Interest Rate Derivatives

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Interest Rate Derivatives

• Jasmine Lee
• Executive Manager Market Risk, Wealth Management,
  CBA
• jalee_at_colonialfirststate.com.au

2
Agenda

• Overview of the interest rate derivatives market
• Market conventions
• The swaps market
• More complex derivatives
• .and modelling
• Case study

3
The Market

• Vanilla products dominate
• SFE traded bill and bond futures
• Vanilla interest rate swaps
• Who buys the more complex derivatives (ie. with
  optionality)

4
Conventions traps for new players

• BBSW / BBSY What is it?
• Continuous rates vs market quotations
• Conventions matter!
• Compounding frequency
• Actual / 365 vs Actual / 360
• When are the payments actually made?

5
The products

• Interest Rate Futures
• Interest Rate Swap
• Interest Rate Cap
• Interest Rate Collar
• Digital Cap/Floor
• Knockout Swaps
• Layered Swaps
• Cross Currency Swap
• Swaptions

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Interest Rate Futures

• Predominately the Bank Bill Futures, 3yr Futures
  10yr Futures.
• 90 Day Bills Characteristics
• 1m Face Value, Maturity Mar/June/Sept/Dec,
  Settle 2nd Friday of Delivery month
• Delta Approx 24, quoted to 1bp
• 3 Year Bond Futures Characteristics
• 100 Face Value, 6 Coupon, 3yr, Maturity
  Mar/June/Sept/Dec, 15th Day of Contract Mth
• Delta Approx 28, quoted to 1bp
• 10 Year Bond Futures Characteristics
• 100th Face Value, 6 Coupon, 10yr, Maturity
  Mar/June/Sept/Dec, 15th Day of Contract Mth
• Delta Approx 80, quoted to .5bp
• Utilised by Traders as a hedging instrument, and
  as a basis for curve creation.

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A vanilla swap
Loan
Lending Bank
Client
Floating 3mth BBSY
Fixed
Floating 3mth BBSY
Swap party
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Why use swaps?

• To separate the funding decision and the interest
  rate hedging decision
• i.e. local bond market might be a fixed rate
  market
• premium paid by investors for liquidity?
• Buy corporate borrower might want to customise
  their liability side interest rate exposures, for
  example
• Or may want the flexibility to take on different
  exposures, such as part fixed / floating
• Monthly payments rather than semi

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Interest Rate Cap

• Protects against the floating rate rising above a
  certain level, the cap rate.
• When floating BBSW or BBSY sets below the cap
  strike they pay BBSW/BBSY. When floating
  BBSW/BBSY sets above the cap strike they are
  capped and pay the cap strike rate.

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Why Clients are using Caps

• Allows the client to benefit when floating rates
  fall (unlike a swap).
• The notional principal can be tailored to the
  debt structure (same as the swap).
• The option cost. Payable upfront or per roll.

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Interest Rate Collar

• Places a maximum or cap rate and a minimum or
  floor rate.
• When floating BBSW or BBSY sets between the cap
  and floor strike they pay BBSW/BBSY.
• When floating BBSW/BBSY sets above the cap strike
  they pay the cap rate.
• When BBSW/BBSY sets below the floor strike they
  pay the floor rate.

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Why Clients are using Collars

• Compared to paying the swap the client may
  benefit if rates stay towards the bottom of the
  collar.
• Selling the floor reduces the premium.
• Can be tailored to the debt structure (same as
  the others).
• Some Disadvantages
• Client doesnt benefit if rates go below the
  floor rate.
• Option cost. May still be a premium payable.

13
Digital Cap/Floor

• Similar in characteristic to Vanilla Caps/Floors.
• Their payoff profile is not gradual
• Pays out a set amount if option strike price is
  hit, is not dependant on how much in or out of
  the money.
• They have 2 states in or out, Binary in nature
• Eg. If you are long a digital and your strike
  price is hit you will receive a set pay out. As
  below if the 6 cap is hit you will receive 100bp
  for that roll.

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Knock Out Swap

• Two rates are set in a knockout swap. The fixed
  swap rate and the knockout rate. The knockout
  rate is higher than the fixed swap rate.
• If the floating rate sets below the knockout
  rate, you pay the fixed swap rate for that
  particular roll.
• The swap cover remains in place unless the
  floating rate sets at or above the knockout rate.
  On any rate set date, should this occur, you
  immediately revert to paying floating for that
  particular roll.
• The owner of the knockout swap has effectively
  gone long the swap, short a vanilla cap and short
  a digital cap. The pickup from selling the cap is
  used to reduce the swap rate. The obvious risk
  is that they are exposed above the cap level.

15
Layered Swap

• A layered swap entails a worst case rate, and a
  range where the fixed swap rate is applicable
• If the floating rate sets inside the range
  specified, you pay the agreed reduced fixed swap
  rate for that roll
• If the floating rate set at or beyond the range
  specified, then the worst case rate is payable
  for that roll
• The owner of the Layered Swap has effectively
  gone long the swap, short a Digital Cap and short
  a Digital Floor. The pickup from the shorts are
  used to reduce the swap rate within the range.

