fnce 4040 derivatives chapter 4 - leeds-courses.colorado
TRANSCRIPT
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FNCE 4040β Derivatives
Chapter 4
Interest Rates
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Goals
β’ Discuss the types of rates needed for
Derivative Pricing
β’ Continuous Compounding
β’ Yield Curves
β’ Risk
β’ Forward Rate Agreements (FRA)
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Types of Rates
β’ For the purpose of this class there are three
types of interest rates that are relevant
β LIBOR
β Risk-free rates
β Interest Rates on collateral
β’ Important but out of scope rates include:
β Treasuries
β Overnight Interest Rate Swaps (OIS)
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
LIBOR
β’ London Interbank Offered Rate
β This is the rate of interest at which a bank is
prepared to borrow from another bank.
β It is compiled for a variety of maturities ranging
from Overnight to 1 year
β It exists on all 5 currencies β CHF, EUR, GBP,
JPY and USD
β It is compiled once a day ICE Benchmark
Administration (IBA)
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
LIBOR Process
β’ Once a day major banks submit the answer
to the following question
βAt what rate could you borrow funds, were
you to do so by asking and then accepting
inter-bank offers in a reasonable market size
just prior to 11am London time?β
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Uses of LIBOR
β’ LIBOR rates are used for
β Interest Rate Futures β’ This is a futures contract whose price is derived by the interest
paid on 3-Month LIBOR
β Interest Rate Swaps β’ These are derivative instruments that βswapβ LIBOR for fixed
interest rates generally for three or six month period. The maturity
of these tends to be 3 to 50 years
β Mortgages β’ Some Adjustable Rate Mortgages are linked to LIBOR rates
β Benchmark rate for short-term borrowing in the market.
β There has been a scandal surrounding LIBOR for the past
few years. If interested see the appendix.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
RISK FREE RATE
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
The Risk-Free Rate
β’ Derivatives pricing originally depended upon
a βrisk-freeβ rate β The risk-free rate traditionally used by derivatives
practitioners was LIBOR
β Treasuries are an alternative but were
considered to be artificially low for a number of
reasons β’ Treasury bills and bonds must be purchased by financial
institutions to satisfy a variety of regulatory requirements.
Increases demand and decreases yield
β’ The amount of capital a bank has to have in order to support an
investment in treasury bills and bonds is lower
β’ Treasuries have a favorable tax treatment
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
The Risk-Free Rate
β’ In this course we will generally assume that
risk-free rates exist and they will be given to
you.
β’ We will assume that LIBOR is the risk-free
rate
β’ We will give you rates.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Collateral Based Discounting
β’ Derivatives pricing theory has moved to
Collateral Based Discounting β The yield curve relevant for discounting depends
on the collateral agreement
β Every derivatives contract might have a different
yield curve
β’ When we discuss pricing we will work through
at least one collateralized example
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
THE YIELD CURVE
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Yield Curve
β’ When pricing derivatives we will need a yield
curve.
β’ For our purposes a yield curve will consist of β Yields to specified maturities,
β A methodology for interpolating missing yields,
β A methodology for calculating forward rates
(rates that are for borrowing/lending starting in
the future)
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Theories of the Term Structure
β’ Liquidity Preference Theory: forward rates
higher than expected future zero rates
β’ Market Segmentation: short, medium and
long rates determined independently of each
other
β’ Expectations Theory: forward rates equal
expected future zero rates
β The Derivatives market uses this theory.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
CONTINUOUSLY
COMPOUNDED ZERO RATES
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Continuous Compounding
β’ The compounding frequency used for an
interest rate is the unit of measurement
β’ All else being equal, a more frequent
compounding frequency results in a higher
value of the investment at maturity
β’ In this class interest rates will be quoted as
continuously compounded zero rates
β Except when we are discussing a specific
instrument or market β for example LIBOR or
swap rates.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Continuous Compounding
β’ A zero rate (or spot rate), for maturity T is the rate of
interest earned on an investment that provides a
payoff only at time T
β’ Continuous compounding means that an investment
is instantaneously reinvested.
