Multi-CCY Monte Carlo Basket Option

---

Ensuring we correctly model the volatility of FX pairs is difficult due to their interrelationships. The Heston Local Correlation model (De Col & Kuppinger) models this through a stochastic covariance matrix.

There is no guarantee that the covariance matrix is positive-definite. For every timestep and every Monte Carlo path we need to check it is positively definite and, if not, repair it.

A typical FX basket may contain 3-6 currencies. Modern eigenvector libraries are optimized for large matrices and are suboptimal at the domain size found in finance.

Implementing the pricing using the nZetta toolkit we see a 15x speed-up on x86 and over 125x speed-up using a GPU.