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The present volume collects a selection of revised papers which were presented at the 21st Euro Working Group on Financial Modelling Meeting, held in Venice (Italy), on October 29-31, 1997. The Working Group was founded in September 1986 in Lisbon with the objective of providing an international forum for the exchange of information and experience; encouraging research and interaction be­ tween financial economic theory and practice of financial decision mak­ ing, as well as circulating information among universities and financial institutions throughout Europe. The attendance to the Meeting was large and highly qualified. More than 80 participants, coming from 20 different Countries debated on 5 invited lectures and 40 communications in regular sessions. The sessions were located at the Island of San Servolo, on the Venetian lagoon, just in front of the Doges Palace. San Servolo Island is a natural oasis, in the midst of a unique urban setting, offering great relaxation in a peaceful park and a panoramic view of Venice. The friendly atmosphere added great benefit to the formal and informal discussions among the participants, -which is typical of E.W.G.F.M. Meetings. It is interesting to consider the story of the Meeting. The previous locations were held at Cyprus, Crete and Dubrovnik - former mile­ stones of the Venitian Republic influence on the Mediterranean Sea. Therefore, that this Meeting should be harboured in the heart of the Republic itself (namely, the Saint Mark basin), was only a matter of consequence.



Performance Evaluation of Algorithms for Black-Derman-Toy Lattice

Within the framework of sensitivity of the optimal value of the portfolio management problem described in Dupaeová and Bertocchi (1996), Dupaeová and Bertocchi (1997) with respect to lattice calibration, we compare Bjerksund and Stensland approximation algorithm, Kang Pan-Zenios algorithm and a modified Kang Pan-Zenios algorithm to generate short-rate interest rates tree according to Black-Derman-Toy model. Numerical testing of the behaviour of the three algorithms are given. The necessary inputs for Black-Derman-Toy model are yield curve and log-yield volatilities: we provide an evidence on the relatively large sensitivity of the parameters of the fitted lattice on the chosen volatility curve. The reported numerical experience is based on data from the Italian bond market.
Jozsef Abaffy, Marida Bertocchi, Jitka Dupačová, Vittorio Moriggia

Efficient Diversification of International Investments: The Spanish Point of View

The search for the best investments in a return-risk framework has led the investors to the portfolio diversification. The domestic markets liberalisation and a increasingly financial market integration, have made the investors to exceed the national barriers in order to get the international diversification of their portfolios.
In this paper we will analyse which should be the composition of the optimal portfolio from a Spanish investor’s point of view, who decides to take long or short foreign currency positions. Exactly, we will study the possibility of investing or financing in 14 currencies, including the ECU as the predecessor of the European single currency (the Euro), during the period 1989-1997. Our purpose is to provide the Spanish investors with an international performance and, in second term, to advance the role of the European single currency in the international financial markets.
Maria Bonilla, Amparo Medal

Scenarios Identification for Financial Modelling

A cluster analysis approach is proposed for solving a scenario identification problem, using a non parametric method to determine the probability of each scenario, conditioned to the last sampled data. This non parametric approach seems to be quite appealing for a real financial market portfolio management in conjunction with stochastic optimization. The proposed algorithm was then applied to the scenario forecasting of the COMIT index in the Italian Stock Market.
Elio Canestrelli, Silvio Giove

Merton-like Theoretical Frame for Fractional Brownian Motion in Finance

Despite the classical hypothesis states that the asset returns are (log-Normally) identically and independently distributed, in many financial market is detectable significative empirical evidence that there are dependence inside such returns. From a distributional point of view, this dependence can be modelled by the so-calledfractionalBrownian (fB) motion which is a Gaussian stochastic process whose increments are (long-term) dependent with each other. Although there exists an increasing empirical literature about this topic, from a theoretical standpoint there is not an equivalent number of results concerning with the relationships between the fB motion and the financial markets.
Starting from these remarks, in this work we propose a Merton-like system of economic-financial assumptions on the dynamical behaviour of financial asset price by which it is possible to deduce the consistency between the fB motion and the discrete-time trading. Moreover, we also prove the “convergence” of the fB motion to the standard Brownian (sB) one when the discrete-time trading tends to the continuous-time one.
Marco Corazza

