Quantum-Enhanced Principal Component Analysis: Transforming Yield Curve Modeling with the Power of Quantum Computing

Yield curves are crucial for determining the present value of future cash flows in market-consistent valuations. Several regulatory frameworks require credit and liquidity-adjusted yield curves for discounting liabilities. Furthermore, modeling accurate yield curves is essential for insurers managing interest rate risk through Asset-Liability Management (ALM). The interconnected nature of financial markets and recent accounting standards complicate interest rate risk modeling. IFRS 17 mandates yield curves that reflect the financial characteristics of liabilities and backing asset portfolios, necessitating multiple yield curves’ calibration. Principal Component Analysis (PCA) reduces this complexity by transforming the data into a smaller set of principal components that explain most of the variance. However, the computational complexity of PCA increases with dataset size, posing challenges for large-scale financial applications. Quantum computing, offers considerable computational power, enabling efficient handling of complex problems within a reasonable timeframe. Quantum Principal Component Analysis (qPCA) leverages quantum computing to perform PCA efficiently, providing an exponential speed-up over classical methods. This makes it ideal for handling large financial datasets, enabling real-time analysis and decision-making, and offering more precise calculations.  We utilize modern quantum hardware, such as IBM's quantum computers, to apply the qPCA algorithm to historical yield curve data. Our analysis focuses on model stability when forecasting multiple yield curves simultaneously. This involves considering various risk factors such as differing regions and ratings, while accounting for the interdependence of the yield curves. Utilizing qPCA for yield curve modeling represents a considerable advancement in financial risk management, ensuring better compliance with regulatory requirements.