β’ In practical terms this means β $100 grows to $100 Γ ππ ππ when invested at a
continuously compounded rate π πΆ to time π
β Conversely, $100 paid at time π has a present value of
$100 Γ πβπ ππ, when the continuously compounded
discount rate to time π is π π
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Practice
Maturity
(years)
Continuously
Compounded
Zero Rate
Present
Value
Future
Value
1 4.0000% 961 1,000
2 3.0000% 2,000 2,124
1.5 6.0000% -6,398 -7,000
3 1.5000% 4,000 4,184
Remember: PV = πΉπ β πβπ ππ
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Other Interest Rates
β’ The quoting convention for quoted interest
rates involves a daycount convention.
β’ Through this one can compute the interest
owed.
β’ There are two examples we will use in class β ACT/360 β The interest owed is
πππ‘π Γπ΄ππ‘π’ππ π·ππ¦π ππ ππππππ
360
β ACT/365 β The interest owed is
πππ‘π Γπ΄ππ‘π’ππ π·ππ¦π ππ ππππππ
365
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Start
(days)
End
(days) Rate
Daycount
Basis Notional Interest
0 365 3.00% 360 1,000,000 30,417
0 365 4.00% 365 1,000,000 40,000
182 365 3.00% 360 1,000,000 15,250
180 290 2.00% 365 1,000,000 6,027
Practice
πΌππ‘ππππ π‘ = πππ‘πππππ Γ πππ‘π Γπ΄ππ‘π’ππ π·ππ¦π ππ ππππππ
π·ππ¦πππ’ππ‘
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Conversion
β’ We will often have rates given in a particular
form and have to convert to another.
β’ We can do this by computing the investment
return from the given rate and using this to
compute the unknown rate, or equating PVs:
ππππβπππ¦π /365 = 1 + ππ΄πΆπ/360πππ¦π
360
ππ = πβπππβπππ¦π /365 =1
1 + ππ΄πΆπ/360πππ¦π 360
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Practice
Start End ACT/360
Rate
ACT/365
Rate
C. comp.
Rate
0 365 3.00% 3.0417% 2.9963%
0 365 4.00% 4.0556% 3.9755%
182 365 3.00% 3.0417% 3.0187%
1 + ππ΄πΆπ/360πππ¦π
360= 1 + ππ΄πΆπ/365
πππ¦π
365= ππππβπππ¦π /365
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
INTERPOLATION BETWEEN
RATES
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Interpolation
β’ When interpolating between rates we will
linearly interpolate continuously compounded
zero rates.
β’ The advantages of doing this are:
β It is easy to explain and implement
β It has great risk properties
β’ Sophisticated spline techniques are common
in the market.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Linear Interpolation
β’ If we know continuously compounded zero
rates π§1 and π§2 for two times π‘1 and π‘2 then
for time π‘ between π‘1 and π‘2 we define
π π‘ = π1 +π2 β π1π‘2 β π‘1
π‘ β π‘1
π‘1 π‘2
π1
π2
π‘
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Practice
Time 1
years
Rate 1
cc zero
Time 2
years
Rate 2
cc zero
Maturity
years Rate
1 4.0000% 2 5.0000% 1.5 4.500%
1.5 2.0000% 2 1.5000% 1.8 1.700%
2 1.0000% 3 2.0000% 2.2 1.200%
π π‘ = π1 +π2 β π1π‘2 β π‘1
π‘ β π‘1
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FORWARD RATES
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Forward Rates
β’ The forward rate is the future zero rate
implied by todayβs term structure of
interest rates
πππΓ(π2βπ1)
ππ 2Γπ2
ππ 1Γπ1
ππ 1Γπ1πππΓ(π2βπ1) = ππ 2Γπ2
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Formula for Forward Rates
β’ Suppose that the zero rates for time periods
T1 and T2 are R1 and R2 with both rates
continuously compounded
β’ The forward rate for the period between times
T1 and T2 is
12
1122
TT
TRTR
β’ This formula is only approximately true when
rates are not expressed with continuous
compounding
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Practice
Time 1
years
Rate 1
cc zero
Time 2
years
Rate 2
cc zero
Forward Rate
between ππ and ππ
1 4.0000% 2 5.0000% 6.0000%
1.5 2.0000% 2 1.7500% 1.0000%
2 1.0000% 3 2.0000% 4.0000%
πΉ1,2 =π 2π2 β π 1π1π2 β π1
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Industry Calc. of Rate Sensitivity: dv01
β’ Traders in practice use dv01: dollar value of
1bp increase in rates
β’ Shock interest rates by +1bp and compute
dollar change dv01
β’ Also compute bucketed dv01 β Shock interest rates by 1bp at various tenor
buckets
β Compute dollar impact of each individual shock
β You obtain a term structure of dv01s
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Example
β’ Consider an investment which pays
$1,000,000 in 1-years time. The one-year
continuously compounded zero rate is 3.00%.
