Statistics and data analysis for financial engineering pdf

The primary goal of investing in a financial market is to make profits without taking excessive risks. Most common investments involve purchasing financial assets such as stocks, bonds or bank deposits, and holding them for certain periods. Positive revenue is generated if the price of a holding asset at the end of holding period is higher than that at the time of purchase (for the time being we ignore transaction charges). Obviously the size of the revenue depends on three factors: (i) the initial capital (i.e. the number of assets purchased), (ii) the length of holding period, and (iii) the changes of the asset price over the holding period. A successful investment pursues the maximum revenue with a given initial capital, which may be measured explicitly in terms of the so-called return. A return is a percentage defined as the change of price expressed as a fraction of the initial price. It turns out that asset returns exhibit more attractive statistical properties than asset prices themselves. Therefore it also makes more statistical sense to analyze return data rather than price series.

Related Papers

In this paper, we showed that the no-arbitrage condition holds if the market follows the mixture of the geometric Brownian motion (GBM). The mixture of GBM can incorporate heavy-tail behavior of the market. It automatically leads us to model the risk and return of multiple asset portfolios via the nonparametric Bayesian method. We present a Dirichlet Process (DP) prior via an urn-scheme for univariate modeling of the single asset return. This DP prior is presented in the spirit of dependent DP. We extend this approach to introduce a multivariate distribution to model the return on multiple assets via an elliptical copula; which models the marginal distribution using the DP prior. We compare different risk measures such as Value at Risk (VaR) and Conditional VaR (CVaR), also known as expected shortfall (ES) for the stock return data of two datasets. The first dataset contains the return of IBM, Intel and NASDAQ and the second dataset contains the return data of 51 stocks as part of t...

Through the applied literature, the Markov switching with time varying transition probabilities (MS-TVTP) is considered as one of the most relevant models. The aim of this paper is to shed light users of MS-VAR model in the analysis of causal relationships in macroeconomic time series. Through a revision of the Filardo and Gordon’s algorithm and through the adaptation Gibbs sampling, dealing with Bayesian probability, we provided a detailed Matlab code that estimates the MS-TVTP parameters. In our application, we have shown (i) the possibility and relevance of our extension in the analysis of cyclical fluctuations of the bilateral exchange rate TND/USD, and the index of industrial production, (ii) the dependency of the current transition probability of the exchange rate on that of the previous period, of the industrial production, and of economic growth, (iii) the persistence probability of the Tunisian Dinar in the phase of depreciation outweighs that of persistence in the appreciation phase. This is due to the opening of the Tunisian industrial sector to a more competitive industry in Europe, (iv) the necessity to implement this extension for more general applications on cyclical fluctuations in the small open economies.

This study introduces computation of option sensitivities (Greeks) using the Malli-avin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate model, respectively. Therefore, it integrates the recent developments in the Malliavin calculus for the computation of Greeks: Delta, Vega, and Rho and it extends the method slightly. The main results show that Malliavin calculus allows a running Monte Carlo (MC) algorithm to present numerical implementations and to illustrate its effectiveness. The main advantage of this method is that once the algorithms are constructed, they can be used for numerous types of option, even if their payoff functions are not differentiable.

We quantify the effects on contingent claim valuation of using an estimator for the volatility σ of a geometric Brownian motion (GBM) process. That is, we show what difficulties can arise when failing to account for estimation risk. Our working problem uses a direct estimator of volatility based on the sample standard deviation of increments from the underlying Brownian motion. After replacing the direct estimator into the GBM, we derive the resulting distribution function of the approximated GBM for any time point. This allows us to present post-estimation distributions and valuation formulae for an assortment of European contingent claims that are in accord with many of the basic properties of the underlying risk-neutral process, and yet accurately reflect some of the additional quantifiable uncertainties that exist in a Black-Scholes-Merton type of economy. Next we extend our work to the contingent claim sensitivities associated with an assortment of European option portfolios th...

This thesis is set in the intersection between separate types of financial markets, with emphasis on joint risk modelling. Relying on empirical findings pointing toward the ex- istence of dependence across equity and corporate debt markets, a simulation framework intended to capture this property is developed. A few different types of models form building blocks of the framework, including stochastic processes describing the evolution of equity and credit risk factors in continuous time, as well as a credit rating based model, providing a mechanism for imposing dependent credit migrations and defaults for firms participating in the market. A flexible modelling framework results, proving capable of generating dependence of varying strength and shape, across as well as within studied markets. Particular focus is given to the way markets interact in the tails of the distributions. By means of simulation, it is highlighted that dependence as produced by the model tends to spread asymmet...