tenors that are used to interpolate its price. The process of recognising the risk sensitivity across tenors is called risk bucketing. For instance, the present value of a 4 year swap would be impacted by moves in the 2y and 5y par swaps (both benchmark/more liquid tenors) and a linear interpolation effectively would have 1/3rd risk in 2y vs 2/3rd risk in 5y. In other words, the size of component risk on a certain benchmark tenor is inversely proportional to its distance from the non-benchmark tenor.
          • The risk sensitivities are dependent on the way intermediate (and generally less traded) points on the curve are constructed. Different methods of interpolation could use regression analysis, cubic spline interpolation or for that matter try and fit any form of a polynomial interpolation depending on what best depicts the curvature of that rates market.
          • Leverage on a swap – linking the concept of a forward starting swap and risk bucketing – a 1y forward 1y swap has twice as much risk on 2y as it has on 1y as per its bucket components and in the opposite directions. Hence a 1bp move in 2y with no change to 1y would amount to a 2bps move in the total pnl of the swap i.e. that’s a 2x sensitivity which can be understood as leverage of the swap to the 2y point. Defined simply when a 1bp move in any component tenor (all else constant) causes a pnl move in excess of the overall DV01 of the swap, it is understood to have leverage with respect to that tenor.

 Table 1 – Bucketing and Leverage of spot and forward starting swaps

Tenor bucketSpot 6ySpot 8y1y forward 1y4y forward 1y3y forward 2y
1y +10K
2y -20K
3y +15K
4y +40K
5y-5k -50K-25K
7y-5k-6.6k
10y -3.3k
Leverage 2x5x2.5x

* Standard DV01 risk assumed to be $10K, swap direction is received fixed rate

Source: Pandemonium.                                            

        • As an example – for a 1y forward 1y swap a 1bp move in just the 2 year tenor will move the swap pnl by 2x, hence the 2x gearing to the 2y point. Similarly in a 3y forward 2y swap a 1bp move in the 5y bucket only would move the swap pnl by 2.5x hence leverage (gearing) is 2.5x to the 5y point. A simple notation can be:
Leverage multiple on Rxy swap w.r.t (x+y) year tenor =
( x+ y) y
        • Street likes to trade forward starting swaps for the following reasons: a) to avoid exposure to fixings and instead express views on it b) depending on the conviction of the trade (outrights and curvature) take leverage to express it c) administrative ease of managing risk for those who’d like more outright risk.

Unwind Value of swaps

Swap unwinds are computed as the present value of the cash flows (positive or negative) reflected in the difference between the traded fixed rate and the current market fixed rate. As the swap ages and market movement changes the projected floating rate (the current par rate) it results in a non-zero present value relative to the original fixed rate. In addition to the fixed rate differential, the unwind value also needs to be adjusted for any short stub valuation i.e. the residual current floating rate period that uses the updated interpolated floating rate vs the original floating rate to calculate the stub unwind value.

As an example of an aged interest rate swap – Consider a received 5y swap at a fixed rate of 5% against a 3m floating index. The swap has aged by a month since the start date of the swap and the first floating rate was fixed at 4%. I’ll discuss two different methods for the unwind:

Method One

    • Since the original swap now behaves like a fixed short stub cash flow for 2 month tenor and a 2m forward 4y9m fixed float swap – the unwind PV would have two components to it.
    • First component – Assume that the current 2m forward 4y9m rate is at 4.5%. Then the PV of the forward starting component of the original swap is nothing but PV of net cash flows of 50bps every progressive 3 months after the effective start date; first reset in 2 months and first cashflow 5 months from today.
    • Second component – please note that since the first fix was already set the net cash flow amount is already known. It’s the changing discount factor that would change the PV of the residual tenor. After a month therefore, the known net cash flow of 1% (payable for the 3m period) for the front short stub (2 months) would need to be discounted by the current 2m floating rate to obtain the PV.
    • The total unwind value is the sum of the two unwind PV components above.

