SULL'USO DEI PROCESSI STOCASTICI DI LEVY NEI MODELLI PER I TASSI D'INTERESSE

Dopo aver enunciato i principali risultati riguardanti i processi stocastici, si analizzano i processsi di Levy, si parla dell'integrazione stocastica secondo Ito, si definiscono le misure aleatorie e l'integrazione rispetto a queste ultime. Partendo dall'analisi dei modelli classici per i tassi d'interesse, basati su processi di Wiener, si passa a modelli basati su processi di Levy e per questi ultimi si studia il caso in cui il processo short rate è markoviano

Italian open-end funds: performance of asset management companies

We empirically analyse the returns of both Italian and round-trip open-end funds managed by Italian asset management companies (SGRs) in the period 2003-2008. Taking into account a modified version of the capital asset pricing model (CAPM), we estimated a performance measure for each asset management company and for each fund, as is usually done in the relevant literature. The analysis shows that the performance of any asset management company, with reference to its managed funds, is on average no greater than that of the benchmark chosen by the managers. In addition, as expected, the funds’ systematic risk is close to that of the benchmarks. Finally, robust estimation techniques let us control for the heteroskedasticity due to the presence of outliers and also to the different excess returns of individual funds.open-end funds, asset management companies, panel data, robust estimators, normal inverse Gaussian distribution

Tempered stable and tempered infinitely divisible GARCH models

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, these GARCH models allow to find the risk-neutral price process, and hence they can be applied to option pricing. We propose algorithms to generate scenario based on GARCH models with CTS and RDTS innovation. To investigate the performance of these GARCH models, we report a parameters estimation for Dow Jones Industrial Average (DJIA) index and stocks included in this index, and furthermore to demonstrate their advantages, we calculate option prices based on these models. It should be noted that only historical data on the underlying asset and on the riskfree rate are taken into account to evaluate option prices. --tempered infinitely divisible distribution,tempered stable distribution,rapidly decreasing tempered stable distribution,GARCH model option pricing

Tempered infinitely divisible distributions and processes

In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky , a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosinski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric example. --stable distributions,tempered stable distributions,tempered infinitely divisible distributions,modified tempered stable distributions

Time series analysis for financial market meltdowns

There appears to be a consensus that the recent instability in global financial markets may be attributable in part to the failure of financial modeling. More specifically, current risk models have failed to properly assess the risks associated with large adverse stock price behavior. In this paper, we first discuss the limitations of classical time series models for forecasting financial market meltdowns. Then we set forth a framework capable of forecasting both extreme events and highly volatile markets. Based on the empirical evidence presented in this paper, our framework offers an improvement over prevailing models for evaluating stock market risk exposure during distressed market periods. --ARMA-GARCH model,»-stable distribution,tempered stable distribution,value-at-risk (VaR),average value-at-risk (AVaR)