QF5203 Lecture 5
Interest Rate Swaps and their Risk Measures
Part 2
1. References
2. A More Realistic Yield Curve Example
3. Single Currency Tenor Basis Swap
4. Cross Currency Swap
5. Simple Variations of Plain Vanilla Swaps
6. Common Exotic Swaps
7. The Evolution of Yield Curve Construction
8. Summary
9. Homework
10. Project
1. References
• Options, Futures and Other Derivatives, John Hull
• Interest Rate Option Models, Riccardo Rebonato
• Pricing and Trading Interest Rate Derivatives, H. Darbyshire
• QuantLib Python Cookbook, Gautham Balaraman, Luigi Ballabio
• https://www.quantlib.org/quantlibxl/
• For market conventions see https://opengamma.com/wp- content/uploads/2017/11/Interest-Rate-Instruments-and-Market- Conventions.pdf
2. A More Realistic Yield Curve Example
• In the previous lecture we looked at the case of using a flat yield curve in QuantLib Python/Excel in order to focus on the vanilla IRS cash flows
• Obviously, a flat yield curve is not realistic
• We will now show how to build a more realistic yield curve using Deposits, Short
Term Interest Rate Futures (STIRF’s) and Interest Rate Swaps
• We will also look at the functionality that QuantLib provides to study the risk sensitivities of a portfolio of interest rate swaps
2. A More Realistic Yield Curve Example
USD 3M Libor Swap Curve
T enor
Rate Used
Shift (Bp)
ON TN S/N 1W 2W 3W 1M 2M 3M
1.8200 1.7500 1.8000 1.7500 1.7000 1.6600 1.6100 1.4100 1.2200
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
F1
F2
F3
F4
F5
F6
F7
F8
99.4800 99.6200 99.6300 99.6900 99.7000 99.6900
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
99.6700
99.6400
3Y 4Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 30Y
0.4600 0.5100 0.5600 0.6800 0.8100 0.8600 0.9200 0.9700 1.0000 1.0100
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2. A More Realistic Yield Curve Example
General Inputs
Fixed Leg Details
Float Leg Details
Name
Obj ID
Error
Quote Date Result Ccy Spot Date Start Date Maturity End Date Notional
3-Apr-20
Ccy
Notional Start Date Maturity
End Date Pay/Rec
Fwd Swap Coupon Coupon Freq
Basis 30
Bus Day ConvM Pmt CalendUanrit
USD
Ccy Notional Start Date Maturity End Date Pay/Rec Margin Freq Basis
Bus Day ConvM
Pmt CalendUanrit
Reset CalUenditaer
USD
Fixed Leg Schedul
eUISDDFixedL
egSchedule
USD
100,000,000
100,000,000
Fixed Leg ID
USDFixedL
eg#0002
7-Apr-20
7-Apr-20
7-Apr-20
Fixed Leg NPV
7,802,552
7-Apr-20
10y
10y
10y
8-Apr-30
8-Apr-30
Float Leg Schedul
eUSDFloatL
gSchedule
8-Apr-30
REC
PAY
Float Leg Index ID
USDLiborIn
dex#0000
100,000,000
0.80800%
0.00%
Float Leg ID
USDLiborL
g#0000
0.80800%
Quarterly
Fixed Leg NPV
7,802,552
YcID US
Yield Curve#0000
Semiannual
Actual/360
/360 (Bond Basis)
odified Following
Vanilla Swap ID
USDVanilla
Swap#0000
odified Following
dStates::Settlement
dStates::Settlement
Kingdom::Settlement
Swap Engine ID
USDVanilla
SwapDisco
Pricing Engine ID
TRUE
NPV
0
Npv Details
Fixed Leg Float Leg
7,802,552 USD 7,802,552 7.80% -7,801,081 USD -7,801,081 -7.80%