β’ The present value of this investment is:
ππ = $1,000,000 β πβ0.03 = $970,446.53
β’ If interest rates increase by one basis-point
then the new PV will be:
ππ = $1,000,000 β πβ0.0301 = $970,348.49
β’ Thus the dv01 is -97.04 dollars.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Practice
Amount C.C.
Zero rate Maturity Original PV Bumped PV dv01
1,000,000 3.000% 1 $ 970,445.53 $ 970,348.49 $(97.04)
1,000,000 4.000% 1 $ 960,789.44 $ 960,693.37 $(96.07)
1,000,000 3.000% 2 $ 941,764.53 $ 941,576.20 $(188.33)
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FORWARD RATE AGREEMENT
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Forward Rate Agreement (FRA)
β’ A Forward Rate Agreement (FRA) is an OTC
agreement such that a certain interest rate
will apply to either borrowing or lending a
principal over a specified future period of
time.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Example
β’ For example a bank agrees to lend 1m USD
for 1 year starting in 1 year at an interest rate
of 3%. The rate is quoted with an ACT/360
daycount basis.
Year 1 Year 2
today
1π πππ·
1π πππ·
$1π365
3603.00% = 30,416.67
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FRA Mechanics / Valuation β part 1
β’ From the lenderβs viewpoint
β’ A loan of π from π1 to π2 at an agreed rate π πΎ
β’ Let π· be the daycount fraction from π1 to π2
β For an FRA π· =π·ππ¦π π2 βπ·ππ¦π (π1)
360
π1 π2 today
Interest owed:
π Γ π πΎ Γ π·
π
π
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
ππ = βπ β πβπ1π1 +π β 1 + π πΎ β π· β πβπ2π2
FRA Mechanics / Valuation β part 1
β’ We can value the FRA given the continuously
compounded zero rates π1 and π2.
π1 π2 today
Interest owed:
π β π πΎ β π·
π
π
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
The Fair FRA Rate
β’ The fair FRA rate π πΉ is the rate such that the
sum of the PV of both cash flows is zero:
ππβπ1π1 = π 1 + π πΉπ· πβπ2π2
β’ You can use the above to solve for π πΉ:
πβπ1π1 = 1 + π πΉπ· πβπ2π2
π πΉ =π π2π2βπ1π1 β 1
π·
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
The Fair FRA Rate
β’ We know that the PV of a loan from π1 to π2
at an agreed rate π πΎ with daycount fraction π·
from π1 to π2 is
ππ = βππβπ1π1 +π 1 + π πΎπ· πβπ2π2
β’ Combine this with the definition of the fair rate
from the previous page and obtain:
ππ = βπ 1 + π πΉπ· πβπ2π2 +π 1 + π πΎπ· π
βπ2π2
π·π½ = π΅ πΉπ² β πΉπ π«πβπππ»π
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Forward Rate Agreement (cont.)
β’ Equivalent to an agreement where interest at
a predetermined rate, RK is exchanged for
interest at the market rate
β’ Value an FRA by assuming that the forward
rate RF, is certain (has been discovered)
β’ So the value of an FRA is the PV of the
difference between:
β the interest that would be paid at rate RF and
β the interest that has to be paid at rate RK
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FRA Mechanics / Valuation β part 2 β’ A loan from π1 to π2
β’ From the lenderβs viewpoint
π1 π2
Fair rate now for
period π1, π2 = π πΎ
today
Interest owed:
π Γ π πΎ Γ π2 β π1
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Think of Mark-To-Market as the cost to offsetting
your position
FRA Mechanics / Valuation β part 2
Interest owed:
π Γ π πΎ Γ π2 β π1
πβπ 2Γπ2
π1 π2 today
Fair rate for period
π1, π2 moves to πΉπ
Interest now prevailing:
π Γ πΉπ Γ π2 β π1 Take the difference
and PV
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FRA example 1
β’ For example a bank agrees to lend 1m USD
for 1 year starting in 1 year at an interest rate
of 3%. The rate is quoted with an ACT/360
daycount basis.
