liv1.tex Week 1: 27.1.2014
I. ECONOMIC BACKGROUND
1. Time Value of Money; discounting
Recall rst the denition of simple interest, at 100x% p.a. With one unit
(a pound, say) invested for one year, at the end of the year we have:
1 + x with interest calcula
liv2.tex Week 2: 3.2.2014
5. Portfolios and Hedging.
Portfolios.
We consider an investor with capital to invest. The simplest model is
that in which he has two (or more) choices: to invest in
(i) a bank account assumed riskless, and yielding interest. For
liv3.tex Week 3: 10.2.2014
Chapter II. PROBABILITY BACKGROUND.
1. Measure
The language of option pricing involves that of probability, which in turn
involves that of measure theory. This originated with Henri LEBESGUE
(1875-1941), in his 1902 thesis, Intg
liv4.tex Week 4: 17.2.2014
One of the great contributions of Kolmogorovs classic book of 1933 was
the realization that measure theory specically, the Radon-Nikodym theorem provides a way to treat conditioning in general, without making assumptions that we
liv0.tex
MATH482 MATHEMATICAL FINANCE
N. H. BINGHAM
Liverpool University, Monday 27 January Monday 28 April 2014
Books
Our main text will be Ch. 1-6 of
[BK] N. H. BINGHAM and Rdiger KIESEL: Risk-neutral valuation: Pricu
ing and hedging of nancial derivati
MATH482 SOLUTIONS to EXAMINATION, 2013
Q1. (a) Types of risk. Institutions encounter risks of various types. Perhaps the biggest one starts at the top: how good is the board? If the board
of directors, and particularly the chairman and CEO, do not have a
livsoln2.tex
SOLUTIONS 2. 11.2.2013
Q1. Barings Bank and Nick Leeson. Barings Bank Britains oldest bank,
and bankers to HMQ collapsed in 1995 after huge losses in unauthorised
trading by one rogue trader, Nick Leeson (see Wikipedia [W below] for
details).
livprob1.tex
SOLUTIONS 1. 3.2.2014
Q1. Money.
(i) History. A simple moneyWikipedia search turns up more than we
need. Some brief notes:
Barter is the exchange of one kind of goods for another; this can also extend
to services. This is informal, and can be
MATH482 SOLUTIONS to MOCK EXAMINATION, 2013
Q1. (i) Arbitrage. An arbitrage opportunity is the possibility of making a
riskless prot a trading strategy in which one starts with nothing, never
makes a loss, but might make a prot.
(ii) The assumption of abs
livsoln3.tex
SOLUTIONS 3. 17.2.2014
Q1. (i) In spherical polar coordinates (r, , ) (r: distance from centre, range
0 to ; : colatitude (= 1 - latitude), range 0 to ; longitude, range 0
2
to 2 ): increase r to r + dr, etc. The element of volume dV is a (to