UCL DEPARTMENT OF STATISTICAL SCIENCE
Courses in Statistical Science
for Mathematics Undergraduates
2015/16
Who should use this document?
This document provides a guide to courses offered by the Department of Statistical Science
that can be taken by undergraduates from the Department of Mathematics who have
successfully completed MATH7501 Probability and Statistics I. Because MATH7501 cannot
be taken before the second term of year 2, Statistical Science courses are not available to
Mathematics students until their third year at the earliest.
This document is not intended for use by the following students:

Students registered on either of the Mathematics and Statistical Science (MASS)
programmes, for whom other arrangements are made. These students should refer to
the separate Undergraduate Student Handbook and information published by the
Department of Mathematics.

Students registered in the Department of Mathematics on undergraduate affiliate
programmes who are enrolled at UCL during the autumn term only. A separate
handbook: Courses in Statistical Science for Undergraduates on Affiliate Programmes
(Autumn Term Only) is provided for these students.
Courses Available
The courses are listed below; syllabuses are given at the end of the document. The courses
are all 0.5 units. In most cases, prerequisites equivalent to those stated are acceptable. All
courses except STAT3101 and STAT3102 are part of the BSc programmes offered to
students in the Department of Statistical Science and the normal prerequisite courses
(which are not those stated below) are from those programmes. Consequently,
Mathematics students may have to do some preliminary reading for some courses (see
footnotes 1 and 3 below).
Year
Course Code
Course Title
Term
Prerequisite
3
STAT2002
1
MATH75011
3 or 4
3 or 4
3 or 4
3 or 4
3 or 4
3 or 4
STAT3003/M011
STAT3004/M009
STAT3005/M018
STAT3006/M017
STAT3020/M020
STAT3022/M022
2
2
2
1
2
2
3 or 4
3 or 4
4
4
STAT3101
STAT3102
STAT3001/M012
STAT3002/M010
Linear Models & the Analysis of
Variance
Forecasting
Decision & Risk
Factorial Experimentation
Stochastic Methods in Finance I
Stochastic Methods in Finance II
Quantitative Modelling of Operational
Risk & Insurance Analytics
Probability & Statistics II
Stochastic Processes
Statistical Inference
Stochastic Systems
STAT3102
MATH7501
STAT2002
STAT31012
STAT3006
MATH7501 &
STAT7001
MATH7501
MATH75013
STAT3101
STAT3102
1
1
2
1
1
STAT2002 requires students to do a small amount of preliminary reading and, during the course, requires
students to be able to interpret output from the Minitab statistical software package which is not used in
MATH7501. Students are given extra help on Minitab output in tutorials.
2
Alternatively, simultaneous attendance on STAT3101.
3
STAT3102 can be, and has been, taken by students without STAT3101 but this requires them to do some
preliminary reading. The required material can be found in "Introduction to Probability Models" by S.M. Ross
(Academic Press, 2007): Sections 2.5 (Jointly distributed random variables, pages 47-60), 2.6 (Moment
generating functions, pages 64-70) and 3.1 to 3.5 (Conditional probability and expectation, pages 97-132).
1
Course STAT2002 is at Intermediate level. All of the courses with codes beginning
STAT3### are at Advanced level. Courses with codes beginning STATM### are at Masters
level and may only be taken by students in the final year of an MSci degree.
Students requiring advice on preliminary reading should obtain it BEFORE they leave for
the summer vacation at the end of the year preceding that in which they intend to take the
course (see below for names of staff to approach for advice).
Advice and registration
For general advice and information about statistics courses and BEFORE registering for a
course on Portico, Mathematics students MUST consult a member of the Statistical Science
staff, who will determine whether they have the necessary academic prerequisites.
The Department of Statistical Science is located on the first and second floors of 1-19
Torrington Place and the offices of the staff named below are all in this location. The
registration procedure is as follows.


During the first week of term 1, see:
Date
Time
Staff Member
Room
Monday 28 September
Tuesday 29 September
Wednesday 30 September
Thursday 1 October
Friday 2 October
12:00 – 14:30
13:00 – 15:30
13:00 – 15:30
14:00 – 17:00
14:00 – 17:00
Dr Matina Rassias
Dr Matina Rassias
Dr Matina Rassias
Dr Ricardo Silva
Dr Ricardo Silva
140
140
140
139
139
Before and after the first week of term 1, see Dr Ricardo Silva (room 139) during his
regular office hours (Mondays 11:00-12:00, Wednesdays 12:00-13:00 and Fridays
14:00-15:00).