Method Two - the more popular/widely observed

    • Let’s think of the original swap which now has a tenor of 4yr 11 month which is unwound by trading a live 4y 11 month swap in the opposite direction at 4.4% with a short front stub of 2m. Assume the interpolated 2 month fix is at 3.5%.
    • First component – the differential of the fixed rates amounts to a present value of 60bps of the swap notional, starting in 2 months for every 3 months thereafter. Please note that this unwind value already incorporates the interpolated 2m stub since 4y 11mnth rate was traded to unwind the original swap.
    • Second component – the difference in the front stub fixings will need to be adjusted. We have made 60 bps on the original fixed rate swap for 4y11m tenor but we have lost 50 bps on the 1st fixing for the residual 2 month tenor (paid 4% original fix received 3.5% on unwind). This cash flow discounted at the 2m rate of 3.5% will have to be deduced from the first component PV.
    • Third component – The first month accrual of 1% as part of the final payout at the end of 2 months from today would also be discounted by the 2 month interpolated rate of 3.5% and added to the overall unwind PV.

IRS - Crucial Other Considerations
(CVA, FVA, ...)

Other considerations while entering into a swap are counterparty credit risk and funding of cash flows (variation margin, CSA, CVA, FVA, wrong way risks to be discussed in detail in the risk section later).

What is counterparty credit risk for an interest rate swap?

Importantly on any swap, the 0 PV at the time of entering it is the result of PV of the expected average cash flows of the floating leg being offset by the PV of the expected average cash flows of the fixed leg, “average” being the key word. In other words for both a steep and or inverted yield curve there will be cash flow mismatches between floating and fixed legs on select reset periods (can very well be at the start of the swap too) even though the sum of the PV of all mismatches would be 0. These mismatches create counterparty credit risks (assuming no CSA/credit mitigation documents) and the risks change with movements in the underlying market.

    • These credit risks are an inherent part of swaps pricing with hedging charges based on the counterparty credit risk profile and the volatility of the underlying product.
    • Note that swap levels quoting in the market assume inter-bank/cleared risk (with credit mitigation) for the dealers, but while facing non-inter bank counterparties the credit risk hedging charges termed as CVA (credit value add) need to be reflected in the swap levels.
    • Measurements of these charges are governed by a) movement in yields b) correlation between counterparty credit risk and the IRS movement (which if highly correlated is also known as “wrong way risk” c) Implied/expected Rates volatility to assess average and peak credit exposures. These risks are managed by CVA desks in banks.
    • An intuitive way to think about CVA hedging – The CVA desk of a bank takes a fraction of the same risk that the bank dealer gets on the client flow (i.e. opposite of client risk). Which means a fraction of the mismatches as generated by the original risk is now in the CVA books. If the client loses money on the swap, the CVA desk’s position retains some gains for the bank which would have been lost otherwise if dealers had fully hedged the market risk. The CVA desk can also then use these gains to hedge the credit risk via buying protection on the counterparty’s obligations or via an instrument that reflects mitigation of the counterparty’s credit risk.
    • CVA charge is mostly accommodated in the bid-offer of the swap. These credit risks can also be eliminated by simply exchanging the MTM of the swap on a daily basis as against an upfront CVA charge in the transaction. This gave rise to the concept of Collateralised Swap Agreements (CSA).

Funding of IRS cash flows

Now comes the funding of these mismatches. The rate of interest at which a counterparty funds these cash flows is the discount rate (which determines the discount curve) to calculate the PV of these cash flows. The traded swap curve however is the projection curve i.e. projects the expected floating benchmark across tenors. THE TWO CAN BE DIFFERENT. In case the CSA is in place the discount rate is the rate the two parties pay each other on the variation margin (CSA discounting), while in the absence of a CSA, discount rate is the rate at which the dealers fund their variation margin. For the latter, banks reflect them as FVA (funding value add) to be charged to the client that differs for different dealers depending on their respective funding curves.

As an example when you trade a USD LIBOR swap, the cash flows are projected using LIBOR, but they are discounted using the rate at which the two parties fund the cash flows i.e. USD OIS in most cases for inter-bank CSA participants. Hence while computing the PV of cash-flows, one would notice a LIBOR-OIS basis risk that would need to be hedged. Similarly for a local currency EM swap, say KRW NDIRS – the projection curve would project the 3m CD index while the cash flows would be discounted on USD OIS (assuming benchmark funding rate for dollar-based counterparties). Given that KRW PV would need to be funded against USD OIS the actual discount curve would be the KRW ND CCS vs USD OIS. As of today since ND CCS trades against USD SOFR, while computing the PV we would technically have some SOFR-OIS basis risk even though negligible as market uses these rates interchangeably.

