Numerical Software Development

---

Numerical software is used extensively in finance. The accuracy, stability, and speed of numerical software are critical for the quality and reliability of its results. How software is implemented for mathematical calculations and the choice of algorithms can have a very significant impact on speed, accuracy, reliability and stability of price and risk sensitivity calculations. This course provides an understanding of the issues involved and how to mitigate their impact in real financial calculations.

• Accuracy: The accuracy of numerical software is critical, particularly when it comes to finance applications. If the software produces inaccurate results, it can lead to incorrect trade prices and hedging costs.
• Stability: Numerical software should be stable and reliable, particularly when used for critical applications such as finance. Unstable algorithms can lead to numerical errors, mathematical instabilities and bifurcations resulting in unstable risk calculations.
• Reproducibility: Accurate and stable numerical software is also important for reproducibility. Unstable implementations and algorithm will produce different prices on different compiler options, compiler, hardware and software increasing management costs for e.g., reconciliation.
• Confidence: Traders and risk management need to trust the software in order to make important financial decisions based on its output. Any instabilities erode confidence and trust.
• Efficiency: Instabilities in software can result in slower pricing and risk convergence making it slower or more inefficient. It can significantly impact productivity and the ability to analyze and interpret data in a timely manner.

• Scalars and Integers: The fundamental accuracy limitations of the different floating point and integer data types. Reducing numerical noise in scalar calculations.
• Mathematical Instability: Algorithms that are intrinsically unstable due to the mathematics involved and how to reduce the impact.
• Algorithmic Instability: Algorithms that are unstable, chaos impact, Sinai billiard table and minimization. Also covers domain change within calculations and their impact.
• Convergence Impact: Impact of early termination in root finding and minimization algorithms and how to reduce the impact.
• Environment: How the choice of hardware, compiler and optimisation settings impact stability. Reducing numerical noise on heterogeneous grids.
• Investigation: How to investigate and locate numerical instability in libraries.

Experienced quants with a C++ and numerate background.

Course contents and duration can be modified to align with additional client needs. 

Delivery can be on-site, remote or in recorded form.