16
Swaptions

• Options allow you the flexibility to choose on a
  defined future date whether you, wish to enter
  into a standard swap at a known rate.
• In the event that market rates are above the
  swaption rate, you may enter into the swap at the
  lower rate, for all or part of the agreed face
  value.
• Alternatively, if your need for funds has
  disappeared altogether you may choose to cash
  settle if the contract is in your favour or do
  nothing at all if it is not.
• It gives you the right not the obligation

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Cross Currency Swap

• Generally involves an exchange of principal at
  both the front and back ends
• Generally removes the exchange rate risk as the
  same exchange rate is used at both the front and
  back ends.
• Involves the exchange of fixed interest payments
  in one currency for floating interest payments in
  another currency.
• Why are cross-currency swap used
• Utilised to create a liability in a currency
  different to the underlying funding currency,
  hence attempt to reduce translation risk
• Create a cash flow stream which matches revenue
  stream
• Activity in these products have increased in
  recent times as Australian borrowers have been
  looking to offshore markets for longer tenor
  funding at cheaper pricing, hence once issued
  they then need to swap the funds back into AUD.

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Pricing Valuation
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Pricing the vanilla swaps

• Most products can be priced off the prevailing
  interest rate curve, namely
• Swaps
• Futures and forwards
• Cross currency swaps
• Method
• Just project the payments due under each leg
  and
• Adjust the fixed rate (or margin added to the
  floating rate side) to make the PVs of the two
  payments streams equal

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Pricing Models beyond vanilla

• For the non-linear products, we need a model of
  how the yield curve evolves over time.
• Tread carefully
• Most models relate to continuously compounding
  rates (conventions again)
• But the reference rates relate to market quoted
  rates (e.g. Actual / 360 rates)
• Need to be able to project what the yield curve
  will look like at future times
• This is required is solve for future implied swap
  rates at future times
• How to model the evolution of the whole yield
  curve?
• Model the short rate with the rest of the curve a
  function of this rate?
• Mean reversion non-negative
• Normal sloping vs inverse yield curve
• Volatility across the curve

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Blacks model

• Applied to price vanilla interest rate
  derivatives
• bond options
• Interest rate caps and floors
• Swap-options
• No explicit assumptions made regarding the
  process followed by interest rate
• Assumes interest rates are log-normally
  distributed at the maturity of the option

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Pricing Models

• Short-Rate Models Equilibrium Models
• Models the instantaneous interest rates
• Comprises one-factor models and multiple factor
  models
• One factor models only have once source of
  uncertainty
• Key one-factor models include the following
• Rendleman and Bartter model
• Vasicek model
• Cox, Ingersoll, and Ross model
• May not fit the current yield curve

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Pricing Models

• Short-Rate Models Arbitrage Models
• Models the instantaneous interest rates
• Fits the existing yield curve
• Comprises models
• Key models include the following
• Ho-Lee Model
• Hull-White Model

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Pricing Models

• Partial Differential Equation Approaches eg.
  Black Scholes
• Effective for dealing with early exercise
• Deltas are easily calculated
• Not practical for large dimension problems
• Monte Carlo Method
• Effective for dealing with high dimensional
  problems
• Deltas are difficult to compute, method is
  often slow.
• Can handle early exercise, although is difficult
• One Popular method is the BGM (Brace, Gatarek
  Musiela)
• Models Libor rates which are directly observable
  in the market
• Is a term structure model (ie. Models the
  evolution of the whole yield curve)
• Models the dynamics (Stochastic Differential
  Equation) of the Libor rate which exist between
  discrete dates.

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Hedging
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Interest Rate Swap Hedging
A bank has entered into a swap to receive fixed
rate on 10m for 3yrs swap. For the bank to hedge
the risk it will need to short the futures and
EFP, or take the reverse trade with another
counterparty.

• Calculating the Number of Futures Required to
  hedge.
• Calculate the Delta of the Deal, i.e. The value
  of 1 basis point.
• Calculate the Delta of the relevant futures
  contracts.
• Utilising 3 Year Treasury Bond Futures as traded
  on SFE
• Divide the Deal Delta by the respective futures
  Delta.
• The corresponding number, is the number of the
  respective futures contract that you will need to
  sell to be delta hedged
• Eg. Deal Delta 2755, 3 Year Futures Delta
  27.56
• 2755/27.56 99.96
• Hence to be delta hedged will need to short 100
  3yr futures contract

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Interest Rate Cap Hedging

• Have both delta optionality (vega, gamma, etc)
  to consider
• Only perfect hedge is to do identically opposite
  trade with another counterparty.
• Hedge delta as per swap
• Considerations on hedging optionality
• do i just hedge "bottom line" Vega Gamma or
  match the term structure?
• what strike?
• what product do i hedge with?

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Case Study

• Scenario
• Client has an Offshore Asset
• Client has an offshore revenue stream
• Client will need to repatriate the revenue stream
  back to AUD
• Client has domestic borrowing
• Clients borrowing is all floating at a margin of
  25bp over BBSY
• Question
• What Risks does the Client Face?
• What Steps would you take to address these risk?
• What Products would you recommend be used?

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Answer

• Risks Client Faces
• Translation Risk
• FX Risk on revenue stream (Transaction Risk)
• Interest Rate Risk
• What Steps
• Execute a fixed for floating cross currency swap
  to create an offshore liability to match the
  offshore asset, hence removing the translation
  risk.
• Transaction risk is reduced as the offshore
  revenue can be utilised to pay offshore interest
  in the cross currency swap
• By Fixing in the swap the interest rate risk has
  been minimised by removing exposure to floating
  rates
• Any residual transaction risk exposure could be
  managed by FX Forwards or options, such as an FX
  Collar