FINANCIAL STATISTICS 4
Tutorial Example Sheet 1 Basic Ideas about Interest Rates
SOLUTIONS
1.
r
Amount owed at end of term is P 1
n
nT
.
36
(a)
0.08
1000 1
12
(b)
0.07
1000 1
12
(c)
0.05
1000 1
12
1,270.24
60
1,417.24
120
1,647.01
12
2 (a
Background
Founded in 1999, Alibaba is Chinas largest e-commerce platform for small to
medium sized businesses connecting millions of buyers and suppliers worldwide.
The Alibaba group stocks wholesalers, exporters and manufacturers, in a global
community
CHAPTER 4
USING STOCHASTIC PROCESSES TO PRICE OPTIONS
4.1 Geometric Brownian Motion
The price of an asset, in particular a share, will fluctuate in response to a range
of factors the apparent strength of the company, the perceived health of the
whole eco
FINANCIAL STATISTICS 4
Tutorial Examples
Chapter 1 Basic Ideas about Interest Rates
Simple and Compound Interest
1.
Suppose that you borrow 1,000 for T years, at a nominal interest rate of
100r% p.a. (converted monthly). How much do you owe at the end of
CHAPTER 3 USING BINOMIAL TREES TO PRICE
OPTIONS
In Chapter 2, we looked at pricing strategies for call and put options without
discussing share-price volatility explicitly, so we obtained rather limited
deterministic outcomes (generally upper and lower bo
CHAPTER 2 BASIC IDEAS ABOUT INVESTMENTS
2.1 Asset classes
An asset is a resource with economic value that an individual, corporation or
country owns or controls with the expectation that it will provide future benefit
(http:/www.investopedia.com/terms/a/a
FINANCIAL STATISTICS 4
Solutions to Examples 21 31
21 (a) S0 = 80, r = 0.08, T = 6/12 = 0.5
(b)
F0 S0 e rT = 80 e (0.08 x 0.5) = 83.26
The PV of the dividend income is
I = 6 e0.08 x 2 / 12 = 5.92
F0 S0 I e rT = 74.08 e (0.08 x 0.5) = 77.10
The presence of
CHAPTER 4
USING STOCHASTIC PROCESSES TO PRICE OPTIONS
4.1 Geometric Brownian Motion
The price of an asset, in particular a share, will fluctuate in response to a range
of factors the apparent strength of the company, the perceived health of the
whole eco
FINANCIAL STATISTICS 4
Solutions to Examples 1 5
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
nT
.
36
60
1,270.24
1,417.63
120
2.
1,647.01
In order to find reff, we need to calculate th
CHAPTER 3 USING BINOMIAL TREES TO PRICE
OPTIONS
In Chapter 2, we looked at pricing strategies for call and put options without
discussing share-price volatility explicitly, so we obtained rather limited
deterministic outcomes (generally upper and lower bo
FINANCIAL STATISTICS 4
Solutions to Examples 6 20
6.
(1 r n) k 1
Amount owed at end of kth period is P (1 r n) A
.
r n
(a)
At k = 36, require amount owed to be 0, i.e.
k
12000 (1 0.09 12)
i.e.
(b)
36
(1 0.09 12) 36 1
A
0
0.09 12
0.09 (1 0.09 12) 36
A 1200
School of Mathematics
& Statistics
FINANCIAL STATISTICS
Session 2016-17
Professor John H. McColl
Room 233
[email protected]
COURSE SUMMARY
1. Basic Ideas about Interest Rates
Reminder some important series
Simple and compound interest
Interest rat
School of Mathematics
& Statistics
FINANCIAL STATISTICS
Session 2016-17
Professor John H. McColl
Room 233
[email protected]
COURSE SUMMARY
1. Basic Ideas about Interest Rates
Reminder some important series
Simple and compound interest
Interest rat
CHAPTER 2 BASIC IDEAS ABOUT INVESTMENTS
2.1 Asset classes
An asset is a resource with economic value that an individual, corporation or
country owns or controls with the expectation that it will provide future benefit
(http:/www.investopedia.com/terms/a/a
Background
Jimmy Choo is a 21st century luxury accessories company, dealing in designer
labelled shoes, handbags, small leather goods, fragrances and other accessories.
The brand stems from the East End of London back in the 1990s, when Jimmy Choo
was a b
FINANCIAL STATISTICS 4
Tutorial Example Sheet 3 Using Binomial Trees to Price Options
21.
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 4 Using Stochastic Processes to Price Options
26.
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
Formula Sheet
Repayment on a constant
payment loan
r (1 r n)Tn
A P
n (1 r n)Tn 1
Put-call parity for
European options
c X e rT p S0
Itos Lemma
Suppose that cfw_Xt, t 0 follows the Ito process dX a( X , t ) dt b( X , t ) dZ . Let
G b
CHAPTER 5 PORTFOLIOS FOR MANAGING RISK
5.1 Creating Spreads and Combinations
In Chapters 2 4, we discussed the pricing of financial derivatives without
saying much about how such derivatives are used in practice. When investors
use derivatives to reduce t
Friday, 16th May 2014
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
School of Mathematics
& Statistics
FINANCIAL STATISTICS
Session 2014-15
Professor John H. McColl
Room 233
[email protected]
COURSE SUMMARY
1. Basic Ideas about Interest Rates
Reminder some important formulae
Simple and compound interest
Annuities
CHAPTER 2 BASIC IDEAS ABOUT INVESTMENTS
2.1 Asset Classes
An asset is a resource with economic value that an individual, corporation or
country owns or controls with the expectation that it will provide future benefit
(http:/www.investopedia.com/terms/a/a
Financial Statistics Revision Lecture
Session 2013-14
The Exam
The exam lasts 90 minutes.
You must choose 3 questions from 4. If you attempt more than 3
questions, only your first 3 answers will be marked.
Each question is marked out of 20. So the paper i
FINANCIAL STATISTICS 4
Tutorial Example Sheet 5 Portfolios for Managing Risk
SOLUTIONS
33 (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
26.
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 5 Portfolios for Managing Risk
Creating Spreads and Combinations
33.
(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
o
FINANCIAL STATISTICS 4
Tutorial Example Sheet 1 Basic Ideas about Interest Rates
Simple and Compound Interest
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
th
FINANCIAL STATISTICS 4
Tutorial Example Sheet 2 Basic Ideas about Investments
Asset Classes
12.
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 ca
FINANCIAL STATISTICS 4
Tutorial Example Sheet 3 Using Binomial Trees to Price Options
SOLUTIONS
21.
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
FINANCIAL STATISTICS 4
Tutorial Example Sheet 2 Basic Ideas about Investments
SOLUTIONS
12 (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