The Black-Scholes formula is a continuous-time pricing formula that
calculates the European call and put option value. The formula is f 0 = S0N(d1) exp(-rT)KN(d2). The formula uses the binomial tree model as a basis in which the
binomial tree models the c
Mat h 366
Numerical Project
Name:
St udent ID:
Paramet ers
K
T
r
S0S0
n
tt
R
u
d
p
R^n
120
1
0.07
0.3
105.1
50
0.02
1.0014009805
1.0433392709
0.9584609991
0.5059007498
1.0725081813
Result s
Sum
Option Price
10.58554 54 34
9.86989714 3
Black Scholes
ln(S/K
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6. WEEK 6
Math 366 Winter 2015 Week 6 Assignment Solution
E XERCISE 6.1. A stock price is currently $100. Over each of the next
two six-month periods it is expected to go up by 10% or down by 10%. The
risk-free interest rate is 8% per year with continu
84
7. WEEK 7
Math 366-1 Winter 2014 Week 7 Assignment Solution
E XERCISE 7.1. What are the Cox-Ross-Rubinstein and the Hull-White
Conditions in a binomial tree model? Why do we need them?
S OLUTION . In a one-step binomial tree model, there are three para
50
5. WEEK 5
2. Quiz 4 solution
Problem 1. Suppose that the stock pays dividend at the rate q. At time
t < T the stock price satises
K
.
1 eq( T t)
Show that the value of the European call option satises
St >
c(t, T; K, St ) < St K.
This means that it is
40
4. WEEK 4
Math 366 Winter 2015 Week 4 Assignment
E XERCISE 4.1. Suppose that a $45 call which expires in one year is valued at $7, and a $45 put with the same expiration date is valued at $5.
Suppose also that the market interest rate is 8%. If the sto
98
8. WEEK 8
Math 366 Winter 2015 Week 8 Assignment Solution
E XERCISE 8.1. For a single step binomial tree model (r, u, d, p) representing a stock for a small time t, the random rate of return to be ln(St /S0 ).
We have connected the average rate of retu
12
2. WEEK 2
Math 366 Winter 2015 Week 2 Assignment
Note. For computational problems, you are required to set up numerical
formulas. You can then complete the calculations with a calculator. You
will not be given full credit if you only show the numerical
26
3. WEEK 3
3. Week 3 assignment
Math 366 Winter 2016 Week 3 Assignment
E XERCISE 3.1. (Risk of fixed interest investment) You purchase a bond
which pays interest at a fixed rate.
(1) Suppose that the market interest rate goes up, is your bond more
valua
4. WEEK 4 ASSIGNMENT SOLUTION
43
Math 366 Winter 2016 Week 4 Assignment Solution
E XERCISE 4.1. Suppose that a $45 call which expires in one year is valued at $7, and a $45 put with the same expiration date is valued at $5.
Suppose also that the market in
40
4. WEEK 4
Math 366 Winter 2016 Week 4 Assignment
E XERCISE 4.1. Suppose that a $45 call which expires in one year is valued at $7, and a $45 put with the same expiration date is valued at $5.
Suppose also that the market interest rate is 8%. If the sto
2
1. WEEK 1
Math 366 Winter 2016 Week 1 Assignment
E XERCISE 1.1. Briefly define the following terms:
(1) underlying assets;
(2) call option;
(3) value of an option;
(4) American option;
(5) bond.
E XERCISE 1.2. A butterfly option is a portfolio consistin
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3. WEEK 3
Math 366-1 Winter 2016 Week 3 Assignment Solution
E XERCISE 3.1. (Risk of fixed interest investment) You purchase a bond
which pays interest at a fixed rate.
(1) Suppose that the market interest rate goes up, is your bond more
valuable or les