Modules
PLEASE NOTE: The content of modules and the lecturers' names stated below are indicative only. The content is subject to small changes, and lecturers may have to be replaced from year-to-year, or at short notice for some other reason. Whilst we intend to run all these modules, please note that we may occasionally have to cancel a module. If we have to cancel a module, students who are registered for that module will be contacted and offered an alternative. The dates for any given module on this website may be provisional until a month before the start of the module.
READING LIST for course in general and for specific modules
For a chronological list of Core (Modules 1-4) and Advanced (Modules 5-8) Modules, please see the Course Calendar.
Core Modules 2012
Module 1: Mathematical and Technical Prerequisites
9-13 January 2012
Assignment due: 12 noon, 13 February 2012
Module 2: Black Scholes Theory
12-16 March 2012
Assignment due: 12 noon, 16 April 2012
Module 3: Extensions of the Black-Scholes Framework
23-27 April 2012
Assignment due: 12 noon, 28 May 2012
Module 4: Exotic Options and Advanced Modelling Techniques
25-29 June 2012
Assignment due: 12 noon, 30 July 2012
Advanced Modules (2011-12)
Module 6: Advanced Numerical Methods
29 November-2 December 2011
Assignment due: 12 noon, 3 January 2012
Module 7: Quantitative Risk Management
8-10 & 12 March 2012
Assignment due: 12 noon, 16 April 2012
Module 8: Advanced Modelling Topics 2 (Credit, Energy, More Interest Rates)
17 - 20 April 2012
Assignment due: 12 noon, 21 May 2012
Advanced Modules 2012-13
Module 5: Advanced Modelling Topics 1 (Equity, FX, Interest Rates) (Provisional dates)
18-21 September 2012
Assignment due: 12 noon, 5 November 2012
Module 6: Advanced Numerical Methods (Provisional dates)
27-30 November 2012
Assignment due: 12 noon, 14 January 2013
Short Courses (Advanced Modules only)
Form for registration of interest in attending Short Course
Module 1 Mathematical and Technical Prerequisites
- Probability: basics, review of discrete and continuous random variables, properties,important distributions, measure theory, change of measure, convergence of random variables, limit theorems
- Statistics: review of sampling and estimation, parameter estimation, regression techniques, tests for normality, QQ plots, Bayesian techniques, elementary principal components analysis
- PDEs: parabolic partial differential equations; heat equation, link to random walks, similarity solutions, Fourier transform; qualitative properties of solutions, maximum principles, smoothness
- Introduction to Matlab: basics, plotting, implementation of elementary numerical concepts applied to finance
- Binomial trees, discrete martingales: one-period and multi-period binomial stock price models, arbitrage pricing of options on trees
- Portfolio theory, utility: expected returns, variance and covariances, benefits of diversification, the opportunity set, efficient frontiers and the Sharpe ratio, utility, risk aversion, optimal investment, convex duality
- Stochastic calculus: Brownian motion, constructions, non-differentiability, quadratic variation, stochastic integration, construction of Ito integral and properties, the Ito formula
- SDEs: random walks in continuous time, strong and weak solutions, expectations of solutions
Link to course material for module 1
Back to Core modules (includes module dates)
Module 2 Black-Scholes Theory
- The Black-Scholes model: stochastic differential equation for the asset price in continuous time, the delta-hedged portfolio and self-financing replication, risk-neutral valuation, the Black-Scholes PDE and solutions
- Hedging, Greeks: delta, gamma, theta; vega, rho as out-of-model hedges; less common sensitivities
- Extensions of Black-Scholes: discrete and continuous dividend payments; time-dependent volatility, dividends and interest rates
- Basic exotic options: general payoffs, options on futures, pay-later options; multi-stage options, forward-start options, ratchets, compound options, choosers
- Multi-factor problems, quantos, FX and basket options
- Elementary stochastic differential equations, transition density functions, Feynman-Kac formula, Kolmogorov equations, exit times and hitting probabilities, Girsanov's theorem, maximum/minimum of Brownian motion
- Martingale methods in discrete and continuous time, martingale representation theorem
- Explicit and implicit finite difference schemes, implementation, accuracy and stability, Greeks and smoothing schemes; workshop
- Introduction to the term structure of interest rates, bond price equilibria, duration and convexity, caps, floors, swaps