β’ Assume that the interest rates are as follows:
Maturity
Continuously Compounded
Zero Rate
1 2.50%
2 2.60%
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
cc zero PV
2.50% -975,310
2.60% 978,205
FRA example 1 β Cashflows
Year 1 Year 2
today
1π πππ·
1π πππ·
$1π365
3603.00% = 30,416.67
Maturity Cashflow
1 -1,000,000
2 1,030,417
ππ = 978,205 β 975,310 = 2,895
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FRA example 2
β’ For example a bank agrees to lend 1m USD
for 1 year starting in 1 year at the fair FRA
rate. The rate is quoted with an ACT/360
daycount basis. At what rate do they lend?
β’ Assume that the interest rates are as follows:
Maturity Continuously Compounded
Zero Rate
1 2.50%
2 2.60%
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
FRA - example 2
β’ The cont. comp. forward rate is
π =2.60% β 2 β 2.50% β 1
2 β 1= 2.70%
β’ We need to convert this to an ACT/360 rate
π2.70%β365 365 = 1 + π365
360
π = π. ππππ%
Maturity Continuously Compounded
Zero Rate
1 2.50%
2 2.60%
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
cc zero PV
2.50% -975,310
2.60% 978,205
Combine the two examples
Maturity Cashflow
1 -1,000,000
2 1,030,417
ππ = 978,205 β 975,310 = 2,895
Remember we computed the PV for example 1
We also worked out the PV of the FRA given the
fair rate. In example 2 we computed the fair rate
(we used the same interest rates intentionally),
plug that fair rate and compute the PV again:
ππ = π π πΎ β π πΉ π·πβπ2π2
= $1ππ β 3.00% β 2.6993%365
360β πβ2.6%β2 = $2,895
Fair rate
π = 2.6993%
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
βFloatingβ FRA
β’ An FRA where one party agrees to pay the
other party whatever market interest rate will
prevail on a date π1 for the period π1, π2
β’ In other words: βI will pay you the fair interest
for the period π1, π2 that will be determined
at (some time ππΎ between now and) time π1β
β’ What is the PV of this promise?
β’ Sounds like βI promise to give you what will
be fair at some point in the futureβ
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
RISK ON AN FRA
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
DV01
β’ Remember that the industry standard for
interest rate risk is the dv01 aka dollar value
of one basis point.
β’ Looking at the valuation formula
ππ = βππβπ1π1 +π 1 + π πΉπ· πβπ2π2
We can see that there are two interest rates
used in pricing an FRA: π1 and π2
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Heuristics
β’ Assume that π πΉ is fixed β the contract has
already been entered.
β’ If we increase π1 by a basis point and leave π2
constant then the lender of money makes
money
β’ If we increase π2 by a basis point and leave π1
constant then the lender of money loses
money
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
More Heuristics
β’ The alternative valuation formulas are:
π πΉ =π π2π2βπ1π1 β 1
π·
and
ππ = π π πΎ β π πΉ π·πβπ2π2
β’ If π πΉ increases and π2 stays constant then the
lender loses money.
β’ If π2 increases and π πΉ stays the same then it
depends on the sign of the PV to being with.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
DERIVING CONTINUOUSLY
COMPOUNDED RATES
Appendix
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Measuring Interest Rates
β’ The compounding frequency used for an
interest rate is the unit of measurement
β’ The difference between annual and quarterly
compounding comes that in the latter you
earn interest on interest throughout the year
β’ All else being equal, a more frequent
compounding frequency results in a higher
value of the investment at maturity
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Impact of Compounding
β’ When we compound π times per year at rate
π , A grows to A(1 + π /π)π in one year
Compound. Freq. Value of $100 in 1year at 10%
Annual (m=1) 110.00
Semi-annual (m=2) 110.25
Quarterly (m=4) 110.38
Monthly (m=12) 110.47
Weekly (m=52) 110.51
Daily (m=365) 110.52
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Continuous Compounding
β’ Frequency of compounding matters
β’ At the limit of (compounding time)β0
the interest earned grows
exponentially
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
S
xTNxNT /* Let r=rate and
x=compounding time β
Nxrxrxr *1*1*1 Value End
timesN gcompoundin
NxrNexr *1ln
0x0x lim*1lim
How to derive Rc
Substitute
N=T/x
x
xrT
e
*1ln
0xlim
xdx
d
xrTdx
d
e
*1ln
0xlim
rT
rxr
T
ee
1
*1
1
0xlim
Looks like 0/0.
