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King's College London - MSc Financial Mathematics
London, United Kingdom
Program Contacts: This e-mail address is being protected from spambots. You need JavaScript enabled to view it (Dept of Mathematics), This e-mail address is being protected from spambots. You need JavaScript enabled to view it (Admissions - Dr. Giulia Lori), This e-mail address is being protected from spambots. You need JavaScript enabled to view it (Prog. Director - Professor Lane Hughston)

The Summary:

The Master Programme in Financial Mathematics at King's College London is designed with the following three functions in mind.

(a) Full-time students are expected to acquire knowledge and understanding of the subject that will equip them to enter competitively the pool of potential employees of investment banks and other financial institutions.

(b) Part-time students are expected to enhance their skills in the subject to a degree that can bring a high level of fresh knowledge and expertise to their firms, and can lead to a significant upgrading of their career prospects.

(c) Students who aspire to a research degree in mathematical finance are expected to acquire a sound grasp of the background knowledge and mathematical technique required for this.

The degree course begins in September and entails either one year of full-time study, or it may be taken part-time over two years. The programme, which is designed to be compatible with the needs of those already employed in the financial sector, is based on a series of eight lecture courses, followed by examinations. The lecture courses cover a wide range of material in financial mathematics and important related areas of mathematics.

Course Structure:

Core MSc Lecture Courses

Applied Probability and Stochastics (CMFM01)
Probability spaces, random variables, distributions, independence, product spaces. Expectation and conditional expectation. Moments, generating functions, characteristic functions. Random processes, filtrations and stopping times. Martingales, Brownian motion and the Poisson process. Elements of Itô integration.

Risk Neutral Valuation: Pricing and Hedging Derivatives (CMFM02)
Forward prices, discounting, arbitrage-free pricing; binomial trees, derivatives pricing in discrete time by use of binomial lattices, geometric Brownian motion, volatility and drift, martingales and conditional expectation, Itô calculus, hedging portfolios, replication, Black-Scholes model, put-call parity. Option deltas, gammas, vegas, and other sensitivities. Risk premium, risk-neutral measure. Arbitrage-free multi-asset financial markets.

Financial Markets (CMFM03)
This course presents an overview of the world's financial markets, and a concise mathematical formulation of the main characteristics of financial instruments and trading practice, with an emphasis on quantitative aspects of options, futures, and other derivatives. Topics covered include: Spot markets for stocks, bonds, currencies, commodities. Forward markets. Commodity futures, financial futures. Stock options, index options, currency options, commodity options, interest rate options, options on futures. Interest rate swaps, currency swaps. Corporate bonds, treasury bonds, inflation-linked products. Energy and credit markets. Structured products, OTC derivatives.

Stochastic Analysis (CMFM04)
Itô's isometry and the Itô integral. Levy's characterisation theorem and Girsanov's theorem. Random time changes, martingale representation theorems. Stochastic differential equations and diffusions. Ornstein-Uhlenbeck process, Brownian bridge, Bessel processes. Fokker-Planck equation and Feynman-Kac formula. Cauchy and Dirichlet problems.

Distribution Theory (CMFM05)
Theory of families of discrete and continuous probability distributions. Binomial, Poisson, geometric, negative binomial, hypergeometric distributions. Uniform, exponential, normal, gamma, beta, Student and Cauchy distributions. Compound distributions. Applications of order statistics. Scale and displacement families. Exponential families. Elements of information geometry. Properties of fat-tailed distributions. Stable families. Applications to mathematical finance.

Numerical Methods for PDEs (CMFM06)
Discretisation; multivariable Newton-Raphson. Error analysis in normed vector spaces. Finite-element methods. Stability; the method of Crank and Nicolson. Variational methods and penalty methods. Linearisation. Iterative methods of solution. Computer implementation.

Interest Rate and Foreign Exchange Dynamics (CMFM07)
Discount bonds, interest rates, yield curves. Basic state variable models: Vasicek, Hull-White, Cox-Ingersoll-Ross, lognormal short rate, rational log-normal model and others. Heath-Jarrow-Morton framework; introduction to market models. Pricing formulae for caps, floors, swaptions. Multi-currency interest rate models.

Exotic Derivatives (CMFM08)
This course surveys pricing and risk management techniques for a number of important financial derivatives. Topics covered include: barrier, quanto, forward-starting, Asian, lookback, power and compound options; options to exchange one asset for another, dual-asset knock-out options and basket options. Energy and weather derivatives; insurance linked products.

Portfolio Risk Management (CMFM09)
Theory of risk aversion and utility, with applications. Trading strategies, consumption and portfolio value processes, expected utility from consumption and terminal wealth. Portfolio optimisation, solution of Merton problem. Transaction costs, market incompleteness, portfolio constraints. (Not offered in 2001-02.)

Credit Risk Management (CMFM10)
Default events and survival indicator processes. Price processes for assets with jump risk. Overview of credit derivative structures. Lando's formula for risky discount bonds. Applications to credit default swaps, corporate and sovereign coupon bonds, and structured loan facilities. Duffie-Singleton formula for partial recovery on default. Introduction to structural models for default. Basic elements of copula theory and extremal events with applications to topics in credit risk.

Elective MSc Lecture Courses

Operational Research I, II (CM354X, CM355X)
Linear programming, graphical solutions to two-dimensional problems, convex sets and their application to linear programming, basic feasible solutions, the simplex algorithm, artificial variables, unbounded problems, sensitivity analysis and the revised simplex method, matrix games and their interpretation as linear programming problems, dynamic programming. More advanced topics such as: duality, quadratic programming, transportation problems, stock control, queueing theory.

Neural Networks (CM451Z)
This introductory course covers the basics of neural information processing. Subjects include neuron models (graded response, McCulloch-Pitts, stochastic binary neurons, coupled oscillators), learning in layered neural networks (linear separability, perceptrons, error backpropagation, dynamics of learning) and the operation of recurrent neural networks (creation of attractors, analysis via Lyapunov functions, Hopfield model, analysis of dynamics).

Linear Systems & Control Theory (CM452Y)
First order linear systems of ordinary differential equations, autonomous systems, phase portraits, stability, non-linear system linearisation, Laplace transforms, the transfer function, Routh-Hurwitz criterion for stability and more advanced transfer function methods. The rank criterion for controllability, linear feedback and optimal control, Euler-Lagrange methods and introduction to Hamiltonians, the Hamilton Pontryagin method, bounded control functions, Pontryagin's principle, big-bang control, switching curves.

Non-Linear Dynamics (CM335Z)
This course covers various aspects of the behaviour and analysis of non-linear differential equations, such as phase-plane analysis, critical points and linearisation, integrability, periodic solutions, stability analysis and Lyapunov functions, bifurcation theory, attractors and chaotic systems.

Chaotic Dynamics (CM352Y)
This course covers discrete time dynamical systems. Symbolic dynamics, Sarkovskii's theorem. Fractals: dimension, iterated function systems, Julia sets, Mandelbrot set, collage theorem.

Global Derivatives View:

To Be Compiled.

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Entry Requirements:
--- Strong mathematical background
--- BSc degree of first or upper second class in mathematics or an approved mathematics-based subject, or an equivalent qualification
GMAT: Average -
GPA: Average -
GRE: Average -
International Students:
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Tuition (2009-10): £17,000

Additional Information: