Econ 691
Special Topics in Derivatives
Problem Set III
Lau
Due: 6/6/12
1.
Today is May 21, 2012. The cheapest-to-deliver bond in a September 2012 T-bond futures
contract is a 11% coupon bond, and delivery is expected to be made on September 30, 2012.
Coup
101
VI.
Interest Rate Options (II) (Chapter 28)
15.3 Option Pricing (Black-Scholes) Formulas
c = Se qT N (d1 ) Xe rT N (d 2 )
(15.4)
p = Xe rT N (d 2 ) Se qT N (d1 )
(15.5)
2
S
) + (r q + )T
X
2
d1 =
T
2
S
ln( ) + (r q )T
X
2
d2 =
= d1 T
T
ln(
16.8
Black'
76
IV.
Interest Rate Options (I) (Chapter 28)
Interest rate derivatives are more difficult to value than the equity and foreign exchange derivatives.
i)
The probabilistic behavior of interest rate is much more complicated than that of a stock price
or an
53
III.
Swaps (Chapter 7)
A swap is an agreement between two companies to exchange cash flows in the future. The agreement
defines the dates when the cash flows are to be paid and the way that they are to be calculated.
Note: A forward contract is a swap.
Econ 698 Special Topics in Options and Futures
Lecture Notes
Professor Man-lui Lau
2
I.
Interest Rate Markets (Chapter 4)
4.1
Types of Rates
Treasury rates:
the treasury rates of interest applicable to borrowing by a government in its own
currency.
LIBOR
Econ 691
Special Topics in Derivatives
Problem Set X
Due: 6/29/12 (F)
1.
paper version
PDF file
Lau
3pm in my office
midnight
(20 points) Suppose that the probability of a reference entity defaulting during a year
conditional on no earlier default is 1%.
Econ 691
1.
Special Topics in Derivatives
Problem Set IX
Lau
due: 6/25/12
The value of a companys equity is $3 million and the volatility of the equity is 80%. The debt
that will have to be paid in 1 year is $9.5 million. The risk-free interest rate is 5%
1
Econ 691
1.
Special Topics in Derivatives
Problem Set VIII
Lau
due: 6/22/12 (F)
(20 points) Consider a long position in a 8% coupon bond (payable semiannually) with a
principal of $2 million maturing in 0.9 years.
Use the data in the table on page 137 i
1
Econ 691
Special Topics in Options and Futures
Problem Set VII
Lau
due: 6/19/12 (M)
1.
A corporation knows that in 3 months it will have $5 million to invest for 90 days at =
LIBOR 50 basis points and wishes to ensure that the rate obtained will be at l
Econ 691
Special Topics in Derivatives
Problem Set VI
Lau
Due: 6/13/12
Show all formulas.
1.
Companies A and B have been offered the following rates per annum on a $20 million 5-year
loan.
Fixed rate
5%
6.4%
A
B
Floating rate
LIBOR 0.1%
LIBOR 0.4%
Company
Econ 691
Special Topics in Derivatives
Problem Set V
Lau
Due: 6/11/12
1.
(20 points) The 1-year LIBOR rate is 10%. A bank trades swaps where a fixed rate of interest
is exchanged for 12-month LIBOR with payments being exchanged annually. The 2-year and
3-
Econ 691
1.
Special Topics in Derivatives
Problem Set IV
Lau
Due: 6/8/12
(20 points) Suppose the 8-year spot rate (continuous compounding) is 5% and the 8.25-year
spot rate is 5.2%.
a)
Calculate the forward interest rate between year 8 and year 8.25.
Supp
Econ 691
Special Topics in Derivatives
Problem Set II
Lau
due: 6/4/12
Instruction:
1.
You need to show all the formulas.
1.
Calculate the conversion factor of a 10% coupon bond with 13 years and 7 months to maturity.
2.
Calculate the conversion factor of
Econ 691
Special Topics in Derivatives
Problem Set I
Lau
due: 5/23/12
Instructions:
1.
Answer all questions.
2.
You must do the questions individually.
3.
Show your formulas and steps clearly.
4.
No Excel spreadsheet except question #4.
1.
Calculate the p