Loretta Mastroeni

Cloud storage pricing: a comparison of current practices

Cloud storage is fast securing its role as a major repository for both consumers and business customers. Many companies now offer storage solutions, sometimes for free for limited volumes. The most apparent means of competition is pricing, though the complexity of pricing plans may make a comparison difficult. We have surveyed the pricing plans of a selection of major cloud providers and compared them using the unit price as the means of comparison. We find that all the providers, excepting Amazon, adopt a bundling pricing scheme; Amazon follows instead a block-declining pricing policy. Our comparison of pricing plans is conducted through a double approach: a pointwise comparison for each value of storage volume, and an overall comparison using a two-part tariff approximation and a Pareto-dominance criterion. Under both approaches, most providers appear to offer pricing plans that are more expensive and can be excluded from a procurement selection in favour of a limited number of dominant providers.

A maximum entropy method to assess the predictability of financial and commodity prices

A novel signal processing method for the analysis of financial and commodity price time series is here introduced to assess the predictability of financial markets. Our technique, exploiting the maximum entropy method (MEM), predicts the entropy of the next future time interval of the time series under investigation by a least square minimization approach. Like in conventional ex-post analysis based on estimated entropy, high entropy values characterize unpredictable series, while more stable series exhibit lower entropy values. We first evaluate (by theory and simulation) the performance of our method in terms of mean and variance of the predictions. Then, we apply our technique to several sets of historical financial data, correlating the entropy trend to contemporary socio-political events. The efficiency of our technique for application to financial engineering analysis is shown in comparison with the conventional approximate entropy method (usually applied in econometrics). We propose a novel signal processing method for financial time series analysis.We predict the entropy by a least square minimization approach.We evaluate (by theory and simulation) the mean and variance of the predictions.We apply our technique to several sets of historical financial data.The efficiency of our technique is shown versus conventional econometrics approach.

A real options model for the transferability value of telecommunications licenses

Licenses for telecommunications services are awarded with a number of side obligations and commitments for the licensee. Under such obligations the licensee is typically not allowed to transfer its license to another operator. Such prohibition may cause heavy inconveniences for customers, so that its removal is strongly advocated and already a reality in many cases. Its removal adds value to the original license and may then constitute a valuable option (the transferability option). A method is here proposed to assess such value, by using the framework of real options. The method is applied in a variety of settings and shows that the value of the option depends superlinearly on the reselling price and the market volatility, and linearly or sub-linearly on the expiry time of the option.

Economic decision criteria for the migration to cloud storage

Cloud storage has fast become a widespread alternative to in-house costly storage infrastructures. However, the migration to cloud storage is not necessarily everybody’s best choice and should be evaluated in a rigorous quantitative way against the alternative over a long time horizon. We propose a methodological approach for the comparison of cloud vs in-house solutions, based on the use of the Net Present Value and employing stochastic models for storage prices and memory needs. We analyse two decision criteria, which employ the median and the mean value of the Differential Net Present Value (DNPV), respectively. Through three appropriate risk measures, we show that the mean DNPV is the less risky decision criterion. Since the DNPV is a stochastic quantity, we also consider a protection measure against the risk of taking the wrong decision, which relies on underwriting an insurance policy. Through the real options approach, we propose a pricing formula for such policy, showing that it is an affordable means to hedge against risk for smaller companies and over a limited time horizon. Both the decision criteria and the insurance pricing formula are applied in a typical scenario.

Simulation of Correlated Financial Defaults through Smoothed Cross-Entropy

Credit risk, deriving from borrowers defaulting on their debts, represents an ever growing source of concern for financial operators. An established model to describe the associated risk scenario, where correlation among defaults is present, is the t-copula, whose use allows us to evaluate the probability of losses exceeding a given threshold. However, the typically large number of variables involved calls for a simulation approach. A simulation method, based on the use of the Cross-Entropy (CE) technique, is here proposed as an alternative to non-adaptive Importance Sampling (IS) techniques so far presented in the literature, the main advantage of CE being that it allows to deal easily with a wider range of probability models than ad hoc IS. A full description of the method is provided along with the results obtained for an extended set of model instances. The proposed Cross-Entropy technique is shown to provide accurate results even when the sample size is several orders of magnitude smaller than the inverse of the probability to be estimated.

Solution Space Size in Credit Risk Simulation

In a portfolio of securities, lenders may incur substantial losses if the obligors do not return the money borrowed by them. In credit risk evaluation through simulation, the states of the portfolio associated to large losses are sampled rather than identified exhaustively. Enumeration of all such critical states is however relevant for the early warning of heavy losses. We provide a general enumerative algorithm, and evaluate its computational complexity, which results to be equal to the number of critical states, for three cases of the distribution of losses associated to individual obligors: uniform, linear, and exponential. In the presence of a possibly huge number of critical states, the evaluation of the computational complexity allows us to assess beforehand if the enumeration task is feasible.

Insurance Pricing and Refund Sustainability for Cloud Outages

Cloud outages may cause heavy economic losses for customers, who may ask the cloud provider for compensation. Cloud providers may therefore wish to insure themselves against that risk. Considering a scenario where outages take place according to a Poisson process and their duration follows a generalized Pareto model, we provide formulas to properly set the insurance premium under three measures of outage severity: number of outages, number of long outages, unavailability. We also assess the sustainability of refunds, by setting thresholds on unit refund per damaging events.

A Computational Method for Predicting the Entropy of Energy Market Time Series

This work introduces a new computational method for evaluating the predictability of energy market time series, by predicting the entropy of the series. According to conventional entropy-based analysis, high entropy values characterize unpredictable series, while more stable series exhibits lesser entropy values. Here, we predict the entropy regarding the future behavior of a series, based on the observation of historical data. Our prediction is performed according to the optimum least squares minimization algorithm, as happens in conventional computational minimization approaches. Preliminary results, applied to energy commodities, show the efficacy of the proposed method for application to energy market time series.