HEDGING WITH INTEREST RATE SWAPS PROBLEM
1. (a) You observe the following anticipated floating rate swap payments, each
based on a notional $ 100 M. Assume semi-annual compounding.
Floating Payments
t=0
0.5
1 year swap 1M
1.5 year swap 1M
1
1.5
1.1M
1.1M
MEASUREMENT OF INTEREST RATE RISK: PROBLEMS & ANSWERS
I. PROBLEMS
11. Assuming all four bonds are selling to yield 5%, compute the following for each bond:
a. duration based on a 25 basis point rate shock (L">.y = 0.0025)
b. duration based on a 50 basis p
. - MORGAN STANLEY DEAN WITTER
(imam. Epum Am) DERJVATIWJ MARKETS
Juu I999
FEATURE
WHATS IN THE MARKET? cfw_Amwa
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By Jason: MERICH
ANNA Murwsm
D! K UMELE
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monomer! Stocks move on expectations of earnings growth. economic growth,
Notional
Company A
Company B
$100,000
Expects interest rates to fall - wants floating
Expects interest rates to rise - wants to lock in fixed
Company A will borrow at a fixed rate and swap it's CASH FLOWS for floating
Credit Rating
Annual Fixed rate
Float
Bond Price
Face Value
Coupon Rate
Life in Years
Yield
Frequency
Macaulay Duration
Modified Duration
Convexity
Period
0
1
2
3
4
5
6
7
8
9
10
$1,000.00
1,000
8.00%
10
8.00%
1
$935.82 If Yield Changes By
1000 Bond Price Will Change By
8%
10 Modified Duration
Year
BOP Value EOP Value
2010
100
120
2011
120
90
2012
90
130
2013
130
150
Arithmetic Average
Geometric Average
0.14
10.67%
HPR
1.20
0.75
1.44
1.15
HPY
0.20
(0.25)
0.44
0.15
Market Share
Apple
Tesla
Yahoo
IBM
IBM
Date
Adj Close
3/16/2016 $
144.79
3/15/201
REVIEW OF PROBABILITY AND STATISTICS
Risk and Return
Risk can be generally defined as the uncertainty of outcomes. It is best explained
in terms of probability, which traces its roots to problems of fair distribution. In fact, in
the Middle Ages the word
NEWSLETTER
Understanding
the efficient frontier
High expected reward
i
ter
t fron
en
fi i
efc
he
ward
ts t
nd re
a
se n
f risk
s
hi
T
o
re
i n
ato
ep
r
bin
om
ne
li
al c
Th
i
tm
op
e
For every level of risk, there is some
optimum combination of investment
Asymmetric Wholesale Pricing:
Theory and Evidence*
Sourav Ray*
Department of Marketing
DeGroote School of Business, McMaster University
1280 Main Street, Hamilton, ON L8S-4M4, Canada
Phone: (905) 525-9140 ext. 22370; Fax: (905) 521-8995
Email: sray@mcmast
Problem 2
Annual Average Rate of Standard Deviation of
Return
Return
Portfolio X
S&P 500
T-bills
10%
12%
6%
18%
13%
n/a
Beta
0.6
1
n/a
Sharpe
Ratio
Treynor
Ratio
0.22
0.46
0.07
0.06
Treynor ratio attempts to measure how
well an investment has compensated
Bener Oguz
Spring 2016
FIN 653 CASE III: Bonds and Derivatives
1) The typical measure of interest rate risk for bonds or a bond portfolio is duration and convexity.
