Giuseppe Orlando

A discrete mathematical model for chaotic dynamics in economics

This paper, following Kaldors approach, is written with the intention of interpreting fluctuations of economic systems (i.e trade cycles). In particular, a new discretized Kaldor model is proposed, which is also useful to explain what appears to be random and unpredictable, such as economic shocks. Moreover, by using numerical analysis, the chaoticity of the model is demonstrated.

A New Approach to CIR Short-Term Rates Modelling

It is well known that the CIR model, as introduced in 1985, is inadequate for modelling the current market environment with negative short rates, r(t) . Moreover, in the CIR model, the stochastic part goes to zero with the rates, neither volatility nor long term mean change with time, or fit with skewed (fat tails) distribution of r(t) , etc. To overcome the limitations of the CIR, several different approaches have been proposed to date: multi-factor models such as the Hull and White or the Chen models to the CIR++ by Brigo and Mercurio. Here, we explain how our extension of the CIR framework may fit well to market short interest rates.

A review on implied volatility calculation

This paper aims to summarizing the different approaches in determining the implied volatility for the options. This value is of particular importance since it is the main component of theoptions price and because, among traders, options are quoted in terms of volatility rather than price. After a discussion on the approximation methods, a numerical approach is explained. It is shown that, in order to ensure a fast and reliable convergence, the selection of an appropriate starting point is key. The authors suggestion for choosing the first order approximation or the inflexion as initial point is also illustrated.

A Revised Approach to CIR Short-Term Interest Rates Model

It is well known that the Cox-Ingersoll-Ross (CIR) stochastic model to study the term structure of interest rates, as introduced in 1985, is inadequate for modelling the current market environment with negative short interest rates. Moreover, the diffusion term in the rate dynamics goes to zero when short rates are small; both volatility and long-run mean do not change with time; they do not fit with the skewed (fat tails) distribution of the interest rates, etc. The aim of the present work is to suggest a new framework, which we call the CIR # model, that fits well the term structure of short interest rates such that the market volatility structure is preserved as well as the analytical tractability of the original CIR model.

Introduzione al caos in economia con esempi e applicazioni (Introduction to Chaos in Economics with Examples and Applications)

Italian Abstract: Questo lavoro ha l’obiettivo di descrivere gli elementi basilari riguardo il caos e di illustrarne le possibili applicazioni al campo economico. English Abstract: This paper has the objective of summarizing the key aspects of chaos ant to illustrate some specific examples to economics.

Compendium on Optimization Methods (Summary on Optimization Methods with Applications and Examples)

This paper aims to illustrate the subject in a simple and complete fashion, and it is accompanied by exercises for teaching the related computational techniques. The optimization framework is applicable to decision problems modeled in terms of functions of several variables, in which the optimal points are found with or without constraints (expressed by equations, inequations and possibly by derivatives).The discussion includes linear programming (where the constraints or the objective function are linear) and nonlinear programming (where some of the constraints or the objective function are nonlinear).

An Alternative Approach to Fast Implied Volatility Calculation

This paper has the task of identifying an alternative approach (in terms of a mathematical algorithm) which can determine with speed (i.e. to converge within a few iterations) the value of the implied volatility for the options. This value is of particular importance since it is the main component of the option’s price. The paper after, an initial explanation of the objectives, illustrates various alternatives and proposes the adoption of an algorithm able to quickly converge to the desired solution.

A Brief Guide on Exchanged Traded Products (ETPs)

The objective of this paper is to provide a quick overview on Exchange-Traded Products (i.e. on ETFs, ETNs, ETCs and ETVs) but above all on their risk (especially with regards to synthetic products) and mitigations.

Introduzione all’analisi della politica della spesa pubblica (An Introduction on Public Expenditure and Policy Analysis)

Italian Abstract: Questo lavoro si propone il compito di illustrare brevemente la questione della spesa pubblica con particolare riferimento alla valutazione della rapporto costi benefici. Dopo un primo esame dei beni da sussidiare o disincentivare e si accenna a questioni quali trade-off tra equità end efficienza, incidenza effettiva della spesa, traslazione dei benefici ed effetti distributivi che chiamano in gioco concetti come quello di giustizia sociale. Infine, con l’ausilio di semplici esempi pratici, viene dimostrato come l’analisi di un progetto debba prendere in considerazione alcuni fattori quali costo del capitale, tempo, rischio, ecc. Dato che in funzione di tali parametri i risultati possono fornire dei risultati completamente diversi, proprio su di essi dovrebbe concentrarsi il controllo per evitare che gli indirizzi di governo e la spesa siano improntati a criteri difformi dal pubblico interesse. English Abstract: This paper aims to explain briefly the public expenditure’ subject with particular reference to the of the cost-benefit evaluation. After an initial examination of the goods and to subsidize or discourage it mentions issues such as trade-off between equity end efficiency, actual incidence of expenditure, translation of benefits and distributional effects that call into play concepts such as social justice. Finally, with the help of simple examples, it is shown how the analysis of a project must take into account factors such as cost of capital, time, risk, etc. As a function of these parameters, the results can provide totally different results: For this reason on them should focus the public control in order to prevent that choices are not in line with the public interest.

Chaotic Dynamics in Economics: Kaldor's Model on Business Cycle

This paper, written with the intention of formulating a macroeconomic model of trade cycles - following Kaldor’s approach - explains the fluctuations of economic systems by using some numerical instruments. The reason for choosing a chaotic model will become clear as will the implications which follow during the treatment. Finally, having seen that the model proposed is also useful in explaining what appears to be random and unpredictable such as economic shocks, there will be a numerical analysis to demonstrate its chaoticity.