To register after this discussion, use the Portico system. Ensure that any course codes you
select correspond exactly to those given in the above list. Registrations will NOT be
approved unless they have been agreed with the Department beforehand. Also, for some
courses the Department can only accommodate students up to a certain maximum number,
and no further registrations will be approved once this maximum is reached.
Teaching Arrangements
The courses on offer consist of lectures supplemented by at least one of the following:
tutorials, workshops, problem classes. Workshops are also referred to as "practical classes"
in some departmental literature. The proportions of these activities vary between courses;
details are provided in the next section.
Monitoring attendance and progress
Students' attendance at tutorials and workshops will be monitored. Unsatisfactory
attendance at these classes or an unsatisfactory coursework record will be reported to a
student's Departmental Tutor. An indication of the amount of set work for each course is
provided in the final section of this document.
You may be barred from taking examinations if you have not attended enough tutorials or
submitted enough coursework, EVEN if it does not count towards the final course mark.
2
Timetable
Course timetables are available from http://www.ucl.ac.uk/timetable, usually from midAugust onwards. After making your module selections on Portico, tutorial allocation for
Statistical Science courses will be arranged by the Teaching Administrator before courses
start and your tutorial group will automatically appear in your online timetable. However, it
may take one or two days after registration has been approved before all of the classes
appear on your personal timetable, particularly for tutorials. Check your timetable frequently,
in case alterations have been made. Note also that, once allocated, your tutorial group will
NOT be changed unless you can demonstrate a timetable clash.
Teaching dates:



Lectures and workshops for all Statistical Science courses start in week 2 of term 1.
Term 2 lectures and workshops begin on the first day of term.
Teaching for all Statistical Science courses continues until the last day of each term.
Examinations
For most courses, you are examined by a combination of in-course assessment and written
examination. The final mark is obtained by combining the in-course assessment mark and
the written examination mark. For each course described later in this handbook, a guideline
is given to indicate the scheme used for combining marks. To pass a course at any level
below Masters, a final mark of at least 40% is required. To pass a Masters-level course, a
final mark of at least 50% is required.
In-course assessment
At the beginning of each course, the lecturer will provide details of the method and dates of
any in-course assessment. The assessment dates will also be posted on the course Moodle
page. Students should ensure that they have no other commitments on these dates. Incourse assessment is a form of examination, and should be treated as such.
Each piece of in-course assessment set by the Department of Statistical Science has its
own rubric and the instructions given must be followed. In particular, do pay attention to the
consequences of missing the deadline set, non-submission and plagiarism;4 any of these
can result in your not passing the course. Teaching staff will set aside extra office hours to
discuss assessment-related matters and students should respect the lecturers’ time by
confining queries to these hours.
Some assessments will be in the form of a “take-home” assignment, to be handed in to the
Departmental Office or the course lecturer by a set deadline. For such assessments, you
will need to sign a cover sheet (provided by the course lecturer) containing a declaration
that the submitted work is entirely your own. You will also need to submit your work in a
single securely stapled bundle including the cover sheet.
Deadlines
The Department of Statistical Science aims to allow a reasonable period of time to complete
any item of assessment if you manage your time effectively. Late submissions will incur a
penalty unless there are extenuating circumstances (e.g. medical) supported by appropriate
documentation. Penalties are as follows:
4
Guidance on what constitutes plagiarism (and collusion) is also available from the Department of Statistical
Science Undergraduate Student Handbook.
3

For work submitted after the deadline but before the end of the next working day, the full
allocated mark will be reduced by 5 percentage marks.

For work submitted at any time during the following six days, the mark will be reduced
by a further 10 percentage marks.

For assessments submitted more than 7 days late but before the end of the second
week in term 3, a mark of zero will be recorded. However, the assessment will be
considered complete.
Word counts
Some assessments (usually involving the production of reports) carry a specified maximum
word count. Assessed work should not exceed the prescribed length. If submitted work is
found to exceed the upper word limit by less than 10%, the mark will be reduced by ten
percentage marks, subject to a minimum mark of 40% (50% for fourth year courses)
providing the work is of pass standard. For work that exceeds the upper word limit by 10%
or more, a mark of zero will be recorded. In the case of coursework that is submitted late
and is also over length, the lateness penalty will have precedence.
The word count will be considered to include all text and formulae in the abstract and main
body of the assessment (including figure and table captions), but to exclude the table of
contents, reference lists and appendices. However, this should not be regarded as an
invitation to transfer large amounts of surplus text into an appendix and the mark awarded
will reflect the standard of judgement shown in the selection of material for inclusion.