7,802,552
-7,802,552
Npv Deal
1,471 0.00%
0
e
e
#0002
#0002
untingSwapEngine#00
D
e
e d
0
3. Single Currency Tenor Basis Swap
• In a tenor basis swap, there is no fixed leg, and one party pays/receives a (floating) LIBOR of one tenor (e.g. 3m) and the other party receives/pays a (floating) LIBOR of a different tenor (e.g. 6m)
• Note that in a tenor basis swap the notional on which the rate is applied is in the same currency
• Other important examples of tenor basis swaps include Overnight Index Swaps (OIS) where the underlying index is a one-day rate, versus LIBOR (e.g. 3m)
• Theoretically there should be no basis between LIBOR rates of different tenors (see tenor basis swap spreadsheet included in course material)
• In practice there is a basis and market practice is to add it to the leg with the shorter tenor
3. Single Currency Tenor Basis Swap
General Inputs
Leg 1 Float Details
Leg 2 Float Details
Quote Date Ccy
Set Evaluation
Days to Spot Spot Date
3-Apr-20
Notional Start Date Maturity End Date Pay/Rec Float Margin Frequency
YAieclcdrCuuarlvBeasis
Float Index
tBus Day Conv M
Pmt CalendaUrnit Reset CalenUdnaitre
100,000,000
Notional
Start Date Maturity
End Date Pay/Rec Float Margin Frequency Accrual Basis Float Index
Bus Day Conv M
Pmt CalendaUrnit Reset CalenUdnaitre
100,000,000
USD
7-Apr-20
7-Apr-20
DaTteRUE
5y
5y
2
7-Apr-25
7-Apr-25
7-Apr-20
REC
PAY
0.0000%
0.0000%
Yield Curve Inputs
Quarterly
Semiannual
Handle
Ndays Calendar
Rate
Day Count Compounding Frequency
Yc ID
USDBasisSwapFlatFwd
Actual/360
Actual/360
0
LIBOR3M
LIBOR6M
UnitedStates::Settlemen
odified Followin
g
odified Following
4.00%
dStates::Settlement
dStates::Settlement
Actual/365 (Fixed)
Kingdom::Settlement
Kingdom::Settlement
Continuous
Annual
USDBasisSwapFlatFwdYieldCurve#0005
Npv Details
Leg 1
18,127,948
Leg 2
-18,127,948
Net
-0
ee
dd
4. Cross Currency Swap
• In a cross currency basis swap one party pays (or receives) a foreign floating LIBOR rate (e.g. USD LIBOR 3m) on an notional denominated in the foreign currency, and receives (or pays) a domestic floating LIBOR rate (e.g. JPY LIBOR 3m) on a notional denominated in the domestic currency
• On the start date of the swap there is an initial exchange of notional where the payer (or receiver) of the foreign floating leg receives (or pays) the foreign notional from (or to) the counterparty and pays (or receives) the domestic notional to (or from) the counterparty
• On the maturity date of the swap there is a final exchange of notional where the payer (or receiver) of the USD floating leg pays (or receives) the foreign notional to (or from) the counterparty and receives (or pays) the domestic notional from (or to) the counterparty
4. Cross Currency Swap
General Inputs
Ccy1 Fixed/Float Details
Ccy2 Fixed/Float Details
Quote Date
Set Evaluation
Result Ccy Days to Spot Spot Date
3-Apr-20
Ccy
Notional Notional Exchan Start Date Maturity
End Date Pay/Rec Fixed/Floating Fixed Rate
Float Margin Frequency Accrual Basis Fixing Method
