MSc Mathematical Finance
A research-oriented, proof-based programme for mathematicians who want to engage with the deepest theoretical questions in modern finance. From measure-theoretic probability and martingale theory to backward SDEs and systemic risk — this is mathematical finance at its most rigorous.
Pure Mathematics Applied to Finance
The MSc Mathematical Finance is the most theoretically demanding programme in D'Math University's Finance & Actuarial Mathematics category. It is intended for students with a strong pure mathematics background who wish to engage with financial theory at the level of rigorous proof rather than merely application.
- Measure Theory: Probability spaces, sigma-algebras, Lebesgue integration, and conditional expectation — the rigorous foundations of all stochastic finance.
- Martingale Theory: Discrete and continuous-time martingales, optional stopping theorem, Doob's inequalities, and the Martingale Representation Theorem.
- Optimal Control: Dynamic programming, Hamilton-Jacobi-Bellman equations, and optimal stopping for American option pricing.
- Research Dissertation: A 60-credit dissertation supervised by a faculty member with expertise in mathematical finance, connecting to one of three research clusters.
Three Research Clusters
Students join one of three active research clusters, gaining access to seminars, workshops, and collaborative research opportunities alongside faculty and doctoral students working at the mathematical frontier of finance.
- Stochastic Analysis & Control: SDEs, BSDEs, optimal control theory, and their applications to dynamic portfolio optimisation and derivative pricing.
- Systemic Risk & Market Microstructure: Interbank contagion models, systemic risk measures, mean-field games, and high-frequency market dynamics.
- Non-Linear Pricing & XVA: Non-linear PDEs in finance, CVA, DVA, FVA, and the mathematics of counterparty risk in derivatives markets.
- Seminar Series: Weekly mathematical finance seminars featuring leading academics from Oxford, Princeton, Paris-Dauphine, and ETH Zurich.
- PhD Progression: Over 40% of graduates proceed to PhD programmes at world-leading universities within one year of completing the MSc.
Click any course to view its objective and learning outcomes.
MTF 501 Stochastic Calculus +
Objective
To apply Itô calculus to financial modelling.
Learning Outcomes
- Apply Brownian motion and Itô's lemma.
- Solve stochastic differential equations.
- Apply Girsanov's theorem.
- Use Feynman-Kac formula.
- Apply martingale representation.
MTF 502 Derivatives Pricing +
Objective
To price European, American and exotic derivatives.
Learning Outcomes
- Apply Black-Scholes formula.
- Use binomial trees for American options.
- Price barrier and Asian options.
- Apply local and stochastic volatility models.
- Calibrate to market data.
MTF 503 Interest Rate Models +
Objective
To model interest rates and price IR derivatives.
Learning Outcomes
- Apply Vasicek and CIR models.
- Use HJM framework.
- Apply LIBOR Market Model.
- Price caps, floors and swaptions.
- Calibrate to yield curves.
MTF 504 Credit Risk Models +
Objective
To model and price credit risk.
Learning Outcomes
- Apply structural and reduced-form models.
- Price credit default swaps.
- Use CDO pricing.
- Apply correlation models.
- Discuss CVA.
MTF 505 Numerical Methods +
Objective
To implement numerical algorithms for pricing.
Learning Outcomes
- Implement Monte Carlo simulation.
- Apply variance reduction.
- Use finite difference for PDEs.
- Apply trees for American options.
- Profile quant code.
MTF 506 Portfolio Theory +
Objective
To allocate capital optimally across assets.
Learning Outcomes
- Apply mean-variance optimisation.
- Use Black-Litterman.
- Apply risk parity.
- Use factor models.
- Backtest properly.
MTF 507 Risk Management +
Objective
To measure and manage financial risk.
Learning Outcomes
- Compute VaR and Expected Shortfall.
- Stress-test portfolios.
- Apply coherent risk measures.
- Discuss Basel III.
- Manage liquidity risk.
MTF 508 High-Frequency Finance +
Objective
To analyse and model high-frequency financial data.
Learning Outcomes
- Analyse market microstructure.