  • Trivia

Difference between 3m and 6m USD LIBOR came into prominence during the Global Financial Crisis when the 6m LIBOR curves started baking in a larger credit risk premium vs the 3 month benchmark. Previously cash flows on both 3m and 6m LIBOR swaps were discounted off their respective projection curves (as 6m could be interpolated exactly from the 3m curve) but once the curves started diverging dealers had to rebuild their models to discount them both off the USD funding curve.

This was 3m libor flat for most banks in the pre-CSA world and later changed to OIS once credit mitigation documentation was put in place.

Dual/Multi Currency CSAs

As part of CSA negotiations dealers also discussed the provision for margin posting in different currencies. For e.g. it was quite common in Japan to have CSAs that allowed either USD or JPY cash margins to be posted. More interesting is the fact that the funding rates on different currencies naturally follow their respective money markets and don’t really account for FX equivalent rates (cross currency basis discussed later). This gives rise to an optionality within the CSA whereby dealers can choose to switch between the currencies for margin posting (and effectively the discount curve for their trades) based on which one is cheaper to fund. This optionality is difficult to price due to the non-existence of observable trading prices for the correlation/ volatility between the two discount curves. But if dealers discover a way to hedge it, it could have an impact on pricing of swaps documented on dual currency CSAs.

Cleared and Uncleared/bilateral swaps

Since we haven’t yet discussed the details of a collateral swap agreement and related risk mitigation yet (to be covered later) for the sake of completion I’d just like to mention the concept of a cleared swap. A cleared swap places an exchange/clearing house in between the payer and the receiver to eliminate counterparty credit risk, by taking the onus of margining (initial and variation margins) from both parties. It also helps facilitate block unwinds at portfolio level for swaps traded with different counterparties but facing the same clearing house.

Exchange basis

Exchange basis (LCH-CME, LCH-JSCC etc.) – When net open positions or one sided positions of dealers become large on an exchange, the requirements to fund the Initial Margin increases making it more costly for dealers to trade more of the same direction on those swaps. In other words dealers are willing to pay a higher cost to get the other side of the swap facing that exchange/clearing house compared to what they are willing to pay for the same on other exchanges. This is what leads to a basis to develop for the same swap between two different exchanges. For example, asset managers that mostly dealt on CME and were fixed rate payers (assuming hedges on long bond positions) created sizable received open positions with dealers. These dealers were willing to pay higher for the same swap on CME compared to LCH (basis visible around mid-2015) as the higher cost was being offset by lower margin requirements for positions compressed on CME.

Use and hedging of Interest rate swaps

    • Uses can be: a) unfunded expression of interest rate views on levered basis (recall leverage discussed earlier) b) enhancing portfolio returns i.e. overlays on long/short bond exposure c) hedging assets/liabilities and or converting fixed to floating or vice versa, sometimes by creating non-standard structures to match irregular cash flows.
    • A received fixed position with a dealer can be hedged by a) paying the fixed rate (offsetting the swap) b) selling a futures contract on a similar underlying c) selling bonds/treasuries depending on its hedge value/minimise duration mismatches.

Cross Currency Swaps

  • A variation of interest rate swaps, cross currency swap as the name suggests is a swap between two different currencies exchanged either in a fixed/fixed, fixed/float or float/float format. One can think of a CCS contract as a borrowing of one currency (paying interest rate on it) in exchange of lending the other (receiving interest rate on it). At the end of the contract the notional exchange is reversed i.e. the borrowed currency is returned (sold back) and the one lent comes back (bought back). This determines the direction of the FX swap trade. Market practice generally references the direction of the base currency at the far leg of the contract (USD, EUR, JPY et al.) to address the CCS direction. For instance, lending USD to borrow/generate KRW is equivalent to a sell/buy FX swap or a paying KRW rate/receiving USD rate i.e. buying USD in a USDKRW cross currency swap.
  • FX risk in a cross currency swap – while a CCS is the exchange of interest rates on loans in two different currency notionals, the FX risk in the contract depends on the outstanding cash flows of the trade:
        • When both initial and final exchange are outstanding – magnitude of the FX risk is to the extent of the PV of the local currency leg, that’s much smaller compared to the notional.

        • When only the final exchange is outstanding – magnitude of the FX risk is to the extent of the full local currency notional or PV of the local currency leg of the swap.