FwlodaYtieInldCeuxrve
Bus Day Conv M
t P m t C a l e n d a Ur n i t Reset CalenUdnaitre Days To Spot
USD
Ccy
Notional Notional Exchan Start Date Maturity
End Date Pay/Rec Fixed/Floating Fixed Rate
Float Margin Frequency Accrual Basis Fixing Method Float Index
Bus Day Conv M
Pmt CalendaUrnit Reset CalenUdnaitre Days To Spot
JPY
DaTteRUE
100,000,000
11,000,000,000
USD
ge BOTH
ge BOTH
2
7-Apr-20
7-Apr-20
7-Apr-20
10Y
10Y
8-Apr-30
8-Apr-30
Fx Details
REC
PAY
USD/JPY
110.00
FLOAT
FLOAT
0.0000%
0.0000%
0.00000%
0.0000%
Quarterly
Quarterly
Actual/360
Actual/360
Yield Curve 1 Inputs
ADVANCE
ADVANCE
Handle
Ndays Calendar
Rate
Day Count Compounding Frequency
Yc ID
USDCrossCcySwapFlat
LIBOR3M
LIBOR3M
0
odified Followin
g
odified Following
UnitedStates::Settlemen
dStates::Settlement
dStates::Settlement
4.00%
Kingdom::Settlement
Kingdom::Settlement
Actual/365 (Fixed)
2
2
Continuous
Annual
Ccy1 Bullet Payment Details
Ccy2 Bullet Payment Details
USDCrossCcySwapFl
tFwdYDiealtdeCurve
000A6 mount
Date
Amount
7-Apr-20
-100,000,000
7-Apr-20
11,000,000,000
Yield Curve 2 Inputs
8-Apr-30
100,000,000
8-Apr-30
-11,000,000,000
Handle
Ndays Calendar
Rate
Day Count Compounding Frequency
Yc ID
JPYCrossCcySwapFlatFwdYieldCurve
0
Japan
1.00%
Npv Details
Actual/365 (Fixed)
USD
JPY
Npv (USD)
Continuous
Upfront Pmts
-99,956,174
10,998,794,587
32,868
Annual
Backend Pmts
66,980,603
-9,951,302,946
-23,485,788
JPYCrossCcySwapFla
tFiwxeddY/FieloldaCtiunrgveL#
0g00352,975,571
-1,047,491,640
23,452,920
Fees
0
0
0
Net
0
0
0
ee
dd
a#
e
5. Simple Variations of Plain Vanilla Swaps
• Forward Starting Swaps
➢ A forward starting fixed versus floating interest rate swap is identical to a plain vanilla fixed versus floating interest rate swap except for the fact that it does not start from the spot date (e.g. a 5y 5y forward fixed versus floating interest rate swap starts in 5y from today and ends in 10y from today)
➢ The equilibrium swap rate is obtained in the usual way, namely the fixed rate for which the PV of the fixed leg equals the PV of the floating leg
➢ Note that this is a non-standard swap and would need to be quoted on a bespoke basis by a bank’s trading desk (banks or brokers do not provide screens with these rates)
➢ Forward starting swaps are very sensitive to the forward LIBOR rates, and so interpolation choices are very important
5. Simple Variations of Plain Vanilla Swaps
• Amortising Swaps
➢ Variation of a plain vanilla fixed versus floating swap where the notional on the fixed and/or floating legs amortises according to a pre-specified schedule
• Accreting Swaps
➢ Variation of a plain vanilla fixed versus floating swap where the notional on
the fixed and/or floating legs accretes according to a pre-specified schedule
• Step Up Coupon Swaps
➢ Variation of a plain vanilla fixed versus floating swap where the fixed rate steps up or down
Note that in each case the equilibrium swap rate is obtained in the usual way, namely the fixed rate for which the PV of the fixed leg equals the PV of the floating leg