Use of calculators in examinations
Students are expected to bring a calculator with them to examinations for Statistical Science
courses. There are eight calculator models that the College has approved for use in
examinations. These are the Casio FX83ES, FX83GT+, FX83MS and FX83WA which are
all battery powered, and Casio FX85ES, FX85GT+, FX85MS and FX85WA which are all
solar powered. No other type of calculator is permitted for use in examinations for the
courses described in this document. Students are therefore strongly advised to purchase
one of these calculators as soon as possible. The use of a non-approved calculator
constitutes an examination irregularity (i.e. cheating) and carries potentially severe
penalties.
Course details
The following pages give more detail, including outline syllabuses, of the courses previously
referred to in this document. For most courses, some indication is also given of areas where
the course material may be applied in practice; this is to help students decide which options
might be most suitable for them. For those courses where both Advanced and Masters level
versions are available, details are given for the Advanced version only. The main difference
is in the assessment: the Masters level versions have different, shorter examination papers
(2 hours instead of 2.5 hours) and the pass mark for these versions is 50% instead of 40%.
4
Level: Intermediate
D.S. Moore & G.P. McCabe: Introduction to
rd
the Practice of Statistics (3 edition).
Freeman, 1999, chapters 11 − 13 only.
B.F. Ryan & B.L. Joiner: Minitab Handbook
th
(4 edition).,Duxbury, 2001, chapters 10 and
11 only.
Aims of course: To provide an introduction
Assessment for examination grading:
STAT2002
LINEAR MODELS AND THE ANALYSIS
OF VARIANCE (0.5 UNIT)
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2 ½ hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
to linear statistical modelling and to the
analysis of variance with emphasis on ideas,
methods, applications and interpretation of
results.
Objectives of course: On successful
completion of the course, a student should
have an understanding of the basic ideas
underlying multiple regression and the
analysis of variance; be able to analyse, using
a statistical package, data from some
common experimental layouts and carry out
and interpret simple and multiple regression
analyses; understand the assumptions
underlying these analyses and know how to
check their validity.
Other set work:
About 8 sets of practical exercises. These will
not count towards the examination grading.
Timetabled workload:
Lectures: 3 hours per week, 1 hour of which to
be used as necessary as a problems class.
STAT3001
STATISTICAL INFERENCE (0.5 UNIT)
Applications: Linear models and the
analysis of variance (ANOVA) are two basic
and powerful statistical tools to model and
analyse the relationship between random
variables, and thus are widely used in almost
all of classical and modern statistical practice.
Their use exemplifies the modern, modelbased approach to statistical investigations,
and provides the foundations for more
advanced techniques that may be required for
the study of complex systems arising in areas
such as economics, natural and social
sciences and engineering as well as in
business and industry.
Level: Advanced
Aims of course: To provide a grounding in
the theoretical foundations of statistical
inference and, in particular, to introduce the
theory underlying statistical estimation and
hypothesis testing, and to provide theory
underlying the methods taught in the first and
second years of degree courses offered by
the Department of Statistical Science or jointly
with other Departments.
Objectives of course: On successful
Prerequisites: MATH7501 or equivalent.
completion of the course, a student should be
able to: describe the principal features of, and
differences between, frequentist, likelihood
and Bayesian inference; define and derive the
likelihood function based on data from a
parametric statistical model, and describe its
role in various forms of inference; define a
sufficient statistic; describe, calculate and
apply methods of identifying a sufficient
statistic; define, derive and apply frequentist
criteria for evaluating and comparing
estimators; describe, derive and apply lower
bounds for the variance of an unbiased
estimator; define and derive the maximum
likelihood estimate, and the observed and
expected information; describe, derive and
apply the asymptotic distributions of the
maximum likelihood estimator and related
Course content: Analysis of variance for a
variety of experimental designs. Multiple
regression: model fitting by least squares,
model assessment and selection.
Heteroscedastic and autocorrelated errors.
Emphasis will be placed on ideas, methods,
practical applications, interpretation of results
and computer output, rather than on detailed
theory.
Texts:
R.J. Freund & W.J. Wilson: Regression
Analysis: Statistical Modelling of a
Response Variable. Academic Press, 1998.
2
quantities; conduct Bayesian analyses of
simple problems using conjugate prior
distributions, and asymptotic Bayesian
analyses of more general problems; define,
derive and apply the error probabilities of a
test between two simple hypotheses; define
and conduct a likelihood ratio test; state and
apply the Neyman-Pearson lemma.
Workshops: two 2 hour classes.
Tutorials: 1 hour per week.
Applications: The theory of statistical
Aims of course: To provide a continuation
inference underpins statistical design,
estimation and hypothesis testing. As such it
has fundamental applications to all fields in
which statistical investigations are planned or
data are analysed. Important areas include
engineering, physical sciences and industry,
medicine and biology, economics and finance,
psychology and the social sciences.
