We implemented and verified an extension of the classical Hull-White model. To incorporate the notion of cyclicity, the paper we followed modifies the SDE so that the periodicity is carried by the mean-reversion speed $\kappa$: $$dr_t = \kappa(t)\left(\theta - r_t\right)dt + \sigma\, dW_t, \qquad \kappa(t) = \kappa_0 + A\sin(\omega t),$$ with $\omega = 2\pi/22.5$ rad/yr, a periodicity the authors identified through a Fourier analysis of the interest rate series. To verify their results we retrieved the same data as the one mentioned in the article and plotted the errors of the two models. We then extended the model further by adding a time-dependent $\theta$ term coming directly from the Nelson-Siegel result. The two versions turn out to be complementary: one is more precise in the short term, while the other is more accurate at long maturities.

We developed a closed form for two insurance products, the Guaranteed Minimum Accumulation Benefit (GMAB) and the Guaranteed Minimum Death Benefit (GMDB) — contracts that offer a minimum guaranteed accumulation amount regardless of the performance of the underlying. After deriving the analytical price in full, we computed the value of the products numerically with a binomial tree and a Monte Carlo simulation, and then studied the convergence of the two methods towards the closed-form result.

This was probably my favourite project by far. The goal was to detect whether a patient was suffering from a disease, based first on tabular data but also by processing one image per patient. We proceeded step by step: selecting the relevant features, identifying the ones most correlated with the target, then looking for the non-linear relations between variables that a linear correlation cannot capture. On this basis we trained and compared the relevant machine learning models — XGBoost, Random Forest and an MLP.

We implemented, based on the Gmsh library, a finite element analysis in C to answer one question: what would happen if cardboard were made of a hexagonal form rather than the usual corrugated waves? The application covers the whole chain for the underlying 2D linear elasticity problem — meshing the hexagonal geometry, assembling and solving the global stiffness system, and visualising the resulting displacement and stress fields — so that the deformation of the structure under load can be compared with the classical design.

The goal was to estimate the state of a particle following the Lorenz dynamics $$\dot{x} = \sigma(y - x), \quad \dot{y} = x(\rho - z) - y, \quad \dot{z} = xy - \beta z$$ (with $\sigma = 10$, $\rho = 28$, $\beta = 8/3$) using only observations of its position corrupted by Gaussian noise. We implemented a SIR (Sequential Importance Resampling) particle filter: the particles are propagated through the dynamics with a fourth-order Runge-Kutta step, weighted by the likelihood of the current observation, and then resampled. We coded three resampling schemes — multinomial, residual and systematic — plus a baseline without any resampling, and studied how the filter reacts to the process noise, the time step, the number of particles and the observation noise. The comparison was finally made quantitative by computing the distribution of the RMSE over 50 runs for each resampling method.