Quantitative Deep Dives: Optimisation Methods in Finance
The Quantitative Trading team is excited to release our first deep dives. These reports are an in-depth but accessible explanation into an interesting topic at the intersection of computer science, mathematics and finance, with our first set of deep dives examining a topic within optimisation methods in finance.
The Quest for Optimal Arbitrage Opportunities
Aman Bilkhoo - Head of Quantitative Trading - Deep Dive - Nov 2023
Cross-currency arbitrage, or circular arbitrage, is a variant of arbitrage in which a pricing discrepancies in a foreign exchange market that allow converting between currencies in a cycle, e.g. GBP→EUR→CHF→GBP, are exploited to yield a theoretically risk-free profit. These opportunities are short-lived due to market participants quickly exploiting them, which alter the supply and demand of the assets involved and drive the misplacing to correction. This motivates the development of efficient computational techniques to find and exploit circular arbitrage opportunities quickly to beat the competition.
Graph theory can be used to model this problem, and methods including using the Bellman-Ford algorithm for negative-weight cycle detection being used to detect the existence of arbitrage opportunities. This problem can also be formulated as a maximum network flow problem, using linear programming and the network simplex method to solve the NP-hard problem of finding an optimal arbitrage opportunity. Quantum methods such as optimisation using quantum annealing can also be used to find optimal arbitrage opportunities.
Anyone with an interest in how computational methods and finance intersect is encouraged to learn more by reading the deep dive here.
Dynamic Asset Allocation: Optimisation with Mean Reversion
Pablo Meijer - Quantitative Trading Associate - Deep Dive - Nov 2023
In finance and microeconomics, mean reversion stands as a core concept, asserting that prices and returns tend to revert to their mean over time. This principle is not only crucial for understanding market dynamics but also forms the backbone of dynamic asset allocation strategies, offering valuable perspectives for both investors and microeconomists.
Mean reversion has an integral role in shaping investment decisions and corporate strategies, with notable investors like Joel Greenblatt leveraging the ideas in value investing. One such strategy is dynamic asset allocation (DAA), in which portfolio allocations are dynamically adjusted in response to market changes, and this is shown to be effective in enhancing risk-adjusted returns. Furthermore, mean reversion is an idea that underpins some algorithmic trading strategies such as pairs trading, and has effects in labour economics, such as in the dynamics of wage fluctuations.
You can learn more by reading the deep dive here.
For any questions or comments, contact the Quantitative Trading department at quant@kingscapital.org