Objectives of course: On successful
STAT3002
STOCHASTIC SYSTEMS (0.5 UNIT)
Level: Advanced
of the study of random processes started in
Stochastic Processes (STAT3102), but with
the emphasis now on Operational Research
applications and including queueing theory,
renewal and semi-Markov processes and
reliability theory.
completion of the course, a student should
understand such concepts for stochastic
processes as the Markov property, stationarity
and reversibility and be able to determine
whether such properties apply in
straightforward examples; recognise and
apply appropriately a range of models, as
listed in the course contents, in a variety of
applied situations so as to determine
properties relevant to the particular
application.
Prerequisites: STAT3101 or equivalent.
Course content: Frequentist and Bayesian
approaches to statistical inference. Summary
statistics, sampling distributions. Sufficiency,
likelihood, and information. Asymptotic
properties of estimators. Bayesian inference.
Hypothesis testing. Likelihood ratio tests,
application to linear models.
Texts:
Applications: Stochastic systems arise in
D.R. Cox: Principles of Statistical Inference.
Cambridge University Press, 2006.
P.H. Garthwaite, I.T. Jolliffe & B. Jones:
nd
Statistical Inference (2 edition). Oxford
University Press, 2002.
P.M. Lee: Bayesian Statistics: An Introduction
nd
(2 edition). Arnold, 1997.
J.A. Rice: Mathematical Statistics and Data
rd
Analysis (3 edition). Duxbury, 2006.
G.A. Young and R.L. Smith: Essentials of
Statistical Inference. Cambridge University
Press, 2005.
many areas of application. They play a
fundamental role in Operational Research
which addresses real-world problems through
the use of mathematics, probability and
statistics; topics such as queueing theory and
reliability are important examples. Stochastic
processes are also vital to applications in
finance and insurance, and have many
applications in biology and medicine, and in
the social sciences. Stochastic process theory
underpins modern simulation methods like
Markov-chain Monte-Carlo (MCMC).
Assessment for examination grading:
Prerequisites: STAT3102 or equivalent.
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2 ½ hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
Course content: Markov processes:
revision of general concepts, reversibility and
detailed balance equations. Renewal theory
and reliability: regenerative events and
renewal processes, alternating renewal
processes, renewal reward processes.
Queues: the general single server queue,
Markov queueing models (M/M/k), limited
waiting room, more general queues (M/G/1,
G/M/1), queueing networks. Semi-Markov
processes: properties and simple examples.
Reliability: single repairable units, simple
systems of units.
Other set work:
About 8 sets of exercises. These will not count
towards the examination grading.
Timetabled workload:
Lectures: 2 hours per week.
3
data arise in many application areas including
economics, engineering and the natural and
social sciences. The use of historical
information to estimate characteristics of
observed processes, and to construct
forecasts together with assessments of the
associated uncertainty, is widespread in these
application areas.
Texts:
G. Grimmett & D. Stirzaker: Probability and
rd
Random Processes (3 edition). Oxford
University Press, 2001.
S.M. Ross: Introduction to Probability Models
th
(9 edition). Academic Press, 2007.
nd
S.M. Ross: Stochastic Processes (2 edition).
Wiley, 1996.
D. Stirzaker: Stochastic Models and
Processes. Oxford University Press, 2005.
E.P.C. Kao: An Introduction to Stochastic
Processes. Duxbury, 1997.
F.P. Kelly: Reversibility and Stochastic
Networks. Wiley, 1979.
Prerequisites: STAT3101 and STAT3102,
or equivalent.
Course content: Forecasting as the
Other set work:
discovery and extrapolation of patterns in time
ordered data. Revision of descriptive
measures for multivariate distributions.
Descriptive techniques for time series. Models
for stationary processes: derivation of
properties. Box-Jenkins approach to
forecasting: model identification, estimation,
verification. Forecasting using ARIMA and
structural models. Forecast assessment.
State space models and Kalman Filter.
Comparison of procedures. Practical aspects
of forecasting. Case studies in forecasting.
About 8 sets of exercises. These will not count
towards the examination grading.
Texts:
Assessment for examination grading:
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2 ½ hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
J.D. Cryer: Time Series Analysis. PWS
Publishers, 1986.
C. Chatfield: The Analysis of Time Series: An
th
Introduction (5 edition). Chapman and Hall,
1996.
Timetabled workload:
Lectures: 2 hours per week.
Workshops: two 2 hour classes.
Tutorials: 1 hour per week.
Assessment for examination grading:
STAT3003
FORECASTING (0.5 UNIT)
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2½ hour written examination in term 3.