Duration is the sensitivity in the price of a bond to a change in interest rates. So the h
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.869201
R Square
0.75551
Adjusted R 0.749132
Standard E 2.896713
Observatio
119
ANOVA
df
Regression
Residual
Total
SS
MS
F Significance F
3 2981.871 993.9569 118.4559 5.02E-035
115 964.9586 8.390945
118 394
American Put with Binomial
S
E
T
rf
Sigma
n
50
52
1
0.05
0.1
3
European put with Black Sch
u
d
1.059434
0.9439
d1
d2
Prn
1-Prn
0.631037
0.368963
Exercise at expiraton
t
t+delta t t+2delta t t+3delta t PT
59.4555
0
56.12005
0
52.97171
0
0.632679
52.97171
5
S
E
T
rf
Sigma
50
52
1
0.05
0.1
European put
n
delta t
3 number of periods in the model
0.333333 years
Step 1
u
d
Rf
prn
1-prn
Find inputs into the binomial model with three periods
1.059434
0.9439
1.016806
0.631037
0.368963
Step 2
Construct a binomial tr
Data
S
Sigma
rf
T
N
delta t
45
0.35
0.0585
1
2
0.5
Parameters of the two-period binomial model
u
1.280803
d
0.78076
Rf
1.029682
prn
0.497801
1-prn
0.502199
Evolution of the stock price
Payoffs at expitaion
Price of the Contruct at time t
t
t+delta t t+2*(
Asian Option
S
E
T
rf
Sigma
n
50
u
d
average of the stock prices over the life of the option
1.059434
0.9439
1
0.05
0.1
3
t
t+delta t
Prn
1-Prn
t+2delta t t+3delta t PT
59.4555
0
56.12005
0.016022
52.97171 0.044155
52.9717118481
52.97171
0 1.03296
50
47.1
THE CAPITAL ASSET PRICING MODEL
A.
Introduction: We have hypothesized that the relevant risk of an asset is that
portion of its total risk that cannot be diversified away when the asset is included
in a portfolio.
But what portfolio are we speaking about?
THE BLACK-SCHOLES FORMULA
A. In this set of notes we will review the Black-Scholes formula, its origins and its
use. There are, in particular, two perspectives, which we will consider. Recall also
that out theory to date applies to non-dividend paying sto
THREE PERSPECTIVES ON THE VALUATION OF DERIVATIVE INSTRUMENTS
N. Gershun
A. Introduction: We have introduced two models for the price process on the underlying asset.
They are:
1. Geometric Brownian motion, where at any future time T,
lnST lnS 0 T T ~,
~
FACTOR AND INDEX MODELS
A. Introduction
1. Previously, we observed that the greatest problem with the CAPM may be the
impossibility of finding an adequate real world counterpart to the market portfolio M.
Conceptually, the S&P500 cannot be a perfect proxy
HOMEWORK SET 4
Derivatives
1.
What is a lower bound for the price of a 4 months call option
on a non-dividend paying stock when the stock price is $28, the exercise price is $25
and the risk free interest rate is 8% per annum.
2.
What is a lower bound for
Issues in the Rockets and Feathers Gasoline Price Literature
Report to Federal Trade Commission
John Geweke, University of Iowa
March 16, 2004
1. Preliminaries
(a) Literature surveyed. These notes synthesize the published rockets and feathers
gasoline pri
A Supergame-Theoretic Model of Price Wars during Booms
By Julio Rotemberg and Garth Saloner
Macro motivation: What happens with prices when demand increases? Can fiscal policy affect aggregate production?
Repeated Oligopoly: Prices may decrease when deman
PART 1: MEASURING THE SENSITIVITY OF BOND PRICES TO RATE CHANGES. DURATION
A. Introduction
So far we have reviewed how risk free bonds are priced, and what rate of return
(ROR) we can expect them to pay in the future. In this note set we consider a relate
Basel Accords
History of Bank Regulation
Pre-1988
1988: BIS Accord (Basel I)
1996: Amendment to BIS Accord
1999: Basel II first proposed
Basel III in response to the recent global
financial crisis
Pre-1988
Banks were regulated using balance sheet measure
J OURNAL OF HOUSING RESEARCH VOLUME 19 ISSUE 1
The Mortgage Finance Bubble: Causes and
Corrections
Patrie Hendershott, Robert Hendershott, and James Shilling
Abstract
This paper describes the development of a mortgage bubble in the last dozen years. The
b
Copulas: A personal view
Paul Embrechts
Department of Mathematics
ETH Zurich, Switzerland
First version: November 2007
This version: June 15, 2009
Abstract
Copula modeling has taken the world of nance and insurance, and well beyond,
by storm. Why is this?