 

Table 2 – Comparison between IRS (Single Currency Swap) and CCS

IRSCCS
Notional ExchangeNoMostly yes, though coupon only swaps don't have any notional exchange
FX riskNo Yes as stated above
Type of swapFixed/Float typically, float/float on 2 different indices of the same currencyFixed/Float, Fixed/Fixed (typically used for corporate liability swaps), Float/Float
Discount CurveFunction of CSAFunction of CSA
Credit and Funding chargesCVA and FVA as discussed earlierCVA and FVA charges are larger owing to FX vol risk on foreign currency notional in addition to rates vol
Duration/Rates riskSame as the duration of the fixed rate legThat of fixed rate leg in case of fixed/floating and could be on both legs in case of fixed/fixed
Unwind ValueFunction of change in interest rates for onshore swaps. For USD based investors trading local currency swaps there is spot FX risk on unwind PV.Function of change in interest rates and Spot FX rate.

Source: Pandemonium.

    • Lastly – FX swap is a variation of a zero coupon fixed/fixed cross currency swap where the zero coupon IRR of the local currency leg is determined by the far leg FX rate or the FX outright (also called the FX implied as calculated in Table 3 below) of the contract.

Cross Currency Basis Swap

Cross Currency Basis Swap – is simply a float/float cross currency swap and primarily a financing instrument traded in the inter-bank market as a foreign currency floating rate against the hard/benchmark currency floating rate +/- spread. Basis swap levels therefore are an indicator of the magnitude of funding cost of the local currency in terms of the foreign currency.

In terms of cash flows they can be understood as a series of FX swaps, reset at prevailing market rates.

Indicative terms of a basis swap contract for client ABC: assuming client pays 5y USDJPY cross currency basis swap (JPY TONA/OIS vs USD SOFR)

Trade Date: Today
Swap Start Date: T+2/Spot Date/Forward Start IMM date
Maturity Date: end date as per the tenor of the basis swap (eg. 5y)
Notional Amount: Generally in base currency (eg. USD 100 mio)
Foreign Currency Notional: USD 100 mio x USDJPY FX rate effective on the start date
Notional Exchange: at start date and maturity
JPY Floating Rate: JPY TONA/OIS
USD Floating Rate: SOFR – xxx spread
JPY Floating Rate Payer: ABC i.e. borrows JPY and lend USD
USD Floating Rate Payer: Dealer i.e. lends JPY and borrows USD
JPY Floating Rate index Convention:
USD Floating Rate Convention: 3m USD SOFR compounded
Holiday Convention: Tokyo, New York

  • Trivia

While basis swaps have been dealing for a long time in deliverable and developed market currencies – they have unfortunately not gained as much popularity with developing Asian markets. That’s primarily because the Asian local currency floating benchmarks were non-existent prior to the Asian Financial Crisis. There were literally no domestic interest rate policies or domestic swap (IRS) markets. Whereas there were vibrant long dated FX markets which facilitated the development of Fixed (local currency)/ Float (USD) longer dated cross currency swaps much earlier. To this day one doesn’t readily find liquidity in basis swaps in these Emerging market currencies and basis quotes are backed out of fixed float CCS and IRS / NDIRS separately.

 

Now as a follow-up here’s the intuition behind the cross currency basis product – the term basis refers to the difference between the yield differential that should get reflected in FX swaps as per covered interest parity vs what actually gets reflected owing to the relative demand for the foreign currency vs the base currency or vice versa.

To understand this numerically, it’s best to consider cash flows – let’s take the eg. of one of the more actively traded markets – SGD FX points and the corresponding SGD OIS vs USD SOFR.

FX swap trade

Paying 6m USDSGD points or a sell buy on the 6m FX swap would entail:

Near leg (spot in this case): Lend USD and borrow SGD
At maturity do the reverse: return the SGD and receive back USD

Recall that an FX swap is a fixed base currency notional exchange versus the foreign currency at a zero coupon and the FX points for the tenor of the swap determines the foreign currency notional at maturity which in theory implies the FX rate after 6m as per covered interest parity. But let’s see what happens in reality:

Current Spot: 1.37
Base currency fixed notional: USD 100 mio
SGD notional at spot = SGD 137 mio
Market mid on 6m USDSGD FX points: -50pips
6m FX outright: 1.37 – 0.0050 = 1.3650

