Program content

The CQF Program comprises six modules. Each module covers a different aspect of quantitative finance and consists of lectures, discussions and computer workshops. Delegates are required to complete weekly exercises prior to the commencement of the next class. At the end of each module, delegates take a written exam to gain certification in that module.

Maths Primer
We now include a Maths Primer course at the beginning of the CQF. This primer course is ideal for pre-CQF delegates looking to brush up on their math skills. It is a short but intensive refresher in the areas of calculus, differential equations, linear algebra and probability.

Some things you may wish to consider:

  • Mathematical finance is now a pre-requisite for City practitioners. The Mathematics for Quantitative Finance Primer attracts individuals from a wide range of roles and academic backgrounds. It is extremely useful for those who feel 'rusty' due to a long period away from the mathematics learning / application environment, providing a short and intense refresher. It is also offered at no additional cost to CQF delegates*.
  • This course is designed for those working full time – no time away from the office
  • Delivered via 7 evening lectures, in the classroom in London and New York or via online learning
  • Every class is recorded and available online for play back in perpetuity
  • You will receive continual access to a personal tutor via phone and email or in person
  • You will build a solid mathematical foundation with which to further your career

Click here for further details on the maths primer

Trading Simulator
For those of you who whose goal it is to become a trader then you’ll learn important skills from our in-house Trading Simulator. And even if you are already a trader then you can benefit from the Simulator by trying out strategies and valuation and risk-management methodologies that you have learned in class.
Click here for more details

Module 1
Basic Building Blocks of Finance Theory and Practice
It will be necessary to bring all students up to the same technical level. Most students will be familiar with the contents of this first module, but any gaps in a student’s background will be identified. We introduce the rules of applied Itô calculus as a modelling framework. Simple stochastic differential equations and their associated Fokker-Planck and Kolmogorov equations are introduced.

  • Important mathematical tools and results
  • Taylor series
  • Ordinary differential equations
  • Probabilistic concepts
  • Gaussian, Poisson, Cauchy, Binomial, etc.
  • Central Limit Theorem
  • The random behaviour of asset prices
  • Stochastic calculus and Itô’s Lemma
  • Transition density functions
  • Partial differential equations
  • Martingale theory
  • Change of numéraire
  • The Radon-Nikodym derivative

Module 2
Risk and Return
This unit deals with the classical portfolio theory of Markowitz, the Capital Asset Pricing Model, more recent developments of these theories, also option types and strategies. We see the rudiments of option pricing principles and theory in the binomial model.

  • The Black-Scholes model
  • Hedging and the Greeks
  • Option strategies
  • Early exercise and American options
  • Elementary Monte Carlo simulations
  • Elementary finite-difference methods
  • Martingale theory for pricing
  • Girsanov’s Theorem
  • Parallels between probabilistic and deterministic methodologies

Module 3
Equity, Currency and Commodity Derivatives
The Black-Scholes theory, built on the principles of delta-hedging and no arbitrage, has been very successful and fruitful as a theoretical model and in practice. The theory and results are explained using different kinds of mathematics to make the student familiar with techniques in current use.

  • Hedging and the Greeks
  • The Black-Scholes model
  • Option strategies
  • Early exercise and American options
  • Elementary Monte Carlo simulations
  • Elementary finite-difference methods
  • Martingale theory for pricing

Module 4
Interest Rates and Products
This module starts with a review of fixed-income products and the simple but useful concepts of yield, duration and convexity, showing how they can be used in practice. The limitations of this approach and the need for a more sophisticated theory are explained. Many of the ideas seen in the equity derivatives world are encountered again here but in a more complex form.

  • Fixed-income products
  • Yield, duration and convexity
  • Stochastic spot-rate models
  • Affine stochastic models
  • Change of numéraire
  • Heath, Jarrow and Morton
  • Calibration
  • Data analysis
  • Convertible bonds

Module 5
Credit Products and Risk
Credit risk plays an important role in current financial markets. We see the major products and examine the most important models. The modeling approaches include the structural and the reduced form, as well as copulas.

  • Credit risk and credit derivatives
  • CDS pricing, market approach
  • Synthetic CDO pricing
  • Risk of default, structural and reduced form
  • Copulas
  • Implementation of copula models

Module 6
Advanced Topics
The lognormal random walk and the Black-Scholes model have been very successful in practice. Yet there is plenty of room for improvement. The benefits of new models will be discussed from theoretical, practical and commercial viewpoints. When pricing complex products it is necessary to be able to correctly value vanilla products. Modern models adopt frameworks that ensure that basic products are perfectly calibrated initially. The models derived in earlier parts of the course are only as good as the solution. Increasingly often the problems must be solved numerically. We explain the main numerical methods, and their practical implementation.

  • Exotic options
  • Static hedging
  • Transaction costs and discrete hedging
  • Deterministic volatility and calibration
  • Stochastic volatility and jump diffusion
  • Non-probabilistic volatility models
  • Correlation, problems and solutions
  • Hidden risks in CDOs, and solutions
  • Brace, Gatarek and Musiela
  • Monte Carlo methods, Brownian bridge, advanced schemes
  • Quasi-Monte Carlo methods, Sobol’, and more
  • Finite-difference methods, multi factor, implicit, Crank-Nicolson

C++ in finance

Want to learn C++ programming but have no experience? Or just want to brush up or take your skills to the next level? The C++ course is included in the CQF Package. The vast majority of professional software development in quant finance is in C++. To be an effective member of a quant team you need to write high-quality code, and you must also be able to understand the C++ written by others.

Goals of the syllabus

By the end of this syllabus you will be able to take important pricing models, and translate them into working C++ code. Starting with elementary C++, the 25 sessions will cover both the principles and practicalities of producing robust code in a quant finance environment. You will learn not only the theory of design, but also specific details of implementing hardcore techniques in financial maths, as well as connecting your software to applications such as Excel. Uniquely, this course covers the pitfalls and problems that you will face in debugging and faulty design, equipping you for the realities of programming in banks.

Mathematical finance in C++

You will learn the techniques necessary to convert pricing models into the algorithmic form suitable for coding in C++. A wide variety of numerical schemes used in quantitative finance will be used for examples.

Extending the CQF

C++ is critical to a role as a modern quant in a top-tier investment bank, so as part of the continual improvement of the CQF program we are including the entire Computational Finance series as a self-contained subset of the recorded Alumni Classes. CQF delegates who want to take this syllabus are advised to do so after they have completed the CQF, or in parallel with the CQF after discussion with a Course Director.

Course Reading

Delegates will be provided with the following course reading material:

  • Paul Wilmott Introduces Quantitative Finance (P. Wilmott)
  • Paul Wilmott On Quantitative Finance (P. Wilmott)
  • FAQs in Quantitative Finance (P. Wilmott)
  • Advanced Modelling in Finance Using Excel and VBA (M. Jackson and M. Staunton)
  • Derivatives: Models on Models (E.G. Haug)
  • Monte Carlo Methods in Finance (P. Jäckel)
  • Subscription to Wilmott magazine
  • Structural Credit Products: Credit Derivatives and Synthetic Securistisation (M.Choudhry,)

» Exams and Assessments
» Maths Primer
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Lifelong Learning

Continuing education is paramount in the world of mathematical finance. To ensure CQF delegate are supported after they have obtained their qualification, additional regular classes and masterclasses are delivered on both technical and topical issues. These classes are delivered by the CQF faculty in addition to world-class practitioners. For more information click here.