- Overview of instruments in rates markets, interpolation of yield curves and volatility term structures, bootstrapping
Lecturers
- Dr Jamil Baz
- Dr Jeff Dewynne
- Dr Greg Gyurko
- Dr Ben Hambly
- Dr Hanqing Jin
- Dr Jan Obloj
- Dr Christoph Reisinger
- Mr Jan Witte
- Mr Thomas Hosking
Link to course material for module 2
Back to Core modules (includes module dates)
Module 3 Extensions of the Black-Scholes Theory
- Girsanov's theorem, maximum/minimum of Brownian motion
- Introduction to Monte Carlo: uniform random number generators, sampling non-uniform distributions, implementation of MC methods, simple variance reduction techniques, workshops
- American options: early exercise, linear complementarity problem, perpetual put, free boundary formulation, smooth pasting
- Finite differences for American options: explicit methods, projected itertations, a penalty method; workshop
- Asset allocation: one-period and multi-period discrete portfolio optimisation, continuous trading, Merton problem, stochastic control, Hamilton-Jacobi-Bellmann equations, martingale interpretation of dynamic programming, consumption
- Asset pricing: equivalent measures, martingale measures, numeraires, risk-neutral pricing, market price of risk, arbitrage pricing in binomial models,completeness, trinomial trees, fundamental theorems of asset pricing in discrete and continuous time, stopping times and American options
- Interest rate trees, the role of numeraires for interest rate derivatives
- Models for the short rate, use and calibration: Vasicek, CIR, Hull-White, BDT, Ho-Lee
Link to course material for module 3
Back to Core modules (includes module dates)
Module 4 Exotic Options and Advanced Modelling Techniques
- Barrier options: down-and-out and other barrier contracts, intermittent sampling, American digitals, reflection principle
- Further exotic options: Asians, rate and strike options, similarity reductions, discretely sampled options and jump conditions; lookbacks, continuous and discrete sampling, probabilistic methods via reflection
- Monte Carlo for exotic options: continuity corrections for discretely sampled paths for barriers and lookbacks; correlation and basket options; variance reduction; workshop
- Implied and local volatility, Shimko's method and Dupire's formula; stochastic volatility models: stylised facts, econometric models, complete stochastic volatility models; two-factor models, hedging and market completion, special cases
- Jump diffusion and Levy processes: Poisson and Cox process, Ito with jumps, Merton's model; Levy processes, hedging and pricing jump-risk, characteristic functions
- Yield curve modelling, market models (HJM, LMM)
- Practicalities of pricing and hedging interest rate products; SABR; running a swaps desk; managing exotics
- Practicalities of FX and equity derivatives pricing, calibration and implementation
Link to course material for module 4
Back to Core modules (includes module dates)
Module 5: Advanced Modelling Topics 1 (Equity, FX, interest rates)
- Asymptotic methods
- VIX and related volatility products
- Time series analysis of financial data
- Hybrid interest rate products: implementation and calibration
Link to course material for module 5
Back to Advanced modules (includes module dates)
Module 6: Advanced Numerical Methods
- Finite differences
- Fourier methods
- Monte Carlo Greeks, multi-level
- Jumps [PIDEs], Asians, multigrid
- Monte Carlo case studies: variance reduction, Levy processes....
- Advanced Monte Carlo and QMC techniques
- Multi-factor problems, ADI, sparse grids, QMC, PCA
- C++ workshop
- Optimisation
Link to course material for Module 6
Back to Advanced modules (includes module dates)
Module 7: Quantitative Risk Management
Overview of module content
- Risk management in financial institutions
- Taxonomy of risks, risk measurement [VaR, coherent measures,...]
- Utility pricing, incomplete markets
- Behavioural finance
- Regulation (capital requirements, Basel accord)
- Model uncertainty, applications of Bayesian nets to stress testing and risk management
Link to Course Material for Module 7
Back to Advanced modules (includes module dates)
Module 8 Credit, Energy, More Interest Rates
Overview of course content
- Credit risk models and correlation products
- Energy derivatives, electricity markets and energy risk management
- Natural gas markets and derivatives
- Advanced interest rate modelling (SABR-LIBOR market models)
Link to course material for module 8
Back to Advanced modules (includes module dates)
Form to register interest in attending a module as a short course