# Financial Market Modelling and Analysis

## Summary

These lectures provide (i) an overview of practical terminology and concepts relating to the global financial markets, and (ii) a gentle introduction to the field of modelling and analysing financial markets with an emphasis on (a) deterministic and discrete-time methods; and (b) numerical simulation, including agent-based modeling.

## Aims

To provide important practical background to the operation of financial markets. To distinguish between different types of modeling and analysis, and to explain the advantages and disadvantages of each method; to gain an understanding of numerical simulation methods.

## Sections and Lectures

The lectures comprise four sections. Each section contains an overview of content and a number of lectures (each lecture is available as either a PDF without audio or as a Powerpoint show with audio). The PDFs and Powerpoint shows are password protected - passwords are provided to my students and occasionally to others on request.

### Section 1: Introduction to financial markets

This first section is primarily knowledge-based. The material was developed in collaboration with an investment bank and is intended to provide the practical basic knowledge that a student should have if they are interested in a career in investment banking. The following topics will be covered:

*Market Participants.*Financing - the basics (types of participants, examples of each type, examples of key Exchanges). Fund Management - Hedge Funds, Funds of Funds, Private Equity Companies. Key Infrastructure Participants (SWIFT, Euroclear, CLS). FMMA-Lecture1.pdf*Financial Instruments.*Equities, Debt, Derivatives. Options and Option Pricing. Exotic Options. Credit Derivatives. Equity Swaps. Sale and repurchase ("Repo"). Commodities - physical, weather, environmental. FMMA-Lecture2.pdf*Institutional Trading Strategies.*What is a trading strategy? Terminology. Who trades? what is traded? whose money is it? Matching investors to trading strategies. Overview of main institutional trading strategies (long only, active vs. passive, long-short, alternative investments). Performance measurement of traditional fund strategies. Performance measurement of hedge fund strategies. FMMA-Lecture3.pdf FMMA-Lecture4.pdf*Risk Management.*Factors affecting risk exposure. Market risk. Liquidity risk. Operational risk. Credit risk. Use of swaps. Value At Risk. FMMA-Lecture5.pdf*Post-trade Processing (equities).*The investment cycle. Pre settlement (verification, agreement, confirmation, comparison, matching, reporting). Settlement (types, CSD, ICSD, settlement and cash payment). Corporate actions. FMMA-Lecture6.pdf FMMA-Lecture7.pdf*Regulation.*Settlement risk. Systemic risk. global regulators. US, EU and UK Regulators. Example legislation. Need for confidentiality. FMMA-Lecture8.pdf

### Section 2: Markets

This section provides an academic introduction to the study of financial markets. It covers the following material:

*Auctions.*Walrasian auction. Double auction. Call auction. Continuous double auction. FMMA-Lecture9.pdf*Markets and microstructure.*Execution venues. Limit Order Book and orders. Market data and Private data. Market structure, fees and costs. Market protection. FMMA-Lecture10.pdf FMMA-Lecture11.pdf*Market making.*Market makers, dealers and specialists. Market making in a quote-driven market. Market making in an order-driven market. Risk-averse market making. Hot potato trading. FMMA-Lecture12.pdf FMMA-Lecture13.pdf*High frequency trading.*Low latency versus high frequency trading. HFT definitions. Types of HFT. Latency arbitrage. Academic studies of HFT. FMMA-Lecture14.pdf FMMA-Lecture15.pdf

### Section 3: Techniques

This section covers the following topics:

*A simple introduction to Game Theory.*Extensive form and normal form. Nash equilibrium. Payoff tree and payoff matrix. Keynesian beauty competition. The puzzle of the green-eyed tribe. Example payoff matriuces in finance. FMMA-Lecture16.pdf*A simple introduction to Minority Games.*The El Farol Bar problem. The original minority game structure. Stock markets as minority games. FMMA-Lecture17.pdf*Agent-based modelling and simulation of financial markets.*Models. Structure. Validation. Advantages and disadvantages. Examples (ABMs of Limit Order Books).FMMA-Lecture18 FMMA-Lecture19.pdf.pdf*Dynamic Optimisation.*Introduction (dynamic optimisation and dynamic programming). Bellman's Principle of Optimality. The Bellman Equation in discrete time (example, stochastic example, backward induction.FMMA-Lecture20.pdf

### Section 4: Models

This section analyses three research papers in depth, examining how different aspects of market behaviour can be modelled and analysed in different ways. It finishes by building on the third paper with an analysis of dynamically-coupled market making.

*Bulls Bears and Market Sheep (1990) by Richard Day and Weihong Huang.*Models the unpredictable, fluctuating nature of stock market prices and their tendency to generate alternating periods iof "bull" and "bear" markets. Derives this from the interaction between two simple models of trading behaviour. A traditional model of excess demand and price adjustment based on "stylized institutional realities". A simple equational model of contrarian and momentum traders leads to complex market behaviour, which can be analysed by plotting price at time step t+1 against price at time step t. FMMA-Lecture21.pdf*A simultaneous trade model of the foreign exchange hot potato (1997) by Richard Lyons.*A two-period discrete-time model of hot potato trading. Models what information is known at each point in time, and how that informs quoting behaviour and inventory management. Also models the market impact of hot potato trading in a dealer market.FMMA-Lecture22.pdf*Optimal market-making with risk aversion (2012) Kan Huang, David Simchi-Levi and Miao Song.*Discrete-time model of risk-averse market making in a dealer market. Assumes inventory limits, and that inventory is controlled via trades with other dealers. Uses dynamic optimisation to deduce an optimal strategy. Model formulation and exponential utility criterion. Dynamic optimisation. Solving the Bellman equation. Optimal policy rebalances exactly to a dynamic inventory threshold.FMMA-Lecture23.pdf FMMA-Lecture24.pdf FMMA-Lecture25.pdf*Building on the Huang et al model for coupled risk-averse market makers.*Explores the effect of dynamic interaction between two market makers, each executing an optimal Huang et al risk-averse policy. Simple numerical simulation indicates that inventories and profits oscillate wildly. Market makers lose the ability to control their inventories. The provable optimal Huang et al strategy is no longer optimal when assumptions are changed. FMMA-Lecture26.pdf