The final mark is a 4 to 1 weighted average of
the written examination and in-course
assessment marks.
Level: Advanced
Aims of course: To introduce methods of
finding and extrapolating patterns in timeordered sequences.
Other set work:
Objectives of course: On successful
About 7 sets of exercises. These will not count
towards the examination grading.
completion of the course, a student should be
familiar with the most commonly-used models
for time series; be able to derive properties of
time series models; be able to select, fit,
check and use appropriate models for timeordered data sequences; understand and be
able to interpret the output from the time
series module of a variety of standard
software packages.
Timetabled workload:
Lectures: 2 hours per week.
Workshops: two 2 hour classes.
Office hours, during which the lecturer will be
available to discuss students' individual
problems with the course, will also be
provided.
Applications: Time series data take the
form of observations of one or more
processes over time, where the structure of
the temporal dependence between
observations is the object of interest. Such
4
Other set work
STAT3004
DECISION AND RISK (0.5 UNIT)
About 4 sets of exercises. These will not count
towards the examination grading.
Level: Advanced
Timetabled workload
Lectures: 2 hours per week.
Workshops: three 2 hour classes.
Office hours, during which the lecturer will be
available to discuss students' individual
problems with the course, will also be
provided.
Aims of course: To provide an introduction
to the ideas underlying the calculation of risk
from a Bayesian standpoint, and the structure
of rational, consistent decision making.
Objectives of course: On successful
completion of the course, a student should be
able to understand special measures of risk,
understand the concepts of decision theory,
find appropriate probability models for risky
events and check the validity of the underlying
assumptions, and be familiar with
methodology for detecting changes in risk
levels over time.
STAT3005
FACTORIAL EXPERIMENTATION (0.5
UNIT)
Level: Advanced
Aims of course: To introduce 2k
experiments, fractions and blocking. To
introduce designs for response surface
modelling. To discuss experimental designs to
achieve quality control, including Taguchi
ideas.
Applications: The ideas introduced in this
course provide a generic framework for
thinking about risk and decision-making in the
presence of uncertainty. As such, they can be
applied in many diverse areas. The course will
use examples from natural hazards,
environmental hazards, finance, and social
policy.
Objectives of course: On completion of
the course, a student should have an
k
understanding of the basic ideas relating to 2
factorial experiments, including for fractional
designs and with blocking; should be able to
analyse data from these experiments by the
analysis of variance and/or graphical
techniques; be able to design experiments for
response surface modelling; be able to
analyse data from factorial experiments with a
binomial response variable; be able to design
experiments for off-line quality control.
Prerequisites: MATH7501 or equivalent.
Course content
Introduction to Bayesian inference, conditional
probability, Bayes's formula, expectation and
utility. Elicitation of subjective probabilities and
utilities. Criteria for decision making.
Comparison of decision rules. Probability
models for the occurrence of extreme events.
Time series approaches to detecting/
modelling change in risk over time.
Texts
Applications: Factorial experiments are
useful in any situation in which a complex
system has to be investigated or optimised.
The applications tend to be in the fields of
science and technology, though that may be a
result of a lack of imagination rather than a
lack of wider applicability. Some examples are
the optimisation of an industrial production
process, the design of a new drug, the design
of a human-computer interface, the
optimisation of products and marketing
campaigns, computer simulations to explore
the effect of interventions on, e.g., economy or
climate, or the quality of new statistical
methodology.
rd
A. Gelman: Bayesian Data Analysis (3
edition). Chapman & Hall, 2013.
J.O. Berger: Statistical Decision Theory and
nd
Bayesian Analysis (2 edition). Springer,
2010.
Assessment for examination grading
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2½ hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
Prerequisites: STAT2002 or equivalent.
Course content: Experiments: What is an
experiment? Advantages over observational
5
k
studies. Importance of randomisation. 2
factorials: Advantages over one-at-a-time
experiments. Interactions, two-factor and
higher order. Estimation of effects including
relation with regression and orthogonality of
T
X X matrix. Estimation of error using
replication and using pre-specified
interactions. ANOVA table and relation of
sums of squares to effect estimates. Warning
about dangers of error estimation using
smallest effects. Using normal and half-normal
plots for analysis. Fractional factorials,
aliasing, choosing a design. Blocking. Model
checking and diagnostics. Response
k
surfaces: 3 , central composite and BoxBehnken designs. Fitting polynomial response
surfaces. Analysing experiments with a
binomial response variable - logistic
regression with multiple predictors. Taguchi’s
ideas: quality = lack of variability, control and
noise factors, exploiting interactions to reduce
process variability.
industry, in particular stochastic models and
techniques used for financial modelling and
derivative pricing.
