Contents0.1 Introduction 1 The problem of the existence of a Martingale Measure 1.1 Basic definitions of the financial mathematics1.2 The considered model 1.3 The first fundamental Asset Pricing theorem in this model 1.4 Construction of the martingale measure1.5 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;..;Kn2.8.3 From the linear independence of the functions to the non-singularity of M^t;p;1;K1;..;Kn2.8.4 Changing the point of view for the independence of homo-geneous functions2.8.5 A condition of dependence2.8.6 The equation for C, and its boundary conditions. The parityrelation2.8.7 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 sigma3.4 Large deviation principle for hatsigma^2_n3.5 Estimation of gamma^24 The case of a, lambda not known 4.1 Estimation of N^(n;h)_nh4.2 Estimation of sigma4.3 Estimation of gamma^24.4 Estimators of a, lambda 4.5 Variable coefficients
TESI DI DOTTORATO: A jump-diffusion version of the CIR bivariate model
C.Mancini
1999-01-01
Abstract
Contents0.1 Introduction 1 The problem of the existence of a Martingale Measure 1.1 Basic definitions of the financial mathematics1.2 The considered model 1.3 The first fundamental Asset Pricing theorem in this model 1.4 Construction of the martingale measure1.5 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;..;Kn2.8.3 From the linear independence of the functions to the non-singularity of M^t;p;1;K1;..;Kn2.8.4 Changing the point of view for the independence of homo-geneous functions2.8.5 A condition of dependence2.8.6 The equation for C, and its boundary conditions. The parityrelation2.8.7 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 sigma3.4 Large deviation principle for hatsigma^2_n3.5 Estimation of gamma^24 The case of a, lambda not known 4.1 Estimation of N^(n;h)_nh4.2 Estimation of sigma4.3 Estimation of gamma^24.4 Estimators of a, lambda 4.5 Variable coefficients
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