Settlement
Maturity
coupon
yield
1-Mar-12
31-Dec-16
5%
4%
CP
AI
FP
$
$
$
date
taxable Income 2012
Coupons Rec
AI Paid
Total taxable Inc
Taxable Income 2016
Proceeds
Cost
250
250
250
250
250
250
250
250
250
250
$
$
Last coupon
Next coupon
Days from last
Da
1a
Term(month)
Yield
Implied LIB Implied ED Future
3
1.50%
1.72% 98.28%
6
1.61%
1.88% 98.12%
9
1.70%
2.06% 97.94%
12
1.79%
b
In practice, the market ED future prices are slightly lower
than thre implied values.
Since implied ED future price is calculated
YTM: C>B>P
Convexity: P>B>C
Duration: inverse floater>0 coupon>with coupon
Z-spread:C>B>P
A swap is a contract where 2 parties agree to swap cash flows.
Vanilla swap: swap a fixed stream of cash flows with a floating rate steam of cash flows in the same
c
Bond
A
B
settlement
Maturity
YTM
Coupon
30-Sep-15
30-Apr-21
6.25%
3%
30-Sep-15
1-Jun-20
5.75%
7%
last
next
Total
Days to next
31-May-15
30-Nov-14
-182
-304
1-Jun-14
1-Dec-14
183
-303
shif
0.01%
0.01%
price
AI
FP
84.8731314
-1.00549451
83.8676369
105.04466
Winter 2017
MATBUS 471
Assignment #3
1. Consider a 5% coupon 4-year bond (assume semi-annual coupons) callable according to the call
schedule below. Assume that the bond is trading at 102.50. The yield to first call is defined to be
the YTM on the bond as
Winter 2017
MATBUS 471
Assignment #1
1. Today is January 20, 2017. Suppose your company just purchased $500,000 (face value) of a
bond due March 31, 2029 with a coupon rate of 5%, at a clean price of 105.97. Assume the bond
is sold on December 31, 2019 at
Winter 2017
MATBUS 471
Assignment #2
1. Today is February 1, 2017. Consider the following 2 bonds
Bond A is a 3% coupon bond due May 31, 2020 with a YTM of 2.25%
Bond B is a 5% coupon bond due August 31, 2041 with a YTM of 5.15%
(a) Based on $1 million fa
Models of Interest Rates
We have considered the short rate model
dy = dw
and used it to construct trees, value bonds,
options etc.
However, this model implies a decreasing yield
curve, which is not consistent with what we see in
typical markets.
Lets cons
Using Trees
Before we plunge into examining alternative
models for interest rates, lets instead look at
what interest rate trees can be used for.
Find the value of a 7% coupon 3-year bond
(assume the coupons are annual), given the
following interest rate
Intro to Credit Derivatives
We will look at 3 basic credit derivatives
Total Return Swaps
Credit Default Swaps
Credit Spread Products
The second of these being the most popular
instrument in current markets.
Total Return Swaps
These are relatively straigh
ED Futures
Eurodollar
A Eurodollar is a US dollar deposited in a bank,
not located in the US. There are also Euro-Yen
deposits etc, but the US dollar is by far the
largest market
Eurodollars can essentially be traded, much like
any certificate of deposit.
Yield Models
Suppose the 1 year spot rate r1 = 10%, and
suppose there is no volatility in rates. Then the
two year spot rate should also be 10% in order to
prevent arbitrage. Why?
Thus the yield curve must be flat.
Yield Models
Now suppose yields are unce
Plain Vanilla Swaps
Swap
A swap is simply a contract where 2 parties agree
to swap cash flows. When the parties agree to
swap a fixed stream of cash flows with a floating
rate stream of cash flows in the same currency, it
is called a plain vanilla interes
Repos
Repo
A Repo or more formally a Sale and Repurchase
agreement is an agreement to sell and then
repurchase a security at a fixed date at a fixed
price. Repos are typically over a short time
period, often 1 day.
As we will see, repos are really a type
Yield Models (more detail)
Idea: let y = yields (or interest rates). Then
dy = dt + dw
Yield Models (more detail)
Idea: let y = yields (or interest rates). Then
dy = dt + dw
Change in rates
Yield Models (more detail)
Idea: let y = yields (or interest rate
MATBUS 471
Course Workbook
Winter 2017
Peter Wood
1
Part I
1. Consider a bond maturing on September 30, 2023. Assume a coupon rate of 5% and a YTM of
6%. Today is January 1, 2017. (Use Actual/Actual day count convention)
a. Find the clean and dirty prices
Forward Rate Agreement
A FRA is a way to actually trade forward rates.
More specifically:
FRA
A FRA is an OTC contract where one party pays
an agreed rate in exchange for a floating rate,
over one specified interval in the future.
Usually, FRAs are over s
Interest Rates
Simple Interest
A(t) = A0 (1 + ti)
Compound Interest
mt
i
A(t) = A0 (1 + i) or A(t) = 1 +
m
t
Continuous Interest
A(t) = A0 eit
Bonds
Bullet Bond
A Bullet Bond is a bond that pays fixed coupons
plus face value at maturity.
The value of a bu
Tax and Accounting Treatment
Canadian Tax:
Interest on coupon bonds is not accrued, as
it is for loans.
The coupons received are included in taxable
income in the year they are received.
The AI paid (when the bond is purchased) is
deductable in the year i
Case Study
Example
On May 30, 2014, the following government bonds traded
with the following characteristics:
Maturity
June 1/18
June 1/18
Dec 31/18
Coupon
11.25%
4.5%
3%
YTM
1.997%
2.105%
2.232%
So, since all these bonds have the same credit risk (they a
Fall 2016 MATBUS 471 Assignment #3
_
1. Consider a 5% coupon 4-year bond (assume semiannual coupons) callable according to the call
schedule below. Assume that the bond is trading at 96.50. The yield tofirst call is defined to be
the YTM on the bond assum
Fall 2016
1.
MATBUS 471
Assignment #5
You are a dealer and you are currently long $100 million (face value) of bullet bonds with a MD of
8.8 trading at 109.35. You plan to hedge this position by trading ED futures expiring in 3 months.
a. How many futures
Fall 2016
MATBUS 471
Assignment #1
Please assume the following in this assignment:
All rates are BEY, unless otherwise indicated. Use actual/actual day count convention for bonds.
Ignore weekends and holidays (i.e. assume all instruments can be valued and
Practice Midterm 1
1.
Today is November 4, 2014. Calculate the clean and dirty prices of a 6% coupon
bond due March 31, 2024 trading with a YTM of 4%. (HINT: There are 182 days
in the current coupon period)
2.
A 6% coupon 10 year bond is trading with a cl
MATBUS 471 : Fixed Income Securities
Fall 2016
Instructor: Peter Wood
Office: M3 2109
Phone: ext 39-159
Email: [email protected]
Office Hours: MW 1:00-2:00; or by appointment.
Course Webpage : LEARN
Course Description
MATBUS 471 provides an overview of a