Solutions:
1. The present value of the expected regular payments (payment rate is s per year), is
Time
(years)
0.5
1.0
1.5
2.0
Probability
of Survival
Expected
Payment
Discount
Factor
PV of Expected
Payment
0.990
0.980
0.965
0.950
0.4950s
0.4900s
0.4825s

ModelingTheTermStructureof
InterestRates
Current
Currentone
oneyear
yearinterestrateis10%
interest rate is 10%
Allinvestorsexpectoneyearinterestratenext
year to be 10% and in two year to be 10% as
yeartobe10%andintwoyeartobe10%as
well
Allexpectationsar

Bond Analysis
BondAnalysis
Bond Valuation
bondspriceisthepresentvalueofitsfuturecash
flows.
n
P
t 1
C
(1 r ) t
F
(1 r ) n
1
1
C* 1
r
(1 r ) n
F
(1 r ) n
Rateusedtodiscountfuturecashflowsofbondisyield
to maturity (YTM)
tomaturity(YTM).
YTMcanbecalculated

CONVEXITY
Recall the pprice-yield
y
ggraph.
p
Relationshipp between the
price of a bond and its yield to maturity is convex. The
slope of the curve declines in absolute value as yields
increases.
Graph indicates that the greater the convexity of the bond,

Spreadsheet Assignment 2
Suppose you are trying to immunize a year-10 obligation whose present value is $1000,
in other words, at a current interest rate of 6%, this future obligation at the end of year 10
is to make a payment of $1000*(1+0.06)10=$1790.85

Practice Questions 2
1. You will be paying $10,000 a year in tuition expenses at the end of the next two
years. Bonds currently yield 8%.
a. What is the present value and duration of your obligation?
b. What maturity zero-coupon bond would immunize your o

Bond Analysis
BondAnalysis
Bond Valuation
bondspriceisthepresentvalueofitsfuturecash
flows.
n
P
t 1
C
F
(1 r ) t (1 r ) n
1
1
F
C * 1
n
r (1 r ) (1 r ) n
Rateusedtodiscountfuturecashflowsofbondisyield
to maturity (YTM)
tomaturity(YTM).
YTMcanbecalcu

CONVEXITY
Recall the pprice-yield
y
ggraph.
p
Relationshipp between the
price of a bond and its yield to maturity is convex. The
slope of the curve declines in absolute value as yields
increases.
Graph indicates that the greater the convexity of the bon

Credit Derivatives
1
Credit Derivatives
Derivatives where the payoff depends on
the credit quality of a company or
sovereign entity
The market started to grow fast in the late
1990s
By 2005 notional principal totaled $12
t illi
trillion
2
Credit Defaul

Mortgages
MortgageLoans
Amortgageisaloansecuredbythecollateralof
specifiedrealestateproperty,whichobligesthe
b
borrowertomakeapredeterminedseriesofpayments.
t
k
d t
i d i
f
t
Themortgagegivesthelendertherightofforeclosure
on the loan if the borrower def

Forward Contracts
ForwardContracts
Aforwardcontractisanagreementtobuyor
sellasecurityinthefutureatapricespecified
ll
i i h f
i
ifi d
atthetimeoftheagreement.
Forwardprice
Forwarddate,expirationdate,deliverydateor
, p
,
y
maturitydate
Buyer:long
Buyer:

Interest Rate Swaps
1
A swap is an agreement to
exchange cash flows at specified
future times according to certain
specified rules
2
An Example of a Plain
Plain Vanilla
Vanilla
Interest Rate Swap
An agreement by Microsoft to receive
6 month LIBOR & pay a

Extra Example
Suppose that the risk-free zero curve is flat at 6% per annum with continuous
compounding and that defaults can occur at times 0.25 years, 0.75 years, 1.25 years,
and 1.75 years in a 2-year plain vanilla credit default swap with semiannual p

Mortgage Derivatives
MortgageDerivatives
Mortgage Pass-Through Security
A mortgage pass-through security,
security or a passthrough is created when one or more mortgage
h ld form
holders
f
a collection
ll ti (pool)
(
l) off mortgages
t
andd
sell shares o

Futures Contract and Forward Contract
Futures contracts are traded on organized exchanges and are
standardized agreements as to the delivery date (or month)
and quality of the deliverable.
A forward contract traded in the OTC markets, usually has
nonstand