If we were to do the same trade assuming market interest rates:
  • Lend USD at 6m USD SOFR @ 4.70
  • Borrow SGD at 6m SGD OIS @ 4.00
  • Both above interest rates need to be adjusted for day count but for the below calculations we have assumed a semi bond day count convention applicable to the above coupons
  • USD Cash Flow = 
    • 100 mio (1+  4.70% 2 ) 
    = USD 102.35
  • SGD Cash Flow =
    • 137 mio (1+  4.00% 2 ) 
     = SGD 139.74
  • Implied USD SGD outright in 6m =
    •   ( 139.74 102.35 )
    = 1.3653
  • Implied 6m points as per covered interest parity = 
    •   1.3653   −   1.3700  = −47

    In conclusion: market traded 6m USDSGD outright shows a larger SGD FX appreciation than what’s implied by interest rate parity. Thus the implied SGD yield against USD SOFR should be lower than the local market SGD OIS rate. The difference between the two rates is known as the cross currency basis for SGD against USD SOFR.

    Mathematically then for a specific tenor,
    Fixed Rate CCS – Fixed Rate IRS = Basis for that tenor 

    • Connecting the Dots

    We have discussed both FX swaps and cross-currency swaps and now understand that both products are a reflection of the interest rate differential between the two currencies, with just different cash-flow schedules. I’ll share an illustration below that takes market-traded USDINR FX points, to first calculate the implied zero INR rate (or what’s popularly known as the FX implied INR yield) and use those zero rates to calculate the par CCS yields via bootstrapping. 

    INR FX implied yield

    INR FX implied yield – is effectively the zero rate implied by USDINR FX points and the USD zero rate. In the Quantitative easing era zero rates for several years were literally close to zero, such that FX implied yield was almost interchangeably used with the cost of generating local currency funding; dollar liquidity glut made USD funding available at almost 0 spread over risk free rate. But as USD rates went up and steep spreads on USD risk free rates were baked into funding costs the investment carry dynamics completely changed (more on this in the financing section).

        • Let’s apply the interest rate parity cash flows to an FX swap transaction (refer to the Cash FX section in Time Value of money) to obtain the INR Zero rate

     

        • USDINR Spot FX rate = 76.515, Outright forward = spot + points

     

        • Initial exchange of USD with INR notional would earn the respective zero rates on those notionals for the tenor of the swap. Therefore for a 3 month tenor,
    { 1 ×  ( 1 + 1.35%) 0.25 } × 77.24 = 76.515 ×  ( 1 + y%) 0.25

            ,where y is the annualised implied INR zero rate.

        • Future value of $1 in INR terms =
    = { 1 ×  ( 1 + 1.35%) 0.25 } × 72.50 = 77.50
        • Thus, implied INR zero rate =
     [ 77.50 76.515 ]   ( 1 0.25 ) − 1 = 5.25%

    Table 3 – Conversion of FX points to FX implied Zero Rates

    TenorTime in yearsUSDINR FX pointsO/R forward price$ zero rateFuture value of 1$INR future valueImplied INR Zero rate
    3m0.3 72.5 77.21.4%1.077.5 5.3%
    6m0.5143.578.02.0%1.078.75.8%
    9 m0.8218.078.72.3%1.080.1 6.2%
    1 y1.0298.5 79.5 2.6%1.081.66.6%
    18 m1.5459.581.12.9%1.084.77.0%
    2 y2.0619.682.73.1%1.187.87.6%
    3 y3.0 932.685.83.1%1.194.1 7.2%
    Source: Pandemonium.

    Par CCS yields (semi-annual in this case as per convention) - would follow bootstrapping on zero INR yields as below:

    Table 4 – Bootstrapping Zero rates to Par rates

    TenorTime in yearsImplied INR Zero rateDiscount FactorsPar semi CCS Yield
    3m0.3 5.3%1.05.2%
    6m0.55.8%1.05.8%
    9 m0.86.2% 1.06.1%
    1 y1.06.6% 0.96.5%
    18 m1.5 7.0% 0.96.9%
    2 y2.0 7.2% 0.97.0%

    *Zero rates and CCS yields have been rounded up to the second decimal

    Source: Pandemonium.                                            

      • Recall that cash-flows are discounted using zero rates, so let’s calculate discount factors for every tenor as
    1 ( 1 +  R z,t ) t

    ,where Rz,t is the zero rate for tenor t. 

