Mathematical Finance MSc

Institution University of Manchester
Method At the institution
Location Manchester
Type Masters

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Mathematical Finance MSc

Entry requirements Entry requirements: To gain a place on the MSc Mathematical Finance course you must have top ranking academic results. We are looking for a UK bachelor degree with first or upper second class honours (overall average 65%), or the overseas equivalent with excellent results in maths and quantitative subjects. When assessing your academic record, we take into account your grade average, position in class, references and the standing of the institution where you studied your qualification. We particularly welcome applications from institutions of high ranking and repute. You need to have studied or be studying a degree in mathematics. We can also consider excellent candidates with degrees in finance, engineering, physics or economics if a high level of mathematics has been studied.
Academic title Mathematical Finance MSc
Course description MSc Mathematical Finance – Course structure

All taught course units are 15 credits.

Semester one

• Derivative Securities
This course unit covers the valuation and application of financial derivatives instruments, and
the use of no-arbitrage arguments and risk neutral valuation for the relative pricing of financial
derivatives.

• Foundations of Finance Theory
This course unit provides a foundation in the most important models in finance: general noarbitrage
relationships (forward parity, put-call parity, MM theorem, the law of one price),
stock valuation models (APT, CAPM, TSP) and option pricing models.

• Martingales with Applications to Finance
The course unit content includes: probability, measures and random variables; integration
with respect to a probability measure; price processes, self-financing portfolios and value
processes; arbitrage opportunities and equivalent martingale measures; market
completeness; options and option pricing; stopping times and the optional sampling
theorem.

• Stochastic Calculus

The course unit content includes: Wiener process; continuous local martingales; the quadratic
variation process; Ito’s integral with respect to a continuous semi-martingale; the Levy
characterisation theorem; the martingale representation theorem; optimal prediction of the
maximum process; Bassel process; the Ornstein-Uhlenbeck process; branching diffusion;
Brownian bridge; the Shiryaev process; the sequential testing equation; the quickest detection
equation; the existence and uniqueness of solutions in the case of Lipschitz coefficients.

Semester two

• Brownian Motion
This course unit covers: heat equation, diffusion equation, Einstein’s derivation of the diffusion equation,
the Wiener process, the Ornstein-Uhlenbeck process, strong Markov property, diffusion processes,
boundary classification, the Kolmogorov forward and backward equations, probabilistic solutions of
PDEs.

• Computational Finance*
This course unit covers computational methods, including Monte Carlo and Lattice methods
for option pricing, finite difference methods for parabolic PDEs with emphasis on Crank
Nicolson methods for parabolic systems, point and line relaxation and PSOR methods, and
quadrature methods.

• Financial Econometrics
This course unit covers OLS, ML and GMM estimation methods, univariate time series
analysis and various topical issues such as ARCH, Vector Autoregressive Models, unit roots,
error correction, co-integration and nonlinear time series models.

• Stochastic Modelling in Finance
The unit focuses on mathematical models in financial mathematics. This includes: hedging
strategies and managing market risk using derivatives; binomial model; risk-neutral valuation;
diffusion-type models for stock prices; Black-Scholes formula; stochastic volatility models and
option pricing with transaction costs.

* There will be a pre-course training session for students who have not previously studied

C++ programming.

Research dissertation (60 credits)

You carry out an original piece of research on a subject relating to the course. Our MSc
dissertation topics align with the research interests of leading financial institutions from the
City of London and internationally. Senior members of these organisations propose several of
the dissertation topics, which, subject to approval, members of academic staff supervise.
Successful completion can require consultation with officers of the financial institution, leading
to a final presentation of findings.