Objectives of course: On successful
completion of the course, a student should
have a good understanding of how financial
markets work, be able to describe basic
financial products, have a good knowledge of
the basic mathematical and probabilistic tools
used in modern finance, including stochastic
calculus, and be able to apply the relevant
techniques for the pricing of derivatives.
Applications: The techniques taught in this
course are widely used throughout the
modern finance industry, including the areas
of trading, risk management and corporate
finance. They also have applications in other
areas where investment decisions are made
under uncertainty, for example in the energy
sector where decisions on whether or not to
build (i.e. invest in) new power plants are
subject to uncertainty regarding future energy
demand and prices.
Texts:
D.C. Montgomery: Design and Analysis of
Experiments (5th edition). Wiley, 2000.
G.K. Robinson: Practical Strategies for
Experimenting. Wiley, 2000.
Prerequisites: previous or simultaneous
attendance on STAT3101 or equivalent.
Assessment for examination grading:
Course content: Financial markets,
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2 ½ hour written examination in term 3.
The final mark is a 4 to 1 weighted average of
the written examination and in-course
assessment marks.
products and derivatives. The time value of
money. Arbitrage Pricing. The binomial pricing
model. Brownian motion and continuous time
modelling of asset prices. Stochastic calculus.
The Black-Scholes model. Risk-neutral
pricing. Extensions and further applications of
the Black-Scholes framework.
Other set work:
Texts:
About 8 sets of exercises. These will not count
towards the examination grading.
J. Hull: Options Futures and Other Derivative
Securities. Prentice Hall, 2000.
M. Baxter & A. Rennie: Financial Calculus.
Cambridge University Press, 1996.
Timetabled workload:
Lectures: 2 hours per week.
Workshops: two 2 hour classes.
Office hours, during which the lecturer will be
available to discuss students' individual
problems with the course, will also be
provided.
Assessment for examination grading:
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2 ½ hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
STAT3006
STOCHASTIC METHODS IN FINANCE
(0.5 UNIT)
Other set work:
Several sets of exercises. These will not count
towards the examination grading.
Level: Advanced
Aims of course: To introduce mathematical
concepts and tools used in the finance
6
Timetabled workload:
Course content: Utility theory; Real
Lectures: 2 hours per week.
Workshops: four 2 hour classes.
Office hours, during which the lecturer will be
available to discuss students' individual
problems with the course, will also be
provided.
options, including dynamic programming,
optimal investment rules, and managerial
flexibility; Risk management, including valueat-risk and credit risk modelling; More
advanced techniques in derivative pricing.
Texts:
J.Hull: Options Futures and Other Derivative
Securities. Prentice Hall, 2000.
M. Baxter & A. Rennie: Financial Calculus.
Cambridge University Press, 1996.
A.K. Dixit & R.S. Pindyck: Investment under
Uncertainty. Princeton University Press,
1994.
P. Wilmott: Wilmott Introduces Quantitative
Finance. Wiley, 2007.
STAT3020
STOCHASTIC METHODS IN FINANCE II
(0.5 UNIT)
Level: Advanced
Aims of course: To explore advanced
topics in finance via mathematical and
statistical methods in order to gain a better
understanding of optimal decision making, risk
management and derivative pricing
techniques. The course will be built on
material covered in STAT3006.
Assessment for examination grading:
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2½ hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
Objectives of course: On successful
completion of the course, a student should be
able to: Define the concepts of risk aversion
and stochastic dominance, and apply
them to manage risk in, and rank capital
projects; Understand how dynamic
programming can be used to make optimal
decisions under uncertainty; Understand how
to apply mathematical and statistical
modelling techniques to credit risk modelling,
value-at-risk measurements and capital
adequacy assessments; Understand a range
of modelling techniques used in derivative
pricing, and the concepts and assumptions
that underpin them; Criticise and understand
the limitations of these techniques as they are
used in the modern finance industry.
Other set work:
Several sets of exercises. These will not count
towards the examination grading.
Timetabled workload
Lectures: 2 hours per week.
Workshops: two 2 hour classes.
Office hours, during which the lecturer will be
available to discuss students' individual
problems with the course, will also be
provided.
STAT3022
QUANTITATIVE MODELLING OF
OPERATIONAL RISK AND INSURANCE
ANALYTICS (0.5 UNIT)
Applications: The techniques taught in this
course are widely used throughout the
modern finance industry, including the areas
of: business investments decisions (for
example in the energy sector where decisions
on whether or not to invest in and build new
power plants are subject to uncertainty
regarding future energy demand and prices);
in corporate finance; in trading activities in the
financial markets; in financial and other forms
of risk management; in valuing and
accounting for assets; and in the prudential
regulation of the banking industry.
Level: Advanced
Aims of course: To develop a core
mathematical and statistical understanding of
an important new emerging area of risk
modelling known as Operational Risk which
arose from the development of the Basel II/III
banking regulatory accords. This will equip
students with the necessary tools to undertake
core modelling activities required in risk
management, capital management and
quantitative modelling in modern financial
institutions.
Prerequisites: STAT3101, STAT3102,
STAT3006 or MATH3508.
7
functions, basic asymptotics of compound
processes, modelling truncated and censored
data constant threshold Poisson process,
negative binomial and binomial processes,
effects of ignoring data truncation, time
varying thresholds, stochastic unobserved
thresholds. Measures of risk: coherent and
convex risk measures, comonotonic additive
risk measures, value-at-risk, expected
shortfall, spectral risk measures, distortion risk
measures, risk measures and parameter
uncertainty. Capital Allocation: coherent
capital allocation, Euler allocation, allocation
of marginal contributions, estimation of risk
measures and numerical approximations.
Modelling dependence: dependence
modelling in the LDA framework, dependence
between frequencies, dependence between
severities, dependence between annual
losses, common factor models, copula
modelling. Combining different data sources:
internal, external and expert opinions,
Bayesian methods, minimum variance,
credibility methods. Loss aggregation:
calculation of the annual loss distribution,
calculation of the institution wide annual loss.
Objectives of course: On completion of
the course, a student should be able to:
describe the key quantitative requirements of
the Basel II/III banking accord; describe the 56
risk cells (business units and risk types)
required under the standard Basel II/III
regulator frameworks; describe the basic
indicator, standardized and advanced
measurement approaches; describe the key
components of a loss distributional approach
model; develop frequency and heavy tailed
severity models for Operational risk types
including estimation or the model parameters
and model selection; describe properties and
asymptotic estimators for risk measures that
are required for capital calcultion; describe the
coherent allocation of capital to business units
from the institutional level; introduce and
understand the influence of dependence
modelling within an LDA model structure;
obtain familiarity with particular classes of
copula statistical models of basic relevance to
practical Operational risk modelling; decide
upon appropriate combining approaches for
different sources of data required by
regulation to be considered in OpRisk
settings; develop loss aggregation methods to
aggregate OpRisk loss processes.
Texts:
M.G. Cruz, G.W. Peters & P.V. Shevchenko:
Fundamental Aspects of Operational Risk
and Insurance Analytics: A Handbook of
Operational Risk. Wiley, 2014.
G.W. Peters & P.V. Shevchenko:
Advances in Heavy Tailed Risk Modelling: A
Handbook of Operational Risk. Wiley, 2014.
M.G. Cruz: Modelling, Measuring and Hedging
Operational Risk. The Wiley Finance Series,
2002.
M.G. Cruz (Editor): Operational Risk
Modelling and Analysis: Theory and
Practice. RISK, 2004.
G.N. Gregoriou: Operational Risk Towards
Basel III: Best Practices and Issues in
Modelling, Management and Regulation.
Wiley Finance, 2011.
Applications: An integral part of modern
financial risk involves Operational Risk, the
third key risk type that financial institutions
must model and hold capital for according to
the international banking regulations of Basel
II/III. The key set of concepts and
mathematical modelling tools developed in
this course will equip the future risk modellers
and quantitative analysts with the appropriate
core mathematical and statistical background
to undertake development of such risk models
in industry.
Prerequisites: Familiarity with distribution
theory and generating functions, for example
as encountered in MATH7501 or equivalent.
Also some basic experience in either Matlab,
Python or R is needed, as taught in
STAT7001 or equivalent..
Assessment for examination grading:
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2½ hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
Course content: Key components of
operational risk frameworks, external
databases, scenario analysis, operational risk
in different financial sectors, risk organization
and governance. Basic indicator approach,
standardized approaches, advanced
measurement approach. Loss distributional
approach: quantiles and moments, frequency
distributions, severity distributions and heavy
tailed models, convolutions and characteristic
Other set work:
About 8 sets of exercises. These will not count
towards the examination grading.
8
moments, least squares, maximum likelihood,
Cramér-Rao lower bound.
Simple examples will be used throughout to
motivate and illustrate the topics discussed.
Timetabled workload:
Lectures: 2 hours per week.
Workshops: two 2 hour classes.
Office hours, during which the lecturer will be
available to discuss students' individual
problems with the course, will also be
provided.
Texts:
J.A. Rice: Mathematical Statistics and Data
rd
Analysis (3 edition). Duxbury, 2006.