Use de lβHΓ΄pital
Q.E.D.
Make x very
small. Then
use A=eln(A)
Checks: r=0 βEnd Value=1
T=0 βEnd Value=1
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Continuous Compounding
β’ So in the limit as we compound more and
more frequently, we obtain continuously
compounded interest rates
β’ $100 grows to $100 Γ ππ ππ when invested at
a continuously compounded rate R for time T
β’ Conversely, $100 paid at time T has a
PV=$100 Γ πβπ ππ, when the continuously
compounded discount rate is π π
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
US TREASURY MARKET
Appendix
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Treasury Rates
β’ Rates on instruments issued by a
government in its own currency
β’ The rate is different by country and reflects a
combination of credit and economic
considerations
β’ We will focus only on the US treasury market
Many interesting links, for example: Treasury
http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-Yield-Data-Visualization.aspx
Bloomberg
http://www.bloomberg.com/markets/rates-bonds/government-bonds/us/
Stockcharts
http://stockcharts.com/freecharts/yieldcurve.html
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
US Treasury Market
β’ There are three primary types of instruments
issued by the US Treasury β T-bills
β’ Discount instrument issued in 4,13,26 and 52 week
maturities. No Coupons, just a redemption payment.
β T-notes β’ Coupon instruments issued in 2, 3, 5, 7 and 10 year
maturities
β’ Pays semi-annual coupons, plus a redemption payment
β T-bonds β’ Coupon instruments issued in a 30 year maturity
β’ Pays semi-annual coupons, plus a redemption payment
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
US Public Debt
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
US Public Debt
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
US Public Debt
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
US Public Debt
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
T-bills
β’ Minimum denomination = $100
β’ Quoted as a discount rate
β’ The present value of a T-bill is
ππ = $100 Γ 1 β ππππ¦π
360
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
T-notes and T-bonds
β’ The difference between notes and
bonds is simply the maturity
β Minimum denomination = $100.
β Pays interest every 6 months.
If the coupon rate is π then the interest paid
is π 2 every 6 months.
β At maturity the notional of the note is paid
to the holder
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Treasury Strips
β’ Separate Trading of Registered Interest and
Principal of Securities
β’ STRIPS let investors hold and trade the
individual interest and principal components
of T-notes and T-bonds
β’ Popular because they let an investor receive
a known payment on a specific future date
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
Treasury Strips
β’ We will use STRIPs as our instrument of
choice when building a Treasury yield curve β It is quoted as a price. This simplifies the
mathematics
β Frequent maturities.
β’ These are not as liquid as the underlying
treasury so in practice would not choose to
use these.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
LIBOR SCANDAL
Appendix
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
LIBOR Scandal
β’ No inter-bank lending market β During the financial crisis there was no inter-bank lending
market
β The answer to the daily questions should have been βAt
no rate.β or
β Maybe another bank would lend money at an extortionate
rate.
β’ What would have happened to Barclayβs Bank if the
market found out that they didnβt think they could
borrow money from other banks? Or that they
answered the question with a 50% rate?
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
LIBOR Scandal
β’ Manipulation of fixings
β Imagine a 10m USD bet on 3-month USD
LIBOR. If LIBOR>=3.00% then receive 10m
USD. If LIBOR<3.00% then receive nothing.
β What happens if on the morning of the bet
LIBOR is trading at 2.98%? What can a trader
do to win the bet? β’ Pressure the person making the submission in his
bank to give a higher submission
β’ Speak to traders at other banks so that they will do
the same.
University of Colorado at Boulder β Leeds School of Business β FNCE-4040 Derivatives
LIBOR Scandal
β’ June 2012
β Barclayβs Bank paid fines of GBP290m for manipulation of the
rates
β Chairman and CEO resigns
β’ Dec 2012
β UBS is fined a total of USD1.5bn
β’ Feb 2013
β Royal Bank of Scotland expecting penalties of USD 612m
β’ Dec 2013
β 6 financial institutions in Europe fined by European Commission
70-260m EUR.
β UBS avoided fines of 2.5bn EUR by revealing the existence of
cartels.