Polynomial Chaos Expansion Approach to Interest Rate Models

摘要: The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions given stochastic quantity , hence acting as kind basis. PCE methodology has been developed mathematically rigorous Uncertainty Quantification (UQ) method aims at providing reliable numerical estimates for some uncertain physical quantities defining the dynamic certain engineering models and their related simulations. In present paper, we use approach in order analyze equity interest rate models. particular, take into consideration those based on, example, Geometric Brownian Motion, Vasicek model, CIR model. We theoretical well concrete approximation results considering, without loss generality, one-dimensional case. also provide both an efficiency study accuracy our by comparing its outputs with ones obtained adopting Monte Carlo approach, standard enhanced version.