6. Common Exotic Swaps
• LIBOR-in- Arrears Swap
➢ With a plain vanilla swap the LIBOR rate fixes at the beginning of the accrual period and
pays at the beginning of the period
➢ With a LIBOR in arrears swap the LIBOR rate fixes at the end of the period and pays at the end of the period
➢ A convexity adjustment is required because the forward LIBOR rate is no longer a Martingale under the measure induced by the zero coupon bond associated with the start of the accrual period
• Constant Maturity Swap
➢ A constant maturity swap (CMS) is a fixed versus floating swap where the floating index is a
forward swap rate
➢ As with the LIBOR-in-arrears swap a convexity adjustment is required for accurate pricing
• Quanto Swap
➢ A quanto swap is a fixed versus floating swap where the floating index (e.g. LIBOR) is
associated with a different currency than the notional it is applied to
➢ A quanto adjustment to the LIBOR forward rate is required for accurate pricing
7. Yield Curve Construction – Pre GFC
• Before the financial crisis there was little or no difference between Libor rates of different tenors and similarly the Libor-OIS spread was relatively small and stable
• A single zero coupon curve used for both projecting Libor forwards and discounting future cash flows
• Implicitly assumed Libor funding
• No tenor basis
• Yield Curve Instruments included: ✓ Cash
✓FRAs/Futures (eventually included convexity adjustment) ✓ Swaps
• Combined with an interpolation scheme one bootstraps the discount factors
• Leads to a simple expression the PV of the floating leg (see next slide)
7. Yield Curve Construction – Pre GFC
• Recall the interest rate pricing constraints from the previous lecture: 𝐿𝑡;𝑡,𝑡 = 1 𝑍(𝑡;𝑡𝑗) −1
σ𝑁𝐹𝑙𝑡𝐿 𝑡;𝑡 ,𝑡 𝛿 𝑡 ,𝑡 𝑍(𝑡;𝑡) 𝑗=1 𝑗−1 𝑗 𝑗−1 𝑗 𝑗
𝑗 𝑗+1
𝛿(𝑡,𝑡 ) 𝑍(𝑡;𝑡 ) 𝑗 𝑗+1 𝑗+1
𝑆𝑡=
𝑃𝑉 𝐹𝑙𝑜𝑎𝑡𝑖𝑛𝑔 𝐿𝑒𝑔 = 𝑍(𝑡; 𝑡𝑠) − 𝑍(𝑡; 𝑡𝑒)
σ𝑁𝐹𝑖𝑥𝛼𝑡 ,𝑡𝑍(𝑡;𝑡)
• In the above 𝑆 𝑡
present value of the fixed and floating legs are equal
𝑗=1
𝑗−1𝑗 𝑗
is ‘equilibrium’ swap rate, namely the fixed rate for which the
7. Yield Curve Construction – Pre GFC
• The next level of sophistication came about with the need to include FX related instruments (i.e. FX Forwards and Cross Currency Basis Swaps) into a consistent framework
• This was the first attempt by a few (notably USD based banks) to incorporate a separate forecasting and discounting curves
• Yield Curve Instruments included: ✓ Cash
✓ FRAs/Futures (eventually included convexity adjustment)
✓ Swaps
✓ FX Forwards (up to about 1y) and then Cross Currency Basis Swaps
• Two curves must be bootstrapped together and therefore requires an optimisation approach rather than simple bootstrapping
• The pricing constraints and screen shot of a cross currency swap are shown on the next two slides
7. Yield Curve Construction – Pre GFC
• The generalization of the pricing constraints is given by:
𝑈𝑆𝐷
1 𝑍𝑈𝑆𝐷(𝑡;𝑡𝑗) 𝐶𝐶𝑌
1 𝑍𝐶𝐶𝑌(𝑡;𝑡𝑗) 𝛿(𝑡𝑗,𝑡𝑗+1) 𝑍𝐶𝐶𝑌(𝑡;𝑡𝑗+1)
𝐿 𝑡;𝑡,𝑡
𝑗 𝑗+1
σ 𝑆𝑈𝑆𝐷 𝑡 = 𝑗=1
=
𝑁𝐹𝑙𝑡 𝑈𝑆𝐷 𝑈𝑆𝐷
𝑡;𝑡,𝑡
𝑗 𝑗+1
