Numerical method for Mathematical finance

In this mini-course we will discuss various numerical methods for the pricing of financial instruments, with a particular focus on applications to the energy markets. We will start from the simulations of some of the most common continuous-time models, such as the geometric Brownian motion and the Ornstein-Uhlenbeck process. Stochastic volatility models, such as the Heston model, may also be discussed. We will then consider different approaches for options pricing, such as the PDE and the Monte Carlo approach. State-dependent options may also be discussed. Finally, forward contracts with delivery period typical of the energy markets will be treated from the Heath-Jarrow-Morton modelling point of view. If time allows, we will also discuss (simulations of) SPDEs for Hilbert space-valued forward curves. The course will be given in Python.