Valuation of Hybrid Capital Instruments using Lévy Processes

This master thesis introduces a pricing procedure for hybrid capital instruments issued by insurance companies when the underlying interest rate process is modeled by α−stable Lévy processes, as several empirical researches have shown that models based on normal distribution might be improper for financial modeling. Increments of these stochastic processes are independent and follow an α−stable distribution. This distribution is a generalization of normal distribution, only with heavier tails and infinite variance. To obtain the instrument prices, I solve a partial integro-differential equation (PIDE), which is the generalization of the Black-Scholes PDE for Lévy processes. This PIDE is solved by a finite difference method. To improve the stability and the precision of the standard pricing procedure, I provide my own refinement based on interpolation and extrapolation of instrument prices. In comparison to the Gaussian models, the Lévy models provide lower instrument prices and therefore are closer to the market values and allow more flexibility for the price modeling.