FINANCIAL STATISTICS 4
Tutorial Example Sheet 3 Using Binomial Trees to Price Options
SOLUTIONS
20.
At the end of one month, the stock price (ST) will be either 42 (with a
payoff on the call option of 3) or 38 (with a payoff of 0). Let be the
probability
Friday, 6th May 2011
6.30 pm 8.00 pm
EXAMINATION FOR THE DEGREES OF M.SCI AND B.SC. (SCIENCE)
_
STATISTICS
MATHEMATICS AND STATISTICS
HONOURS
Financial Statistics
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used
in ex
FINANCIAL STATISTICS (LEVEL M) - PROJECT
Comparing how forward and futures contracts are priced
From the brief description given in the lecture notes, it might appear that a
forward contract and a futures contract are just the same thing. It is true that
FINANCIAL STATISTICS 4H
End-of-Course Examination, May 2011
SOLUTIONS
1(a) Any 3 of the following or other sensible comments; 1 mark for mentioning a relevant
feature of the loan and 1 mark for discussing its impact from the point of view of the
borrower:
FINANCIAL STATISTICS 4H
End-of-Course Examination, April/May 2013
SOLUTIONS
1. (a)
(i) At t = 4, a sum of 10,000 deposited at t = a will be worth:
10000 exp
4
a
(0.02 0.01t ) dt 10000 exp 0.16 0.02a 0.005a 2
So P(4) 10000 exp 0.16 10000 exp 0.10 22,786.81
Friday, 3rd May 2013
2.00 3.30 pm
EXAMINATION FOR THE DEGREES OF M.A., M.SCI AND B.SC.
(SCIENCE)
FINANCIAL STATISTICS
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used in
examinations. No calculator which can store or
FINANCIAL STATISTICS 4
Tutorial Example Sheet 3 Using Binomial Trees to Price Options
20.
The current price of a stock is 40. It is believed that, at the end of one
month, the same stock will be priced at either 42 or 38. The risk-free
interest rate is 8%
FINANCIAL STATISTICS 4
Tutorial Example Sheet 2 Basic Ideas about Investments
10.
Briefly describe the main features of each of the following as a form of
investment: (a) commercial property; (b) UK Government bonds; (c)
equities. In each case, you should
FINANCIAL STATISTICS 4
Tutorial Example Sheet 5 Portfolios for Managing Risk
32.
(a)
(b)
(c)
A bear spread can be created by dealing in two European call
options on the same stock with the same expiration time T, buying
one at a strike price X2 and (short
FINANCIAL STATISTICS 4
Tutorial Example Sheet 1 Basic Ideas about Interest Rates
1.
Suppose that you borrow 1,000 for T years, at a nominal interest rate of
100r% p.a. (compounded monthly). How much do you owe at the end of
the term if: (a) T = 3, r = 0.0
FINANCIAL STATISTICS 4
Tutorial Example Sheet 4 Using Stochastic Processes to Price Options
25.
Suppose that S is a stock price that follows the usual model of Geometric
Brownian Motion, dS S dt S dZ , where Z is a Weiner Process.
Find dY when (a) Y = Sk,
FINANCIAL STATISTICS 4
Tutorial Example Sheet 1 Basic Ideas about Interest Rates
SOLUTIONS
nT
1.
r
Amount owed at end of term is P 1
n
(a)
0.08
1000 1
12
(b)
0.07
1000 1
12
(c)
0.05
1000 1
12
2.
(1 r n) k 1
Amount owed at end of kth period i
FINANCIAL STATISTICS 4
Tutorial Example Sheet 5 Portfolios for Managing Risk
SOLUTIONS
32 (a) For the bear spread created from two call options,
( ST X 1 )
c
2
( ST X 1 )
ST X 2 c2
c
Profit 1
c1 ST X 1
c1 c2
c1 c2 ST X 1
c c X X
2
2
1
1
( ST X 2 )
FINANCIAL STATISTICS 4
Tutorial Example Sheet 4 Using Stochastic Processes to Price Options
SOLUTIONS
25.
G
G 1 2G 2
G
Use Itos Lemma, dG
a
b dt
b dZ .
2
X
t 2 X
X
dY
d 2Y
k 1
Y S
kS 2 k (k 1) S k 2
dS
dS
k
(a)
So
1
dY kS k 1 ( S) 0 k (k 1) S k 2 S
FINANCIAL STATISTICS 4
Tutorial Example Sheet 2 Basic Ideas about Investments
SOLUTIONS
10 (a) An investor in commercial property (e.g. shopping centre, office block)
receives regular income in the form of rent from the tenant company.
There is potential
Friday, 11th May 2012
2.00 pm 3.30 pm
EXAMINATION FOR THE DEGREES OF M.A., M.SCI AND B.SC.
(SCIENCE)
FINANCIAL STATISTICS
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used in
examinations. No calculator which can store