σ
𝑗 ;𝑆𝐶𝐶𝑌 𝑡 = 𝑗=1
−1
𝛿(𝑡𝑗,𝑡𝑗+1) 𝑍𝑈𝑆𝐷(𝑡;𝑡𝑗+1)
−1 ;𝐿
=
𝑁𝐹𝑙𝑡 𝐶𝐶𝑌
𝐿
𝑡;𝑡 ,𝑡 𝛿𝑡 ,𝑡 𝑍 𝑗−1 𝑗 𝑗−1 𝑗
(𝑡;𝑡)
𝐶𝐶𝑌
𝑗−1 𝑗 𝑗−1 𝑗 𝑗
σ𝑁𝐹𝑖𝑥 𝛼 𝑡 ,𝑡 𝑍𝐶𝐶𝑌(𝑡;𝑡 ) 𝑗=1 𝑗−1 𝑗 𝑗
(𝑡;𝑡𝑒) +
𝐿 𝑡;𝑡 ,𝑡 𝛿𝑡
,𝑡 𝑍
(𝑡;𝑡)
𝑈𝑆𝐷
𝑡;𝑡𝑗 −𝑍
σ𝑁𝐹𝑖𝑥 𝛼 𝑡 ,𝑡 𝑍𝑈𝑆𝐷(𝑡;𝑡 ) 𝑗=1 𝑗−1 𝑗 𝑗
𝑁𝐹𝑙𝑡 𝑈𝑆𝐷
𝑡;𝑡𝑠 −σ𝑗=1 𝐿 𝑡;𝑡𝑗−1,𝑡𝑗 𝛿 𝑡𝑗−1,𝑡𝑗 𝑍
𝐶𝐶𝑌
𝑈𝑆𝐷
𝑈𝑆𝐷
𝑀 = 𝑍
𝑍
σ𝑁𝐹𝑖𝑥 𝛼 𝑡𝑗−1,𝑡𝑗 𝑍𝐶𝐶𝑌(𝑡;𝑡𝑗) 𝑗=1
𝑁
𝑡;𝑡𝑠 −σ𝑗=1 𝐿 𝑡;𝑡𝑗−1,𝑡𝑗 𝛿 𝑡𝑗−1,𝑡𝑗 𝑍
σ𝑁𝐹𝑖𝑥 𝛼 𝑡𝑗−1,𝑡𝑗 𝑍𝐶𝐶𝑌(𝑡;𝑡𝑗) 𝑗=1
𝐹𝑙𝑡 𝐶𝐶𝑌 𝐶𝐶𝑌
𝑡;𝑡𝑗 −𝑍
𝐶𝐶𝑌
(𝑡;𝑡𝑒)
7. Yield Curve Construction – Post GFC
• In the aftermath of the first credit crisis, single currency tenor basis swaps no longer traded with a zero basis due to a combination of credit and liquidity concerns
• Now tenor basis must be explicitly included in our curve construction and separate Libor projection curves are needed for each index
• Yield Curve Instruments needed to include: ✓ Deposits
✓ FRAs/Futures (eventually included convexity adjustment)
✓ Swaps
✓ FX Forwards (up to about 1y) and then Cross Currency Basis Swaps ✓ Tenor basis swaps (e.g. 3m versus 6m, etc.)
• Earlier in this lecture we went through the cash flows for a USD LIBOR 3m versus USD LIBOR 6m tenor basis swap
7. Yield Curve Construction – Post GFC
• Another consequence of the GFC is that the LIBOR-OIS basis dramatically widened, and whereas before the GFC this spread amount to less than 10bp, during the GFC it widened to more than 300bp
• This called into question the long standing assumption that LIBOR was a good proxy for the risk free rate required in derivatives valuation
• The overnight index swap (OIS) became the market standard risk free rate to be used for discounting cash flows
• Overnight Indexes are indexes related to interbank lending over a one day time horizon
• The OIS rate is paid on a compounding basis (see Open Gamma page 43)
• The main OIS indices are: ➢ FED FUNDS
➢ EONIA ➢ SONIA ➢ TONAR
7. Yield Curve Construction – Post GFC
• A further level of complexity was introduced into the swap yield curve construction as a result of the realization that the collateral arrangements with counterparties directly impacted the rate to be used for discounting
• There seems to be widespread agreement that the appropriate funding curve to use is the one associated with the collateral rate specified in the CSA (hence the name CSA discounting)
• However, due to the variety of CSA agreements, I need to be able to discount any swap using any one of a number of funding curves (e.g. with EUR swap with an assumed USD OIS funding
• With one counterparty I might have a EUR swap with a CSA which specifies a USD OIS collateral rate but with another counterparty I might have a EUR swap with a CSA which specifies JPY OIS and furthermore I will almost certainly have swaps cleared through LCH for which EUR OIS is the relevant collateral rate
• The extra funding curves are constructed similarly to the extra index curves where we now our discount factors are indexed according to the relevant funding curve
7. Yield Curve Construction – Post GFC
• What is a CSA?
