DerivaGem - Version 2.01
For Excel 2000 and more recent versions of Excel
Applications created from the Applications Builder Software that
accompanies John Hull's texts:
"Options, Futures and Other Derivatives" 8/E
"Fundamentals of Futures and Options Mar
1.
2.
3.
4.
MATBUS 470 Winter 2017
assignment 2.
Due: March 20th at the beginning of class
Suppose that a stock price has an expected return of 13% p.a. and a volatility of 25% p.a.
The stock price today is $50. Calculate the following:
a. The expected pr
DerivaGem - Version 2.01
For Excel 2000 and more recent versions of Excel
This is the Options Calculator Software that has been designed to
accompany John Hull's texts:
"Options, Futures and Other Derivatives" 8/E
"Fundamentals of Futures and Options Mark
1.
2.
3.
4.
5.
MATBUS 470 Winter 2017
assignment 1.
Due: February 27rd at the beginning of class
You are giving the following information:
The current price of copper is $230 per 100 lbs.
The risk-free rate of interest is 4% p.a. for all maturities with
MATBUS 471
Assignment #1 - Solutions
Q 1 and 2 are in the Excel sheet.
Q3 a)
D=
t C t
1 1
mP
r
1+
m
P=
t
( )
Ct
r
1+
m
t
( )
Thus
MD=
t C t
1 dP 1 1
1
=
=
D
t +1
P dr
P m
r
r
1+
1+
m
m
( ) ( )
b) You can either take the limit of (a) as
P= C t ert and D=
m
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
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 #4
1. Suppose the yield curve is a follows: (Assume these rates are expressed in annual compounding)
Term (years)
1
2
3
4
Spot Zero-coupon rate
5%
6%
6.5%
7%
(a) By estimating forward rates, construct an interest rate tre
Winter 2017
1.
MATBUS 471
Assignment #5
You are a dealer and you are currently long $100 million (face value) of Ford Motor Company
bullet bonds with a MD of 8.1 trading at 112.5. You plan to hedge the risks of this position by
trading ED futures expiring
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