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
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
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*(
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
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
. - MORGAN STANLEY DEAN WITTER
(imam. Epum Am) DERJVATIWJ MARKETS
Juu I999
FEATURE
WHATS IN THE MARKET? cfw_Amwa
o i set.
rat/4MP"!
By Jason: MERICH
ANNA Murwsm
D! K UMELE
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monomer! Stocks move on expectations of earnings growth. economic growth,
HOMEWORK SET FOR MODULE 8
HEDGING WITH OPTIONS
Problem 1
What does it mean to assert that the delta of a call option is 0.7? How can a short
position in 1,000 options be made delta neutral when the delta of each option is 0.7?
Problem 2
Calculate the delt
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
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
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
PROJECT 4
OPTION PRICING
PART 1: THEORETICAL PROBLEMS
Please solve problems #13 and 17 from the problem set on Derivatives
PART 2: MONTE CARLO SIMULATION OF OPTIONS PRICE
A. Introduction
This part of the project has two objectives. The first objective is
TUTORIAL FOR SOLVER
To define a problem in Solver, you need to follow these essential steps:
1. Choose a spreadsheet cell to hold the value of each decision variable in your model.
2. Create a spreadsheet formula in a cell that calculates the objective fu
Return on F
expected return on A
sd(a)
10
0.2
0.2
(a).
CML
the CML of this risk-free asset F and risky asset A is not efficient.
(b).
Security A
Return
-10
50
Prob
0.5
0.5
Security B
Return
-20
60
(a)
Expected Return on A=
variance=
sd(a)=
Expected Return
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 ~,
~
HOMEWORK SET for EQUITY PORTFOLIOS
1. Assume an investor may invest his wealth in a single, risky asset A and the risk-free
asset F in any desired proportion.
The return on F is rF = 10, the expected return on A is E[rA ]= .20, and std (RA) = .2.
(a) Desc
DIVERSIFICATION AND ITS CONSEQUENCES: RISK REDUCTION VIA THE PORTFOLIO
PERSPECTIVE
A. Introduction and Overview:
1. So far we have one valuation model for stocks, the
fundamental-present-value-of-dividends approach. This
approach is not generally useful,
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?
CAPM AND FACTOR MODELS
Part I: CAPM
1. Request a password for WRDS (Wharton Research Data Service) database.
2. In WRDS, find Compustat database. There you can find information on the book
value of equity. Also, find information on the market value of equ
FIXED INCOME SECURITIES
A. Introduction
The title fixed income securities normally refers to debt style securities. They
can differ in many respects:
Short (<1 yr)(T-bill, CDs, Commercial Paper)
(i) Term
Long (>1yr) (T-bill, Corporate Bonds etc.)
(ii) Iss
THE PRICING OF STOCKS THROUGH TIME: A PURELY STATISTICAL HIGH
FREQUENCY MODEL OF STOCK PRICE BEHAVIOR
A. Introduction
1. Our previous discussion was conceptually useful and forms the basis of
the fundamental approach to stock valuation. But many questions
FIN 653
EMPIRICAL PROBLEM FOR MODULE 4 HOMEWORK
DERIVATION OF THE EFFICIENT FRONTIER
Part 1
1. Log into WRDS (Wharton) database, using the following information:
Userid: sseechar
Pwd: Plza.123
a.
b.
c.
d.
Choose CRSP (Center for the Research of Security P
DIVERSIFICATION AND THE EFFICIENT FRONTIER: CONCEPTUAL PERSPECTIVE
A. Introduction: We are focusing on the principles of diversification because the
usefulness of a stock for diversification in part determines its price, and thus its
expected return.
Thus