• A CSA stands for Credit Support Annex and is essentially an agreement which specifies the details as to how two parties in an OTC derivative transaction will exchange collateral
• Important information in a CSA includes:
➢ frequency at which collateral is to be exchanged and any associated haircuts ➢ type of collateral to be exchanged (e.g. cash, government bonds, etc.)
➢ specification of any thresholds (e.g. zero threshold or …)
➢ rehypothecation rights (defines what I can do with the collateral)
➢ bilateral/unilateral
7. Yield Curve Construction – Post GFC
• CSA agreements often grant one or more counterparties the choice of posting one of several types of collateral (e.g. cash in one 3 currencies, say)
• Such a CSA has embedded in it a chooser type option
• The rational counterparty will choose the collateral for which he obtains the
highest rate of return
• In principle one needs to have a complex term structure model containing various basis spread volatilities and numerous correlations
• Some (albeit less accurate) alternatives to such a complete framework would be
• Assume a spot cheapest to deliver collateral rate and use this to discount all
future cash flows
• Calculate the intrinsic value of the embedded option on each future cash flow date and use this as the relevant discounting rate
7. Yield Curve Construction – The Future
• As a result of a few high profile scandals, largely on the back of the global financial crisis (GFC), the various regulators have decided that IBOR is
• SOFR (Secured Overnight Financing Rate) has been chosen by the U.S. Federal Reserve’s Alternative Reference Rates Committee (ARRC) as the alternative reference benchmark to replace U.S. LIBOR
• In Europe, ESTR is the replacement for EONIA, SONIA will continue as the risk free rate for the United Kingdom, and TONAR will continue as the risk free rate for Japan
8. Summary
• Before the GFC the use of LIBOR as a discounting curve was market practice
• There was no appreciable basis between LIBOR rates of different tenors
• The use of the same set of discount factors for forward LIBOR rate projection and the discounting of future cash flows led to a simple formula for the floating leg of a swap
• The first attempt to separate forecasting from discounting arose as a result of some (mostly US based) banks using the cross currency basis swap to introduce a USD LIBOR 3m funding assumption into the valuation of their multi-currency swap books
• A simple algebraic bootstrapping process was therefore no longer possible and the determination of the (two) discount curves required the use of a multi- dimensional solver
8. Summary
• From a derivatives valuation perspective, there were two important consequences that emerged as a result of the GFC
• First, tenor basis swap no longer traded a flat and so going forward any yield curve construction algorithm needed to explicitly incorporate this non-zero basis as a constraint that needed to be satisfied
• Secondly, LIBOR-OIS basis swaps widened dramatically, calling into question the use of LIBOR as a risk free rate
• Therefore, even for the case of single currency yield curve construction, the separation of projection and discounting became the market standard and quickly led to clearing houses like LCH adoption OIS discounting for their valuations
8. Summary
• The realisation that OIS discounting was required to reflect the requirement to use a risk free rate, was quickly followed by the realisation that discount curves need to be ‘CSA aware’
• CSA agreements had previously include the option to post different types of collateral (e.g. UST’s or Gilts or JGBs) and a modern yield curve infrastructure needs to incorporate this collateral optionality
•
9. Homework 5.1
• UsingQuantLibPython,implementtheUSDyieldcurvewithdata provided on slide 5 in a Jupyter notebook.