    So,

    3m discount factor =  1 ( 1 + 5.25%) 0.25  = 0.9873
      • Since coupon exchange on a par INR ND CCS swap is semi-annual, there are no interim cash-flows for less than 1 year tenors. But that still doesn’t mean that up to 6 month tenors on par CCS yields are the same as FX implied yields because – the former is a semi-annual coupon (C) that’s discounted by an annually compounded zero rate scaled by the time period of the swap. For the sake of simplicity, consider this notation for a 6 month par CCS yield assuming $1 as the par value today, 
    1 =  ( 1 +  C 2 ) ( 1 +  R z,6m ) 0.5
    which clearly shows:
    C t  ≠  R z,t ,
      • Assuming a present value of CCS cash-flows for a 9m period at par, the CCS semi yield of C being the coupon, the first 3 months would be a short stub that would have a 3 month cash flow followed by a regular 6 monthly payment thereafter:
     1 = (   C   4   ) × 0.9873 + (   C  2  ) × 0.9557 + 1 × 0.9557 = 6.11%
    • The above solves for C=6.11%
    • Connecting the Dots

    Let’s crack down on some frequently used interest rates lingo to define the frequency of their payments/compounding so all terms used in this section are absolutely clear:

        • Interest rate paid semi-annually – Is a per annum (annual) rate payable every six months. As an example from Table 4, the 2 year par CCS yield of 7% is an annual rate of 7% per annum paid as 3.5% every 6 months.
        • Annualised rate accommodates compounding as per its payment frequency assuming reinvestment at the same rate. Taking the same example, the 2y par CCS yield paid semi-annually is equal to an ‘annualised’ yield of 7.1225% compounded every 6 months i.e. a dollar invested at 7% per annum paid semi-annually would earn an annualised rate of 7.1225% if compounded semi-annually.

    MTM risk of a basis swap

    Given that this is an exchange of notional in two different currencies on floating rates there is negligible rates duration in a basis swap. Risk on it largely comes from the FX movement in course of the tenor of the swap and only pending final exchange of notional.

    • Trivia

    Pre-CSA basis swaps in Japan would reset the notional on every coupon date. Basis swaps – since floating – are less sensitive to movements in rates due to short duration tenors of the floating legs. However mark-to-market is sensitive to FX rates as the trade’s notional exposure to the FX rate. This also implies a higher counterparty credit exposure. The JPY-USD basis market tackled this issue by resetting the foreign (JPY) notional on each coupon reset date. For example if a basis swap was entered for 5 years at a spot rate of 100 JPY per USD and the FX rate at the end of the 1st floating rate period moved to 120, the difference of 20 JPY would be additionally lent by the JPY lender to the JPY borrower thus changing the JPY notional lent/ borrowed on the swap for the next period. Notice then, that not only are the respective currency coupons floating, the foreign/local currency notional are also floating. This matching of JPY lent or borrowed was to be done every interest reset period to exchange the mark-to-market on FX movements, which is exactly what happens under a CSA (albeit daily) thus reducing the credit exposure on these swaps. These were known as basis swaps with resetting notional.

    Table 5 – Comparison between Long Term FX Swap and CCS

    Long Term FX SwapCCS
    DurationEquivalent to the duration of a zero coupon bondEquivalent to the duration of a fixed coupon bond
    Cash flows No interim cash flows, only initial and final cash flowsCash flows of fixed vs floating rate bonds based on payment frequency
    Credit and Funding ChargesCharges are higher as no interim cash flow exchange increases counterparty exposureCVA and FVA charges subject to FX risk on foreign currency notional
    FX riskEqual to FX notional on the foreign currency legEqual to FX notional on the foreign currency leg
    Rates RiskOn both fixed notional (interest rate) legs as swap PV changes with interest rate differentialEquivalent to the fixed leg of the swap since floating leg has minimal duration
    Source: Pandemonium.

    Fixed-Fixed Cross Currency Swap

    For the sake of completion of all payment frequency types of CCS consider an exchange of different currency notionals at fixed coupons. Salient Features below:

        • Sensitivity to interest rates and full duration risk in both currencies
        • FX risk is the same as any cross currency swap
        • As a dealer hedges this instrument the risk can be broken down to a fixed/float cross currency swap and a fixed interest rate swap against the floating benchmark on the CCS. For eg. a USDKRW fixed/fixed cross currency swap is composed of a USD SOFR float/KRW fixed rate cross currency swap and a USD SOFR fixed interest rate swap

     

    I do hope I’ve been able to keep you engaged and intrigued so far by following a building blocks approach to learning. Extending it further let’s combine ALL that we have discussed so far to build a bigger block of Cash and Financing products.

    Look forward to meeting you there.

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