Question 3
Yield to Maturity
6%
Bond 1
Coupon Rate (CR)
Maturity (T)
Face Value (PAR)
Interest Payment (IR)
Bond Price
4.50%
20
$1,000
$45.00
$827.95
Face Value equals $1000 of Mkt Value
$912.69
12.8964
203.89
10
97.8996
Vex Calculation - Bond 1
Time Peri

Question 2
Yield to Maturity
6%
Bond 1
Coupon Rate (CR)
Maturity (T)
Face Value (PAR)
Interest Payment (IR)
Bond Price
$
Face Value equals $1000 of Mkt
Value
Bond 2
Bond 3
6.70%
6.985%
5.90%
10
15
30
$1,000
$1,000
$1,000
$67.00
$69.85
$59.00
1,051.52 $ 1,

Bond pricing
Input
Basics
Annual coupon rate(CR)
Yield to matruity(Annualized)(y)
Number of payments/year(NOP)
Number of periods to maturity(T)
Face value (PAR)
4.0%
7.1%
2
10
$100
Outputs
Discount rate/period (r.)
Coupon rate payment (PMT)
3.55%
$2
Calcu

Yield to Maturity
6%
Bond 1
Coupon Rate (CR)
Maturity (T)
Face Value (PAR)
Interest Payment (IR)
Bond Price
$
Face Value equals $1000
of Mkt Value
$
Duration
Bond 2
Bond 3
6.70%
6.985%
5.90%
10
15
30
$1,000
$1,000
$1,000
$67.00
$69.85
$59.00
1,051.52
# $

Yield to Maturity
6%
Bond 1
Coupon Rate (CR)
Maturity (T)
Face Value (PAR)
Interest Payment (IR)
Bond Price
Face Value equals $1000 of Mkt
Value
D
Vex
Obligation Duration
Obligation Convexity
Vex Calculation - Bond 1
Time Period (t)
Vex (Bond 1)
Vex Calcu

Practice Questions 5
1. Suppose that the risk-free zero curve is flat at 6% per annum with continuous compounding and
that defaults can occur at times 0.25 years, 0.75 years, 1.25 years, and 1.75 years in a 2-year
plain vanilla credit default swap with se

Bond pricing
Inputs
Five Bond Variables
a
Annual Coupon Rate (CR)
Yield to Maturity(Annualized) (y)
Number of Payments/year(NOP)
(1) Number of Periods to Maturity (T)
(2) Face Value (PAR)
(3) Discount Rate/Period (r.)
(4) Coupon Payment (PMT)
(5) Bond Pri

Yield to Maturity
6%
Bond 1
Coupon Rate (CR)
Maturity (T)
Face Value (PAR)
Interest Payment (IR)
Bond Price
$
Face Value equals $1000 of Mkt Value
$
Duration
Bond 2
6.70%
10
$1,000
$67.00
1,051.52 $
951.00
$
7.6655
Bond 3
6.985%
15
$1,000
$69.85
1,095.67

Annual coupon rate(CR)
Yield to matruity(Annualized)(y)
Number of payments/year(NOP)
Number of periods to maturity(T)
Face value (PAR)
Outputs
Discount rate/period (r.)
Coupon rate payment (PMT)
Chart Outputs
Yield to Maturity (Annualized)
Discount Rate/P

Bond pricing
Inputs
Dynamic Chart
Annual coupon rate(CR)
Yield to matruity(Annualized)(y)
Number of payments/year(NOP)
Face value (PAR)
4.0%
4
7.1%
7.1
2
2
$100
1
Outputs
Discount rate/period (r.)
Coupon rate payment (PMT)
Dynamic Chart Outputs
Time to Ma

Practice Question 4
The following tree gives the true six-month rate process.
6%
5%
4%
The prices of six-month ($100 face value) zero and one-year ($100 face value) zero are
$97.561 and $95.0908 respectively.
a)
Write down the price trees for the six-mont

Question 1
Yield to Maturity
6%
Bond 1
Coupon Rate (CR)
Maturity (T)
Face Value (PAR)
Interest Payment (IR)
Bond Price
Face Value equals $1000 of Mkt Value
Duration
$
$
If the interest rate is 6% and stays at 6%
Yield to Maturity
Bond 2
6.70%
10
$1,000
$6

Pricing Fixed Income Derivatives
PricingFixedIncomeDerivatives
The Relative Pricing of Interest Rate
Contingent Claims
Any security whose cash flow depends on the level of
interest rate is called interest rate derivative or interest
rate contingent claim