• Assume the same curve construction date of 3 April 2020
• Demonstrate that your yield curve is able to reproduce the same
inputs that were used to bootstrap the curve.
• Please submit by 13 June 2020
10. Term Project 1 – A Modern Yield Curve
• Using QuantLib Python or QuantLib Excel bootstrap a multi-yield curve which bootstraps a USD swap yield curve using the instruments shown on slide 30, namely LIBOR 3m deposits, Interest Rate Futures, OIS swaps, 1m/3m and, 3m/6m tenor basis swaps
• Assume a curve construction date of 3 April 2020
• The instrument definition for USD OIS swaps are
➢ Up to and Including 1y: Annual fixed rate versus OIS compounded and paid at maturity on an A/360 basis
➢ Beyond 1y: Annual A/360 fixed rate versus OIS compounded annually and paid on an A/360 basis
• Assume that the LIBOR-based instruments shown on slide 30 are OIS discounted
• Confirm that your bootstrapped yield curve is self-consistent by demonstrating
that you can recover the inputs of the instruments used to bootstrap it
• Consider the following portfolio of FRAs, forward starting swaps and tenor basis swaps
10. Term Project 1 – A Modern Yield Curve
• Consider the following portfolio of FRAs, forward starting swaps and tenor basis swaps
1. USD 200m of a 9×12 ATM Payer FRA
2. USD 150m of a 6×12 ATM Receiver FRA
3. USD 300m of a 10y 10y ATM forward starting Payer swap
4. USD 100m of a 5y 5y ATM forward starting Receiver swap
5. USD 100m of a 5y Pay LIBOR 3m versus Receive OIS tenor basis swap + Spread
• For the FRAs and Swaps in 1-4 what is the ATM rate?
• For the LIBOR/OIS tenor basis swap, what is the equilibrium (i.e. fair) spread?
• Produce a risk report showing the sensitivity of this portfolio to a 1bp change in each of the yield curve inputs
• Please submit by 15 June 2020 and be sure to include plenty of comments in your notebook/Excel Spreadsheet
7. Term Project 1
USD OIS Curve
USD 3M Libor
USD 1M/3M Libor
USD 3M/6M Libor
T enor
Rate Used
T enor
Rate Used
T enor
Spread (bp)
T enor
Spread (bp)
ON TN S/N 1W 2W 3W 1M 2M 3M 6M 9M
1.6000 1.5900 1.5900 1.5900 1.5900 1.5900 1.5900 1.5800 1.5700 1.5100 1.4500
ON TN S/N 1W 2W 3W 1M 2M 3M
1.7500 1.7500 1.7500 1.7500 1.7500 1.7500 1.7500 1.7500 1.7500
ON TN S/N 1W 2W 3Y 4Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 30Y
15.0000 12.0000 10.0000 9.0000 8.0000 8.0000 8.0000 8.0000 8.0000 8.0000 8.0000 8.0000 8.0000 8.0000 8.0000
ON TN S/N 1W 2W 3Y 4Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 30Y
20.0000 15.0000 12.0000 11.0000 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
F1
F2
F3
F4
F5
F6
F7
F8
98.3500 98.4700 98.6000 98.6400 98.7500 98.7900
1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y 12Y 15Y 20Y 25Y 30Y
1.3800 1.2200 1.1200 1.1400 1.1500 1.1600 1.1800 1.2100 1.2400 1.2700 1.3100 1.3700 1.4300 1.4500 1.4600
98.8100
98.7800
3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y 12Y 15Y 20Y 25Y 30Y
1.3400 1.3300 1.3300 1.3500 1.3700 1.4000 1.4300 1.4600 1.5100 1.5700 1.6300 1.6500 1.6600