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University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

FNCE 4040– Derivatives Chapter 4

Interest Rates

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

Goals

• Discuss the types of rates needed for

Derivative Pricing

• Continuous Compounding
• Yield Curves
• Risk
• Forward Rate Agreements (FRA)

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Types of Rates

• For the purpose of this class there are three

types of interest rates that are relevant –LIBOR –Risk-free rates –Interest Rates on collateral

• Important but out of scope rates include:

–Treasuries –Overnight Interest Rate Swaps (OIS)

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LIBOR

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LIBOR

• London Interbank Offered Rate

– This is the rate of interest at which a bank is prepared to borrow from another bank. – It is compiled for a variety of maturities ranging from Overnight to 1 year – It exists on all 5 currencies – CHF, EUR, GBP, JPY and USD – It is compiled once a day ICE Benchmark Administration (IBA)

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LIBOR Process

• Once a day major banks submit the answer

to the following question “At 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?”

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Uses of LIBOR

• LIBOR rates are used for

– Interest Rate Futures

• This is a futures contract whose price is derived by the interest

paid on 3-Month LIBOR

– Interest Rate Swaps

• These are derivative instruments that “swap” LIBOR for fixed

interest rates generally for three or six month period. The maturity

• f these tends to be 3 to 50 years

– Mortgages

• Some Adjustable Rate Mortgages are linked to LIBOR rates

– Benchmark rate for short-term borrowing in the market. – There has been a scandal surrounding LIBOR for the past few years. If interested see the appendix.

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RISK FREE RATE

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The Risk-Free Rate

• Derivatives pricing originally depended upon

a “risk-free” rate

– The risk-free rate traditionally used by derivatives practitioners was LIBOR – Treasuries are an alternative but were considered to be artificially low for a number of reasons

• Treasury bills and bonds must be purchased by financial

institutions to satisfy a variety of regulatory requirements. Increases demand and decreases yield

• The amount of capital a bank has to have in order to support an

investment in treasury bills and bonds is lower

• Treasuries have a favorable tax treatment

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The Risk-Free Rate

• In this course we will generally assume that

risk-free rates exist and they will be given to you.

• We will assume that LIBOR is the risk-free

rate

• We will give you rates.

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Collateral Based Discounting

• Derivatives pricing theory has moved to

Collateral Based Discounting

– The yield curve relevant for discounting depends

• n the collateral agreement

– Every derivatives contract might have a different yield curve

• When we discuss pricing we will work through

at least one collateralized example

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THE YIELD CURVE

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Yield Curve

• When pricing derivatives we will need a yield

curve.

• For our purposes a yield curve will consist of

– Yields to specified maturities, – A methodology for interpolating missing yields, – A methodology for calculating forward rates (rates that are for borrowing/lending starting in the future)

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Theories of the Term Structure

• Liquidity Preference Theory: forward rates

higher than expected future zero rates

• Market Segmentation: short, medium and

long rates determined independently of each

• ther
• Expectations Theory: forward rates equal

expected future zero rates

– The Derivatives market uses this theory.

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CONTINUOUSLY COMPOUNDED ZERO RATES

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Continuous Compounding

• The compounding frequency used for an

interest rate is the unit of measurement

• All else being equal, a more frequent

compounding frequency results in a higher value of the investment at maturity

• In this class interest rates will be quoted as

continuously compounded zero rates

– Except when we are discussing a specific instrument or market – for example LIBOR or swap rates.

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Continuous Compounding

• 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

• Continuous compounding means that an investment

is instantaneously reinvested.

• In practical terms this means

– $100 grows to $100 × 𝑓𝑆𝑑𝑈 when invested at a continuously compounded rate 𝑆𝐷 to time 𝑈 – Conversely, $100 paid at time 𝑈 has a present value of $100 × 𝑓−𝑆𝑑𝑈, when the continuously compounded discount rate to time 𝑈 is 𝑆𝑑

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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 = 𝐺𝑊 ∗ 𝑓−𝑆𝑑𝑈

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Other Interest Rates

• The quoting convention for quoted interest

rates involves a daycount convention.

