TESI DI DOTTORATO: A jump-diffusion version of the CIR bivariate model

Contents 0.1 Introduction 1 The problem of the existence of a Martingale Measure 1.1 Basic definitions of the financial mathematics 1.2 The considered model 1.3 The first fundamental Asset Pricing theorem in this model 1.4 Construction of the martingale measure 1.5 Evaluation of some market security 1.6 Appendix 2 Hedging strategies and completeness of the model 2.1 The model and the candidate basic assets 2.2 Nominal zero coupon bond 2.3 European Call Option's price 2.4 Bond indexed to the level of price 2.5 Pricing other claims 2.6 Checking the market basis property 2.7 From the existence of a market basis to the completeness property 2.8 The case of n jumps 2.8.1 The new formulas for the prices 2.8.2 The special structure of M^{t;p;1;K1;..;Kn} 2.8.3 From the linear independence of the functions to the non- singularity of M^{t;p;1;K1;..;Kn} 2.8.4 Changing the point of view for the independence of homo- geneous functions 2.8.5 A condition of dependence 2.8.6 The equation for C, and its boundary conditions. The parity relation 2.8.7 Conclusion for the proof of the linear independence prop- erty of the functions pCp(p); (Delta_j C)(p) 2.9 The Integro-differential partial derivatives equation for the Call price 3 Estimators of sigma, gamma and N_T with a, lambda known 3.1 Tool ideas 3.2 Estimation of N_T , the number of jumps untill T 3.3 Estimation of sigma 3.4 Large deviation principle for hat{sigma}^2_n 3.5 Estimation of gamma^2 4 The case of a, lambda not known 4.1 Estimation of N^{(n;h)}_{nh} 4.2 Estimation of sigma 4.3 Estimation of gamma^2 4.4 Estimators of a, lambda 4.5 Variable coefficients