Calibration of complex equity-linked and interest rate derivatives pricing models: theory and practice

Derivatives pricing procedures have to take into account different features and peculiarities of these contracts and, consequently, refine the model or different circumstances. The knowledge of assumptions and limitations (theoretical and practical) of implemented models is extremely significant. This work aims to analyze the most diffuse models developed by the industry. I will define the best practice techniques in order to explain the procedure usually implemented for the derivatives fair value estimation and the risks related with these contracts. First of all, I introduce the analysis defining the motivations and, subsequently, the theoretical reasons for implementing different categories of pricing methods. Moreover, a specific relevance is given to the models calibration procedure: the sensitive process used for the estimation of the models parameters. The paper is divided as follows. In the second chapter, I describe the theoretical tools necessary for understanding different pricing models used in the work. Models for equity-index derivatives are presented in the third chapter. The analysis starts with the simplest ones and, then, I improve the description defining the new industry improvements as stochastic skew and stochastic volatility. In the fourth section I describe the evolution of interest rate derivatives pricing models highlighting the trade-off between practical advantages and theoretical limitations. For both interest rate derivatives and equity linked derivatives I set up, implement and calibrate the most diffuse models. Finally, I test the efficiency (in terms of computational time) and the efficacy (in terms of value) a few models used in the industry estimating the fair price for the most common and complex OTC derivative contracts.