This module provides you with comprehensive knowledge of modern asset pricing theories and investment strategies, bridging theoretical foundations with practical applications. You will develop a deep understanding of financial markets and risk and return trade-offs, beginning with utility-based frameworks, consumption-based models, and contingent claim pricing. You will then learn about factor-based approaches that define the modern investment landscape.

The module covers fundamental theories, such as the Capital Asset Pricing Model and market efficiency. It examines how these have evolved into multi-factor models that better explain asset returns.

We also cover quantitative techniques for textual analysis of financial information and sentiment analysis. You will gain hands-on experience constructing and evaluating investment portfolios through various optimisation techniques.

This module covers the latest concepts in machine learning and big data in finance. You will gain skills in financial econometrics to carry out advanced quantitative data analysis, modelling and forecasting. These are highly valuable and transferable skills for jobs in the finance industry.

You will cover material that includes the latest techniques to model and analyse complex and high-dimensional data, such as multivariate financial time series models, variable selection techniques, and artificial neural networks for forecasting purposes, together with modern forecasting evaluation methods.

The module focuses on developing your understanding and modelling of volatility and variance-covariance matrices as key risk measures in finance. You will cover the construction of these matrices using traditional data and modern irregular big and high-frequency databases. You will learn to implement all key techniques in a modern programming language used in the finance industry, such as Python or R.

This year-long module, co-delivered with careers consultants from the LUMS Careers team, will enhance your skillset, knowledge, and experience, giving you a head start on your future career.

You will receive dedicated career and professional training and the basis to develop software and coding skills essential to the professional life of an Accounting and Finance graduate.

The module's content is tailored for your programme and covers a range of skills that are essential in an increasingly competitive job market, including:

• data management (eg SQL, Excel, VBA, Xero)
• databases (eg Bloomberg, Datastream)
• programming (eg Python, R).

By identifying and developing your employability skills, you will get practical opportunities to prepare for the future.

This module covers the core material to enable you to model and analyse financial data proficiently. It provides the necessary toolbox for advanced modules in finance and investments and the dissertation modules. The module also provides the foundation for techniques such as machine learning and artificial intelligence in the context of forecasting.

You will cover material that includes:

• the established linear regression model framework
• discrete choice models
• linear financial time series models
• a modern toolbox for model selection and forecasting.

You will learn:

• estimation techniques such as least squares and maximum likelihood optimisation
• how to choose the right model for data analytics
• how to interpret and make informed decisions based on regression outputs
• how to implement all key techniques in a modern programming language used in the finance industry such as Python and R.

This module allows you to integrate knowledge and skills gained during your MSc programme. You will formulate research questions, develop appropriate methodologies and analyse financial data to address real-world challenges in your field of study. You will investigate topics relevant to your career aspirations, whether in corporate finance, accounting, investment analysis, risk management or financial technology. Through this process, you will develop essential transferable skills including:

• research planning
• critical thinking
• data analysis
• academic writing.

This dissertation will prepare you for advanced roles in the financial industry or further academic study.

This module examines how technology is transforming financial markets and instruments. You will cover traditional and digital financial systems across multiple asset classes. You will explore advanced topics in trading using stocks, options, futures, foreign exchange, fixed income and commodities, including:

• high-frequency trading
• algorithmic strategies.

The module will introduce market microstructure concepts, focusing on liquidity dynamics and price discovery mechanisms.

You will explore cutting-edge technologies such as:

• blockchains
• digital assets
• cryptocurrencies.

You will explore these technologies' practical applications in finance. You will also learn about private equity firms, hedge funds, and other financial institutions, along with the key concepts of behavioural finance.

This module develops your knowledge and skills in quantitative methods for identifying, measuring, and mitigating financial risks. You will examine fundamental concepts of risk and uncertainty, various risk measures, and AI applications for comprehensive risk management.

You will analyse interest rate risk through classical term structure models, such as Vasicek and Hull-White, alongside modern machine learning approaches to yield curve modelling. You will explore equity risk beyond Gaussian distributions, focusing on tail risk and copula methods for complex dependency structures. You will examine credit risk through classical frameworks, such as logit models and the Merton approach, and innovative machine learning techniques using neural networks and other classifiers.

Advanced topics you will cover in this module include:

• natural language processing for fraud detection
• machine learning methods for market manipulation identification in high-frequency data
• AI applications in cybersecurity and operational risk management.

You will practice implementing risk-management techniques using various software packages such as MATLAB or Python.

This module provides an in-depth examination of modern investment strategies and portfolio construction techniques. You will develop advanced skills in portfolio optimisation, applying different objective functions and constraints to create portfolios with specific risk-return characteristics.

The module covers sophisticated backtesting methodologies, including techniques to mitigate common pitfalls such as overfitting and selection bias. The module explores investment factors beyond traditional market, size, and value factors, often referred to as the ‘factor zoo’. You will equip yourself with methodologies for rigorous factor construction and evaluation.

You will examine asset allocation frameworks, including strategies such as Risk Parity, portfolio insurance, and other risk-managed approaches.

The module introduces applications of machine learning for investment decision-making, covering:

• variable selection techniques
• dimensionality reduction
• pattern recognition in financial data.

Throughout the module, the theoretical concepts you learn will be reinforced through practical applications using real market data.

Co-taught with practitioners from IBM, this module equips you to architect secure, resilient information systems in today’s threat-laden digital landscape. Taking a systems-of-systems perspective, the module frames cybersecurity and digital infrastructure as closely linked rather than isolated components.

You will learn to apply architectural thinking, which involves concepts such as:

• layered decomposition
• patterns
• trade-off analysis
• zero-trust principles.

You will use architectural thinking to weave protection, detection and recovery mechanisms throughout the technology stack, including cloud services, APIs, edge devices and data pipelines.

In hands-on labs, you will use IBM best practices for architecting IT systems, reference architectures and threat-model tooling. In the labs, you will:

• design secure platforms
• evaluate attack surfaces
• meet compliance requirements.

You will engage with case studies that reveal how design choices affect risk, performance, and cost over a system’s life cycle. At the end of the module, you will be able to translate business objectives into security-by-design architectures that withstand emerging threats while enabling innovation.

This module provides you with a comprehensive knowledge of advanced derivatives pricing and hedging methodologies. It covers advanced option pricing techniques beyond the Black-Scholes framework, including, for example, stochastic volatility models. You will examine interest rate derivatives and the pricing of related instruments, such as swaps, caps, floors, and swaptions.

You will also learn about commodity derivatives and credit default swaps. The module extends to exotic derivative structures, including path-dependent options and multi-asset derivatives and explores dynamic hedging strategies.

Stochastic calculus is a theory that enables the calculation of integrals with respect to stochastic processes. You will begin by studying discrete-time stochastic processes, defining key concepts such as martingales and stopping times. This will then lead to the exploration of continuous-time processes, in particular, Brownian motion.

You’ll learn how to derive basic properties of Brownian motion and explore integration with respect to it, while examining the derivation of Itô's formula and how to apply this to Brownian motion.

Over the course of the module, you will be able to justify and critique the use of stochastic models for real-world applications and learn how to use the stochastic calculus framework to formulate and solve problems involving uncertainty – a skill that underpins financial mathematics.