Winter 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

Boeing v Airbus: Nose to nose | The Economist
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Boeing v Airbus
Nose to nose
Why has the trade dispute between the world's two big aircraft-makers
suddenly become so bitter?
Jun 23rd 2005 | PARIS | from the print edition
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Mortgage Market
The mortgage market is huge:
$14 trillion in the US
Over $1 trillion in Canada
Thus the mortgage market comprises a large
percentage of all debt outstanding.
A large portion of mortgages are packaged
and sold to investors (more on this lat

More on Duration
Let r(t) be the yield curve. Recall
M D = Sensitivity to changes in YTM
ED = Sensitivity to changes in r(t) (parallel shift)
P D = Sensitivity to changes in one rate r(ti )
Suppose you hold a large bond portfolio, with
bonds maturing out

Repos
Repo
A Repo or more formally a Sale and Repurchase
agreement is an agreement to sell and then
repurchase a security at a xed date at a xed
price. Repos are typically over a short time
period, often 1 day.
As we will see, repos are really a type of
s

Return Decomposition
If we hold a bond portfolio at time t and sell it
later at say t + 1, we expect a change in value
V = V (t + 1) V (t).
Naturally, we hope that V > 0.
It is often useful to understand the drivers of
these changes in value.
Return Decom

Synthetic CDOs
The idea of a synthetic CDO is vaguely similar to
a regular CDO, except that the assets are
essentially CDS instead of actual bonds and
loans.
Synthetic CDOs
The idea of a synthetic CDO is vaguely similar to
a regular CDO, except that the a

Plain Vanilla Swaps
Swap
A swap is simply a contract where 2 parties agree
to swap cash ows. When the parties agree to
swap a xed stream of cash ows with a oating
rate stream of cash ows in the same currency, it
is called a plain vanilla interest rate swa

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

Models of Interest Rates
We have considered the short rate model
dy = dz
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

Duration
Duration is essentially both a measure of how
long a bond has left to mature on average as
well as a measure of the sensitivity of the bonds
price to changes in interest rates. There are
several types of duration measures we wish to
consider.
Dur

More Interest Rate Derivatives
We will look primarily at caps, oors and collars.
Caps
An interest rate cap is a type of option on interest
rates. Given a notional of N , the cap pays
N max(actual rate - cap , 0)
at intervals
Caps
Suppose 1 year rates at s

ED Futures
Swap
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 certicate of deposit. The maj

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

Introduction
Our focus will be on xed income securities (i.e.
bonds) and their markets.
We will look at the instruments, pricing,
sensitivity measures, derivatives on interest rates,
interest rate models, and other topics.
US Bond Market Segments
Segment

Interest Rates
Simple Interest
A(t) = A0 (1 + ti)
Compound Interest
t
A(t) = A0 (1 + i) or A(t) =
Continuous Interest
A(t) = A0 eit
i
1+
m
mt
Bonds
Bullet Bond
A Bullet Bond is a bond that pays xed coupons
plus face value at maturity.
The value of a bulle

Issues in Portfolio Management
The CFA text chapters 16-21 discuss xed
income portfolio management from a more
institutional perpective.
In Chapter 18, the text discusses managing a
portfolio in order to track an index (since
investing in the index is usu

Hedging Example
Example
Suppose a market maker agrees to buy (at the
bid price) $100 million of relatively illiquid 20
year bonds. Now what should she do?
Ideally, sell the bonds (at the ask price) to
another customer and pocket the spread.
Note a spread

Eective Duration
In the last case study, what rates did we expect
to move?
Q: If the 2 year zero rate rises and all other rates
stay constant, what should happen to the 20 year
YTM?
Eective Duration
In the last case study, what rates did we expect
to move

Case Study
Example
On May 30, 2011, the following government bonds traded
with the following characteristics:
Maturity
June 1/15
June 1/15
Dec 31/15
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

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

Yield Models (more detail)
(In this section, we will assume continuous
compounding and bonds that pay a continuous
coupon)
Idea: let y = yields (or interest rates). Then
dy = dt + dz
Yield Models (more detail)
(In this section, we will assume continuous
c

CHAPTER 35
Real Options
Practice Questions
Problem 35.1.
Explain the difference between the net present value approach and the risk-neutral valuation
approach for valuing a new capital investment opportunity. What are the advantages of the
risk-neutral va

MATBUS 471
Assignment #3 Due Wednesday November 27 at noon.
You will likely want to use Excel or something similar to answer many of these questions. It
suffices to attach an annotated copy of an Excel printout to your assignment.
1. Suppose the table bel

Q1
a)
Current LIBOR
Expiry
Today
3 months
6 months
9 months
12 months
1.70%
Spot
1.70000%
1.84997%
2.23295%
2.54934%
2.93872%
b)
1 Year Swap Rate
c)
Given our position, we anticipate that the LIBOR will fall. To hedge against an increase in int. rates we

Settlement
Maturity
Coupon
YTM
Last coup
next coup
Days in Period
Days from Last
1-Jan-15
30-Sep-21
5%
6.000000000%
30-Sep-14
31-Mar-15
182
93
CP
AI
FP
94.510421016 945104.21016004
1.277473
95.7878935435
(A)
95.8565749
95.8657101734
Loan Size
Int charge
9

MATBUS 470 Winter 2014 assignment 2.
Due: February 28th at the beginning of class
1. Problem 10.26.
Consider an option on a stock when the stock price is $41, the strike price is $40, the risk-free
rate is 6%, the volatility is 35%, and the time to maturi

MATBUS 470 Winter 2014
Assignment 3
Due: Noon March 21th in M3 2001.
1. Problem 13.14 A companys cash position, measured in millions of dollars, follows a
generalized Wiener process with a drift rate of 0.1 per month and a variance rate of 0.16
per month.

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MATBUS 470 Fall 2013 assignment 1.
Due: October 8th at the beginning of class
1. Problem 1.32.
On July 15, 2010, an investor owns 100 Google shares. As indicated in Table 1.3, the share price
is about $497 and a December put option wit