Portfolio Analysis with Symmetric Stable Paretian Returns

We analyze a portfolio selection problem in a market where asset returns have jointly symmetric stable Paretian distribution. Univariate stable distributions are characterized by four parameters: the stability index a, the (scale or) dispersion parameterathe (mean or) location parameter p and the parameter of asymmetry ß. We consider portfolios having stable distribution with 1 < a < 2 and = 0. Since stable distributions have infinite variance, Markowitz’ mean-variance rule does not apply to this case. With stable distributions risk is measured by dispersion. The main result is given by a linear relation between expected return and the efficient level of dispersion in the single agent portfolio selection problem. Hence, the efficient set is convex, permitting us to derive an equilibrium model, called stable-CAPM. Moreover, we find that the efficient level of risk in a stable Paretian market is higher the lower the stability index, a.
Andrea Gamba

Dynamics of Bond Returns in the Emerging Markets: A Study of the Thai Bond Market

The distributional properties of securities prices, and rate of returns have important implications for financial modeling. Mean and variance are the key variables in the valuation models. Considerable amount of work has been done to identify the distribution of securities price changes and the rates of return as characterized by volatile-variance and stationary period. The general conclusion of these studies is that the speculative price changes and return series are nonlinear and intertemporal dependence in nature (Bollerslev, 1987). This conclusion is based a phenomenon that was been observed by Mandelbrot (1963), large changes of returns and variance of returns tend to be followed by other large changes in the same direction either upward or downward movements. Moreover, the absence of serial correlation in the time series of the rate of returns, does not necessary means statistical independence. However this phenomenon has been studied in the past only for stocks and foreign exchange rates only and to our knowledge not for the corporate bonds.
Tippawan Pinvanichkul, Jyoti P. Gupta

Modelling Option-Implied Return Distributions: A Generalized Log-Logistic Approximation

We propose a method to uncover risk-neutral return distributions of financial assets from option prices. The goal is to account for implied Black & Scholes volatility smiles by manipulating the form of the underlying asset’s distribution. We start from a quasi-binomial option pricing model, in which an option’s payoff is evaluated at the extremes of the expected range of the future price of the underlying asset. This quasi-binomial approach implies that the lognormal distribution is approximated by a suitable transformation of the log-logistic distribution. By generalizing the transformation of the log-logistic distribution, skewness and kurtosis effects can be incorporated. We show how option prices change relative to Black&Scholes prices when skewness and kurtosis effects are introduced.
Winfried G. Hallerbach

Dichotomous Rate in Stock-Price Process

This paper identifies the “good news” and “bad news” in the generalization of classical market model with a new source of uncertainty — the dichotomous process, and studies a model with dichotomous expected rate of return. Both the dichotomous and integrated dichotomous process are described, including derivation of exact form of their distribution. The pricing of an European stock option is examined and the first steps to derive a Black-Scholes formula were done. The analytical results are compared both with computer simulations and data from the Prague stock exchange. The analysis of a stock index shows, that the gain is a sum of dichotomous process and some noise. This fact is important especially for forecasting and measuring the risk.
Michael Koňák

How Should We Measure Bank Efficiency? A Comparison of Classic and Recent Techniques Based on Simulated Data

In this paper, a cost function is used to generate the data of six samples of banks producing three outputs by means of two factors; unlike previous studies, the data-generation process used here is designed to reflect some structural characteristics of the banking sector (e.g., big producers are less frequent than small ones, the production levels of loans, deposits and services are highly correlated). A known amount of inefficiency and random noise is then added to each production plan. Finally we compare the “true” inefficiency levels to those estimated through the following techniques: stochastic frontiers, D.e.a., and several models of stochastic D.e.a. (two original models - multiplicative and heteroskedastic stochastic D.e.a. - are also developed). All the “classic” techniques perform well. The stochastic D.e.a. models can outperform the “classics” in some specific situations, but on average they cannot compete with older techniques; however, the two new stochastic D.e.a. models perform better than the standard one.
Andrea Resti

The Scheme of Fuzzy Dominance

In this paper we generalize the duality scheme in [2, 3] introducing the definition of “pseudo-adjoint”, using the semi-rings of fuzzy measures and fuzzy integrals of Choquet and Sugeno instead of the vector spaces of measures with sign and Lebesgue integrals.
Maria Rosaria Simonelli
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