• Through this one can compute the interest
• wed.
• There are two examples we will use in class

– ACT/360 – The interest owed is 𝑠𝑏𝑢𝑓 × 𝐵𝑑𝑢𝑣𝑏𝑚 𝐸𝑏𝑧𝑡 𝑗𝑜 𝑞𝑓𝑠𝑗𝑝𝑒 360 – ACT/365 – The interest owed is 𝑠𝑏𝑢𝑓 × 𝐵𝑑𝑢𝑣𝑏𝑚 𝐸𝑏𝑧𝑡 𝑗𝑜 𝑞𝑓𝑠𝑗𝑝𝑒 365

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives Start (days) End (days) Rate Daycount Basis Notional Interest

365 3.00% 360 1,000,000 30,417 365 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

𝐽𝑜𝑢𝑓𝑠𝑓𝑡𝑢 = 𝑂𝑝𝑢𝑗𝑝𝑜𝑏𝑚 × 𝑠𝑏𝑢𝑓 × 𝐵𝑑𝑢𝑣𝑏𝑚 𝐸𝑏𝑧𝑡 𝑗𝑜 𝑞𝑓𝑠𝑗𝑝𝑒 𝐸𝑏𝑧𝑑𝑝𝑣𝑜𝑢

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Conversion

• We will often have rates given in a particular

form and have to convert to another.

• We can do this by computing the investment

return from the given rate and using this to compute the unknown rate, or equating PVs: 𝑓𝑠𝑑𝑑∗𝑒𝑏𝑧𝑡/365 = 1 + 𝑠

𝐵𝐷𝑈/360

𝑒𝑏𝑧𝑡 360 𝑄𝑊 = 𝑓−𝑠𝑑𝑑∗𝑒𝑏𝑧𝑡/365 = 1 1 + 𝑠

𝐵𝐷𝑈/360 𝑒𝑏𝑧𝑡

360

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Practice

Start End ACT/360 Rate ACT/365 Rate

• C. comp.

Rate

365 3.00% 3.0417% 2.9963% 365 4.00% 4.0556% 3.9755% 182 365 3.00% 3.0417% 3.0187%

1 + 𝑠

𝐵𝐷𝑈/360

𝑒𝑏𝑧𝑡 360 = 1 + 𝑠

𝐵𝐷𝑈/365

𝑒𝑏𝑧𝑡 365 = 𝑓𝑠𝑑𝑑∗𝑒𝑏𝑧𝑡/365

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INTERPOLATION BETWEEN RATES

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Interpolation

• When interpolating between rates we will

linearly interpolate continuously compounded zero rates.

• The advantages of doing this are:

– It is easy to explain and implement – It has great risk properties

• Sophisticated spline techniques are common

in the market.

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Linear Interpolation

• If we know continuously compounded zero

rates 𝑨1 and 𝑨2 for two times 𝑢1 and 𝑢2 then for time 𝑢 between 𝑢1 and 𝑢2 we define 𝑠 𝑢 = 𝑠

1 + 𝑠2 − 𝑠 1

𝑢2 − 𝑢1 𝑢 − 𝑢1

𝑢1 𝑢2 𝑠

1

𝑠2 𝑢

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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%

𝑠 𝑢 = 𝑠

1 + 𝑠 2 − 𝑠 1

𝑢2 − 𝑢1 𝑢 − 𝑢1

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FORWARD RATES

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Forward Rates

• The forward rate is the future zero rate

implied by today’s term structure of interest rates

𝑓𝑔

𝑜×(𝑈 2−𝑈 1)

𝑓𝑆2×𝑈

2

𝑓𝑆1×𝑈

1

𝑓𝑆1×𝑈

1𝑓𝑔

𝑜×(𝑈 2−𝑈 1) = 𝑓𝑆2×𝑈

2

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Formula for Forward Rates

• Suppose that the zero rates for time periods

T1 and T2 are R1 and R2 with both rates continuously compounded

• The forward rate for the period between times

T1 and T2 is

1 2 1 1 2 2

T T T R T R  

• This formula is only approximately true when

rates are not expressed with continuous compounding

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Practice

Time 1 years Rate 1 cc zero Time 2 years Rate 2 cc zero Forward Rate between 𝒖𝟐 and 𝒖𝟑

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%

𝐺

1,2 = 𝑆2𝑈2 − 𝑆1𝑈 1

𝑈2 − 𝑈

1

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RISK

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Industry Calc. of Rate Sensitivity: dv01

• Traders in practice use dv01: dollar value of

1bp increase in rates

• Shock interest rates by +1bp and compute

dollar change  dv01

• Also compute bucketed dv01

– Shock interest rates by 1bp at various tenor buckets – Compute dollar impact of each individual shock – You obtain a term structure of dv01s

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Example

• Consider an investment which pays

$1,000,000 in 1-years time. The one-year continuously compounded zero rate is 3.00%.