D.D. Wackerly, W. Mendenhall & R.L.
Scheaffer: Mathematical Statistics with
th
Applications (6 edition). Duxbury, 2002.
L.J. Bain & M. Engelhardt: Introduction to
nd
Probability and Mathematical Statistics (2
edition). Duxbury, 1992.
R.V. Hogg & E.A. Tanis: Probability and
th
Statistical Inference (6 edition). Prentice
Hall, 2001.
H.J. Larson: Introduction to Probability Theory
rd
and Statistical Inference (3 edition) Wiley,
1982.
A.M. Mood, F.A. Graybill & D.C. Boes:
rd
Introduction to the Theory of Statistics (3
edition). McGraw-Hill, 2001.
V.K. Rohatgi & E. Saleh: An Introduction to
nd
Probability and Statistics (2 edition). Wiley,
2001.
STAT3101
PROBABILITY AND STATISTICS II (0.5
UNIT)
Level: Advanced
Aims of course: This course continues the
study of probability and statistics beyond the
basic concepts introduced in Probability and
Statistics I (MATH7501). It aims to provide
further study of probability theory, in particular
as it relates to multivariate random variables,
and it introduces formal concepts and
methods in statistical estimation.
Objectives of course: On successful
completion of the course, a student should
have an understanding of the properties of
joint distributions of random variables and be
able to derive these properties and manipulate
them in straightforward situations; recognise
the χ²; t and F distributions of statistics defined
in terms of normal variables; be able to apply
the ideas of statistical theory to determine
estimators and their properties satisfying a
range of estimation criteria.
Assessment for examination grading:
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2 hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
Applications: As with other core modules in
Other set work:
probability and statistics, the material in this
course has applications in almost every field
of quantitative investigation; the course
introduces general-purpose techniques that
are applicable in principle to a wide range of
real-life situations.
About 2 sets of exercises. These will not count
towards the examination grading.
Prerequisites: MATH7501 or equivalent.
STAT3102
STOCHASTIC PROCESSES (0.5 UNIT)
Timetabled workload:
Lectures: 3 hours per week.
Tutorials: 1 hour per week.
Course content: Joint probability
distributions: joint and conditional distributions
and moments; serial expectation; multinomial
and multivariate normal distributions.
Transformation of random variables:
distributions; approximation of moments; order
statistics. Moment and probability generating
functions: properties; sums of independent
random variables; Central Limit Theorem.
Relations between standard distributions: ², t
and F distributions. Statistical estimation: bias,
mean square error, consistency; method of
Level: Advanced
Aims of course: To provide an introduction
to the study of systems which change state
stochastically with time and to facilitate the
development of skills in the application of
probabilistic ideas.
Objectives of course: On successful
completion of the course a student should
understand the Markov property in discrete
9
and continuous time; for discrete-time Markov
chains, be able to find and classify the
irreducible classes of intercommunicating
states, calculate absorption or first passage
times and probabilities, assess the equilibrium
behaviour; for simple examples of continuoustime Markov chains, be able to write down the
forward equations, find and interpret the
equilibrium distribution.
time, discrete states): general theory, forward
and backward equations, equilibrium
distributions; Poisson process, interval and
counting properties; birth and death processes
and other simple examples.
Applications: Stochastic processes are vital
Assessment for examination grading:
to applications in finance and insurance, and
have many applications in biology and
medicine, and in the social sciences. They
also play a fundamental role in areas such as
queueing theory and the study of system
reliability. The material in this course can be
applied to simplified real-world situations, and
provides the foundations for further study of
more complex systems.
In-course assessment (see page 3), the exact
method of which will be announced by the
lecturer at the beginning of the course.
2 hour written examination in term 3.
The final mark is a 9 to 1 weighted average of
the written examination and in-course
assessment marks.
Texts:
S.M. Ross: Introduction to Probability Models
th
(10 edition). Academic Press, 2009.
Other set work:
About 8 sets of exercises. These will not count
towards the examination grading.
Prerequisites: Preferably STAT3101 or
simultaneous attendance on STAT3101.
The course can be taken by students with
MATH7501 or equivalent but in that case
students should undertake a small amount of
preliminary reading about which they should
obtain advice at the start of the summer
vacation preceding the year in which they take
the course.
Timetabled workload:
Lectures: 3 hours per week.
Tutorials: 1 hour per week.
The information given in this document is
as far as possible accurate at the date of
publication but the Department reserves
the right to amend it.
Course content: Revision of conditional
probability. Markov Chains (discrete time and
states): transient and equilibrium behaviour,
first passage times, classification of states,
applications. Markov processes (continuous
Department of Statistical Science, UCL,
August 2015.
10