Programming Project

Instructions

Projects are submitted in accordance with the current Brief. It is designed to give an opportunity for further study of numerical methods required to implement and validate a quantitative model. To complete the project, you must implement the topic below plus CVA component.

SECTION 1: Time Series Analysis and Backtesting

SECTION 2: CVA Calculation for an Interest Rate Swap
Note:

The CVA component (section 2) is a mandatory addition as it balances exposure to the quant issues (interest rates, discounting) that would not be in focus otherwise.

Programming environment must have appropriate strengths and facilities to implement the topic (pricing model). Common choices range from Matlab to Python to C++, please exercise judgement as quants.

Use of R/Matlab/Mathematica/Matlab is encouraged where time series or presentation involved. Coding of numerical techniques/use of industry code libraries is expected.

‘Scripted solution' means the ready functionality from toolboxes and libraries is called, but the amount of own coding of numerical methods is minimal or non-existent. This particularly applies to Matlab/R as well as Excel spreadsheet functions (not robust).

The aim of the project is to enable you to code numerical methods and develop model prototypes in a production environment. Excel spreadsheets only or scripted solutions are below the expected standard for completion of the project.

To answer the question, "What should I code?" Delegates are expected to re-code numerical methods that are central to the model and exercise judgement in identifying them. Balanced use of libraries is allowed at the delegate's own discretion and subject to a description of limitations for ready functions/borrowed code (in the report).

It is up to delegates to develop their own test cases, sensibility checks and validation. It is normal to observe irregularities when the model is implemented on real life data. If in doubt, reflect on the issue in the project report.

The code must be thoroughly tested and well-documented: each function must be described, and comments must be used. Provide instructions on how to run the code.

The main purpose of the report is to facilitate access to numerical methods' implementation (the code) and pricing results.

The report must contain a sufficient description of the mathematical model, numerical methods and their properties. In-depth study is welcome but report must be relevant.

Identify numerical methods recorded and include their code/algorithms in an appendix.

Please give due attention and space for presentation and discussion of your pricing results. Present explicit sensitivity and/or risk analysis.
Use charts, test cases and comparison to research results where available.

Mathematical sections of the report can be prepared using LaTeX or Equation Editor (Word). For Mathematica and Python notebooks, make sure they are presentable.

Time Series Analysis and Backtesting

Summary

The aim to this topic is an estimation and analysis of tradeable relationships between two or more financial time series. Identifying and backtesting a robust cointegrated relationship means exposing a factor that drives both (or many) asset prices. The factor is traded by entering the long-short position given by cointegrating weights.

Through implementation you will have a hands-on introduction to Vector Autoregression (for returns) and Error Correction (for prices) models, which are the main variations of the mul- tivariate regression. Instead of econometric forecasing, a range of techniques and considerations applied known as ‘backtesting'. The techniques and quant recipes are specific to statistical ar- bitrage or systematic (algorithmic) strategy selected, for example, statistical arbitrage requires evaluating mean-reversion and optimality of trading of a spread.

A project that solely runs pre-programmed statistical tests on data is a preparation work, not the complete project. The project should have coding of necessary statistical tests from the first principles (explicit regression equations) by yourself. The least deliverables are a. implemented Engle-Granger procedure, b. statistical diagnosis and backtesting (split dataset in half or com- pute rolling estimates), and c. market factor backtesting via regressing returns from your strategy on market index returns or another factor. These are in addition to the underlying numerical methods on matrices and vector autoregression.5

Backtesting

The following notes o↵er choices to implement in aspects and questions of backtesting:
- All project designs (whether learning-level or in-depth) should include backtesting of a strategy. The strategy is realised by using cointegrating coefficients ØCoint as allocations w. That creates a long-short portfolio that generates a mean-reverting spread (cointegrated residual).

- Does cumulative P&L behave as expected (for a cointegration trade)? Is P&L coming from a few or lot of trades/time period? What are the SR/Maximum Drawdown? Behaviour of risk measures (volatility/VaR)? Concentration in assets and attribution?
- Impact of transaction costs (plot an average P&L value vs. number of transactions).

- Optionally, introduce liquidity and algorithmic flow considerations (a model of order flow). How would you be entering and accumulating the position? What impact bid-ask spread and transaction costs will make?

Time Series Analysis and Backtesting

Summary

The aim to this topic is an estimation and analysis of tradeable relationships between two or more financial time series. Identifying and backtesting a robust cointegrated relationship means exposing a factor that drives both (or many) asset prices. The factor is traded by entering the long-short position given by cointegrating weights.

Through implementation you will have a hands-on introduction to Vector Autoregression (for returns) and Error Correction (for prices) models, which are the main variations of the mul- tivariate regression. Instead of econometric forecasing, a range of techniques and considerations applied known as ‘backtesting'. The techniques and quant recipes are specific to statistical ar- bitrage or systematic (algorithmic) strategy selected, for example, statistical arbitrage requires evaluating mean-reversion and optimality of trading of a spread.

A project that solely runs pre-programmed statistical tests on data is a preparation work, not the complete project. The project should have coding of necessary statistical tests from the first principles (explicit regression equations) by yourself. The least deliverables are a. implemented Engle-Granger procedure, b. statistical diagnosis and backtesting (split dataset in half or com- pute rolling estimates), and c. market factor backtesting via regressing returns from your strategy on market index returns or another factor. These are in addition to the underlying numerical methods on matrices and vector autoregression.5

Backtesting
The following notes o↵er choices to implement in aspects and questions of backtesting:
- All project designs (whether learning-level or in-depth) should include backtesting of a strategy. The strategy is realised by using cointegrating coefficients ØCoint as allocations w. That creates a long-short portfolio that generates a mean-reverting spread (cointegrated residual).

- Does cumulative P&L behave as expected (for a cointegration trade)? Is P&L coming from a few or lot of trades/time period? What are the SR/Maximum Drawdown? Behaviour of risk measures (volatility/VaR)? Concentration in assets and attribution?
- Impact of transaction costs (plot an average P&L value vs. number of transactions).

- Optionally, introduce liquidity and algorithmic flow considerations (a model of order flow). How would you be entering and accumulating the position? What impact bid-ask spread and transaction costs will make?

https://www.dropbox.com/s/jcl6f1okikdqfs6/Programming%20Project%20Resources.zip?dl=0