• The present value of this investment is:

𝑄𝑊 = $1,000,000 ∙ 𝑓−0.03 = $970,446.53

• If interest rates increase by one basis-point

then the new PV will be: 𝑄𝑊 = $1,000,000 ∙ 𝑓−0.0301 = $970,348.49

• Thus the dv01 is -97.04 dollars.

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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)

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FORWARD RATE AGREEMENT

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Forward Rate Agreement (FRA)

• 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.

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Example

• For example a bank agrees to lend 1m USD

for 1 year starting in 1 year at an interest rate

• f 3%. The rate is quoted with an ACT/360

daycount basis.

Year 1

Year 2

today 1𝑛 𝑉𝑇𝐸 1𝑛 𝑉𝑇𝐸 $1𝑛 365 360 3.00% = 30,416.67

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FRA Mechanics / Valuation – part 1

• From the lender’s viewpoint
• A loan of 𝑂 from 𝑈

1 to 𝑈2 at an agreed rate 𝑆𝐿

• Let 𝐸 be the daycount fraction from 𝑈

1 to 𝑈2

– For an FRA 𝐸 =

𝐸𝑏𝑧𝑡 𝑈

2 −𝐸𝑏𝑧𝑡(𝑈 1)

360

𝑈

1

𝑈2

today

Interest owed:

𝑂 × 𝑆𝐿 × 𝐸

𝑂 𝑂

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𝑄𝑊 = −𝑂 ∙ 𝑓−𝑠1𝑈

1 + 𝑂 ∙ 1 + 𝑆𝐿 ∙ 𝐸 ∙ 𝑓−𝑠2𝑈 2

FRA Mechanics / Valuation – part 1

• We can value the FRA given the continuously

compounded zero rates 𝑠

1 and 𝑠2.

𝑈

1

𝑈2

today

Interest owed:

𝑂 ∙ 𝑆𝐿 ∙ 𝐸

𝑂 𝑂

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The Fair FRA Rate

• The fair FRA rate 𝑆𝐺 is the rate such that the

sum of the PV of both cash flows is zero: 𝑂𝑓−𝑠1𝑈

1 = 𝑂 1 + 𝑆𝐺𝐸 𝑓−𝑠2𝑈 2

• You can use the above to solve for 𝑆𝐺:

𝑓−𝑠1𝑈

1 = 1 + 𝑆𝐺𝐸 𝑓−𝑠2𝑈 2

𝑆𝐺 = 𝑓 𝑠2𝑈

2−𝑠1𝑈 1 − 1

𝐸

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The Fair FRA Rate

• We know that the PV of a loan from 𝑈

1 to 𝑈2

at an agreed rate 𝑆𝐿 with daycount fraction 𝐸 from 𝑈

1 to 𝑈2 is

𝑄𝑊 = −𝑂𝑓−𝑠1𝑈

1 + 𝑂 1 + 𝑆𝐿𝐸 𝑓−𝑠2𝑈 2

• Combine this with the definition of the fair rate

from the previous page and obtain: 𝑄𝑊 = −𝑂 1 + 𝑆𝐺𝐸 𝑓−𝑠2𝑈

2 + 𝑂 1 + 𝑆𝐿𝐸 𝑓−𝑠2𝑈 2

𝑸𝑾 = 𝑶 𝑺𝑳 − 𝑺𝑮 𝑬𝒇−𝒔𝟑𝑼𝟑

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Forward Rate Agreement (cont.)

• Equivalent to an agreement where interest at

a predetermined rate, RK is exchanged for interest at the market rate

• Value an FRA by assuming that the forward

rate RF, is certain (has been discovered)

• So the value of an FRA is the PV of the

difference between:

– the interest that would be paid at rate RF and – the interest that has to be paid at rate RK

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FRA Mechanics / Valuation – part 2

• A loan from 𝑈

1 to 𝑈2

• From the lender’s viewpoint

𝑈

1

𝑈2

Fair rate now for period 𝑈

1, 𝑈2 = 𝑆𝐿

today Interest owed:

𝑂 × 𝑆𝐿 × 𝑈2 − 𝑈

1

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Think of Mark-To-Market as the cost to offsetting your position

FRA Mechanics / Valuation – part 2

Interest owed:

𝑂 × 𝑆𝐿 × 𝑈2 − 𝑈

1

𝑓−𝑆2×𝑈

2

𝑈

1

𝑈2

today Fair rate for period 𝑈

1, 𝑈2 moves to 𝑺𝑮

Interest now prevailing:

𝑂 × 𝑺𝑮 × 𝑈2 − 𝑈

1

Take the difference and PV

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FRA example 1

• For example a bank agrees to lend 1m USD

for 1 year starting in 1 year at an interest rate

• f 3%. The rate is quoted with an ACT/360

daycount basis.