- Apply order book models.
- Use realised volatility estimators.
- Apply jump-diffusion models.
- Discuss latency arbitrage.
MTF 509 Algorithmic Trading +
Objective
To design and backtest systematic trading strategies.
Learning Outcomes
- Apply mean-reversion and momentum.
- Use statistical arbitrage.
- Implement execution algorithms.
- Apply market microstructure.
- Backtest carefully.
MTF 510 Financial Econometrics +
Objective
To estimate and test econometric models on financial data.
Learning Outcomes
- Apply ARMA and GARCH models.
- Use VAR models.
- Apply cointegration.
- Test for unit roots.
- Apply Markov-switching models.
MTF 511 Behavioural Finance +
Objective
To analyse market behaviour using psychological insights.
Learning Outcomes
- Apply prospect theory.
- Discuss heuristics and biases.
- Analyse market anomalies.
- Apply herding and information cascades.
- Discuss limits to arbitrage.
MTF 512 Master's Dissertation +
Objective
To complete an original mathematical finance research project.
Learning Outcomes
- Identify a research-quality problem.
- Apply rigorous methodology.
- Use real financial data.
- Write a 15,000-word dissertation.
- Defend orally.
Measure-Theoretic Probability
Probability spaces, measurable functions, integration, convergence theorems, conditional expectation, and characteristic functions.
Martingale Theory
Discrete and continuous martingales, stopping times, optional sampling, Doob-Meyer decomposition, and the MRT for Brownian filtrations.
Optimal Stopping & Control
Snell envelope, American option pricing, HJB equations, singular control, and applications to investment under uncertainty.
SPDEs & Financial Models
Stochastic partial differential equations, infinite-dimensional stochastic analysis, and applications to term structure and volatility surface modelling.
Non-Linear Pricing
Non-linear Black-Scholes PDEs, uncertain volatility models, G-Brownian motion, and sublinear expectations in financial mathematics.
Backward SDEs
BSDEs and their connection to PDEs, recursive utility, risk measures, and dynamic hedging in incomplete markets.
Systemic Risk Modelling
Interbank network models, contagion, mean-field games for systemic risk, and mathematical approaches to macroprudential regulation.
Market Microstructure
Adverse selection models, Kyle model, Glosten-Milgrom, limit order book dynamics, and optimal execution mathematics.
Mathematical Finance Researcher
Pursue doctoral and postdoctoral research at leading mathematics departments, publishing in top journals including Finance and Stochastics and Mathematical Finance.
Quant Strategist
Develop advanced mathematical pricing and hedging strategies at elite hedge funds and proprietary trading firms requiring the deepest quantitative expertise.
Central Bank Modeller
Build systemic risk models, macro-financial linkage frameworks, and stress testing methodologies at the Bank of England, ECB, or Federal Reserve.
Hedge Fund Math Lead
Lead quantitative model development at global macro and systematic hedge funds, requiring deep stochastic calculus and optimisation expertise.
Academic Finance Researcher
Pursue tenure-track academic positions at universities, producing original research advancing the mathematical theory of asset pricing and risk.
Derivatives Theorist
Develop next-generation pricing models for complex derivatives at major banks, focusing on model risk, calibration, and theoretical extensions.
Why D'Math University — Our 4-Step Approach
Proof-Based Foundations
Every result is proved rigorously. Students engage with mathematical finance as pure mathematicians, not as users of financial formulas — building genuine long-term expertise.
Research Cluster Integration
Students are embedded within active research clusters from Week 1, attending seminars and working alongside faculty on open research problems in mathematical finance.
Elite Dissertation Supervision
Dissertations are supervised by internationally recognised researchers, and the best are submitted for publication in peer-reviewed mathematical finance journals.
PhD & Industry Pathways
We actively support graduates into PhD programmes at Oxford, Princeton, and ETH Zurich, as well as senior quant roles at elite hedge funds and banks seeking the deepest mathematical expertise.
Speak to an adviser — admissions@dmathu.ac | Research cluster matching available