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Finance & Stochastic

Giandomenico, Rossano (2014): Finance & Stochastic.

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Abstract

The study analyses quantitative models for financial markets by starting from geometric Brown process and Wiener process by analyzing Ito’s lemma and first passage model. Furthermore, it is analyzed the prices of the options, Vanilla & Exotic, by using the expected value and numerical model with geometric applications. From contingent claim approach ALM strategies are also analyzed so to get the effective duration measure of liabilities by assuming that clients buy options for protection and liquidity by assuming defaults protection barrier as well. Furthermore, the study analyses interest rate models by showing that the yields curve is given by the average of the expected short rates & variation of GDP with the liquidity risk, but in the case we have crisis it is possible to have risk premium as well, the study is based on simulated modelisation by using the drift condition in combination with the inflation models as expectation of the markets. Moreover, the CIR process is considered as well by getting with modification of the diffusion process the same result of the simulated modelisation but we have to consider that the CIR process is considered in the simulated environment as well. The credit risk model is considered as well in intensity model & structural model by getting the liquidity and risk premium and the PD probability from the Rating Matrix as well by using the diagonal. Furthermore, the systemic risk is considered as well by using a deco relation concept by copula approaches. Moreover, along the equilibrium condition between financial markets is achieved the equity pricing with implications for the portfolio construction in simulated environment with Bayesian applications for smart beta. Finally, Value at Risk is also analyzed both static and dynamic with implications for the percentile of daily return and the tails risks by using a simulated approach.

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