• Assume that the interest rates are as follows:

Maturity Continuously Compounded Zero Rate 1 2.50% 2 2.60%

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives cc zero PV 2.50%

• 975,310

2.60% 978,205

FRA example 1 – Cashflows

Year 1

Year 2

today 1𝑛 𝑉𝑇𝐸 1𝑛 𝑉𝑇𝐸 $1𝑛 365 360 3.00% = 30,416.67

Maturity Cashflow 1

• 1,000,000

2 1,030,417 𝑄𝑊 = 978,205 − 975,310 = 2,895

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FRA example 2

• 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?

• Assume that the interest rates are as follows:

Maturity Continuously Compounded Zero Rate 1 2.50% 2 2.60%

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FRA - example 2

• The cont. comp. forward rate is

𝑔 = 2.60% ∙ 2 − 2.50% ∙ 1 2 − 1 = 2.70%

• We need to convert this to an ACT/360 rate

𝑓2.70%∙365 365 = 1 + 𝑠 365 360 𝒔 = 𝟑. 𝟕𝟘𝟘𝟒%

Maturity Continuously Compounded Zero Rate 1 2.50% 2 2.60%

University of Colorado at Boulder – Leeds School of Business – 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

𝑄𝑊 = 978,205 − 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: 𝑄𝑊 = 𝑂 𝑆𝐿 − 𝑆𝐺 𝐸𝑓−𝑠2𝑈

2

= $1𝑛𝑛 ∗ 3.00% − 2.6993% 365 360 ∗ 𝑓−2.6%∗2 = $2,895

Fair rate 𝑠 = 2.6993%

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“Floating” FRA

• An FRA where one party agrees to pay the
• ther party whatever market interest rate will

prevail on a date 𝑈

1 for the period 𝑈 1, 𝑈2

• In other words: “I will pay you the fair interest

for the period 𝑈

1, 𝑈2 that will be determined

at (some time 𝑈𝐿 between now and) time 𝑈

1”

• What is the PV of this promise?
• Sounds like “I promise to give you what will

be fair at some point in the future”

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RISK ON AN FRA

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DV01

• Remember that the industry standard for

interest rate risk is the dv01 aka dollar value

• f one basis point.
• Looking at the valuation formula

𝑄𝑊 = −𝑂𝑓−𝑠1𝑈

1 + 𝑂 1 + 𝑆𝐺𝐸 𝑓−𝑠2𝑈 2

We can see that there are two interest rates used in pricing an FRA: 𝑠

1 and 𝑠2

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Heuristics

• Assume that 𝑆𝐺 is fixed – the contract has

already been entered.

• If we increase 𝑠

1 by a basis point and leave 𝑠2

constant then the lender of money makes money

• If we increase 𝑠2 by a basis point and leave 𝑠

1

constant then the lender of money loses money

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More Heuristics

• The alternative valuation formulas are:

𝑆𝐺 = 𝑓 𝑠2𝑈

2−𝑠1𝑈 1 − 1

𝐸 and 𝑄𝑊 = 𝑂 𝑆𝐿 − 𝑆𝐺 𝐸𝑓−𝑠2𝑈

2

• If 𝑆𝐺 increases and 𝑠2 stays constant then the

lender loses money.

• If 𝑠2 increases and 𝑆𝐺 stays the same then it

depends on the sign of the PV to being with.

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APPENDIX

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DERIVING CONTINUOUSLY COMPOUNDED RATES

Appendix

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Measuring Interest Rates

• The compounding frequency used for an

interest rate is the unit of measurement

• The difference between annual and quarterly

compounding comes that in the latter you earn interest on interest throughout the year

• All else being equal, a more frequent

compounding frequency results in a higher value of the investment at maturity

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Impact of Compounding

• When we compound 𝑛 times per year at rate

𝑆, A grows to A(1 + 𝑆/𝑛)𝑛 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

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Continuous Compounding

• Frequency of compounding matters
• At the limit of (compounding time)→0

the interest earned grows exponentially

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x T N x N T / *   

Let r=rate and x=compounding time →

     

N

x r x r x r * 1 * 1 * 1 Value End

times N g compoundin

                

 

 N

x r N

e x r

* 1 ln x x

lim * 1 lim

  

 

How to derive Rc

Substitute N=T/x

 

 

  x x r T

e

* 1 ln x

lim

   

 

              x dx d x r T dx d

e

* 1 ln x

lim

rT r x r T

e e  

  1 * 1 1 x

lim

Looks like 0/0. Use de l’Hôpital

Q.E.D.

Make x very

• small. Then

use A=eln(A)

Checks: r=0 →End Value=1 T=0 →End Value=1

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

Continuous Compounding

• So in the limit as we compound more and

more frequently, we obtain continuously compounded interest rates

• $100 grows to $100 × 𝑓𝑆𝑑𝑈 when invested at

a continuously compounded rate R for time T

• Conversely, $100 paid at time T has a

PV=$100 × 𝑓−𝑆𝑑𝑈, when the continuously compounded discount rate is 𝑆𝑑

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

US TREASURY MARKET

Appendix

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

Treasury Rates

• Rates on instruments issued by a

government in its own currency

• The rate is different by country and reflects a

combination of credit and economic considerations

• 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 – Leeds School of Business – FNCE-4040 Derivatives

US Treasury Market

• There are three primary types of instruments

issued by the US Treasury

– T-bills

• Discount instrument issued in 4,13,26 and 52 week
• maturities. No Coupons, just a redemption payment.

– T-notes

• Coupon instruments issued in 2, 3, 5, 7 and 10 year

maturities

• Pays semi-annual coupons, plus a redemption payment

– T-bonds

• Coupon instruments issued in a 30 year maturity
• Pays semi-annual coupons, plus a redemption payment

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

US Public Debt

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

US Public Debt

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

US Public Debt

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

US Public Debt

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

T-bills

• Minimum denomination = $100
• Quoted as a discount rate
• The present value of a T-bill is

𝑄𝑊 = $100 × 1 − 𝑠 𝑒𝑏𝑧𝑡 360

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

T-notes and T-bonds

• The difference between notes and

bonds is simply the maturity

–Minimum denomination = $100. –Pays interest every 6 months. If the coupon rate is 𝑠 then the interest paid is 𝑠 2 every 6 months. –At maturity the notional of the note is paid to the holder

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

Treasury Strips

• Separate Trading of Registered Interest and

Principal of Securities

• STRIPS let investors hold and trade the

individual interest and principal components

• f T-notes and T-bonds
• Popular because they let an investor receive

a known payment on a specific future date

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

Treasury Strips

• We will use STRIPs as our instrument of

choice when building a Treasury yield curve

– It is quoted as a price. This simplifies the mathematics – Frequent maturities.

• These are not as liquid as the underlying

treasury so in practice would not choose to use these.

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

LIBOR SCANDAL

Appendix

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

LIBOR Scandal

• No inter-bank lending market

– During the financial crisis there was no inter-bank lending market – The answer to the daily questions should have been “At no rate.” or – Maybe another bank would lend money at an extortionate rate.

• What would have happened to Barclay’s Bank if the

market found out that they didn’t think they could borrow money from other banks? Or that they answered the question with a 50% rate?

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

LIBOR Scandal

• Manipulation of fixings

– 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.

– What happens if on the morning of the bet LIBOR is trading at 2.98%? What can a trader do to win the bet?

• Pressure the person making the submission in his

bank to give a higher submission

• Speak to traders at other banks so that they will do

the same.

University of Colorado at Boulder – Leeds School of Business – FNCE-4040 Derivatives

LIBOR Scandal

• June 2012

– Barclay’s Bank paid fines of GBP290m for manipulation of the rates – Chairman and CEO resigns

• Dec 2012

– UBS is fined a total of USD1.5bn

• Feb 2013

– Royal Bank of Scotland expecting penalties of USD 612m

• Dec 2013

– 6 financial institutions in Europe fined by European Commission 70-260m EUR. – UBS avoided fines of 2.5bn EUR by revealing the existence of cartels.