Flavio Pressacco

New insights on testing the efficiency of methods of pricing and hedging American options

Abstract With reference to the evaluation of the speed–precision efficiency of pricing and hedging of American Put options, we present and discuss numerical results obtained on the basis of four different large enough random samples according to the relevance of the American quality (relative importance of the early exercise opportunity) of the options. Here we provide a comparison of the best methods (lattice based numerical methods and an approximation of the American Premium analytical procedure) known in literature along with some key methodological remarks.

Su Una Estensione Bidimensionale del Teorema di Scomposizione di Peccati

Facendo ricorso all’introduzione di una opportuna condizione di sincronia fra due coppie di tassi (i, j), esterna, e (i*, j*), interna, si dimostra che condizione necessaria e sufficiente per la validità finanzíaria di una estensione hidimensionale del teorema di scomposizione di Peccati è che le due coppie (i, j) e (i*, j*) soddisfino tale proprietà di sincronia.SummaryThis paper keeps as starting poing the Peccati’s decomposition of the d.c.f. of an enterpreneural project seen as a present value of single-period results, recently given by the author in an unidimensional framework. The goal of the paper is twofold: the first is to provide a bidimensional extension of the decomposition in order to keep account of mixed projects, that is projects that according to any internal couple (i*, j*) reveal alternance of investment and respectively collection periods. A straightforward extension is given on the basis of a simple analogic argument. But a more careful evaluation of the problem suggests that if we require that the decomposition be meaningful from a financial point of view. things are no more simple either in one or in two dimensions.To solve the problem we introduce a proper synchrony condition: precisely, the pair of couples (i, j) and (i*, j*) are said to satisfy the synchrony condition if and only if the sequences of the signs of the partial balancesMt(i, j) andMt(i*, j*) are the same. After that we are able to show that, with reference to a couple (i, j) of external rates, a bidimensional decomposition centered on an internal couple (i*, j*) is meaningful if and only if the pair (i, j) and (i*, j*) satisfy the synchrony condition. Formally, the result comes as a nice byproduct of a rule on the factorization of particular bivariate polynomials recently given by Stucchi. In particular going back to a one-dimensional world, it turns out that for pure investment (Soper) projects the synchrony condition works as a condition of applicability of the Peccati’s decomposition.

A balanced arbitration scheme for homogeneous weighted majority games

In un gioco omogeneo di maggioranza ponderata le uniche soluzioni « stabili » nel senso di Neumann e Morgenstern sono quelle corrispondenti alla formazione di una qualsiasi coalizione minimale vincente con ripartizione del guadagno solo fra i partecipanti ad essa. Ciò pone dei problemi ad un arbitro chiamato a soddisfare principi di equità per tutti, dando vita allo stesso tempo a situazioni stabili. Presentiamo qui uno schema di arbitraggio probabilistico per giochi omogenei di maggioranza ponderata atto a risolvere, sia pure in ambito incerto, in modo soddisfacente tali esigenze.AbstractThis paper is concerned with a probabilistic model of arbitration scheme for homogeneousn-person weighted majority games.It is well known that in games of this type a normalizedn-tuple of homogeneous weights, called a representation of the game, reflects the power of the players and seems to be a “fair” proposal for an arbitrated solution of the game.On the other hand Von Neumann Morgenstern solution theory suggests that (at least for an accettable type of non discriminatory social organization) the only stable outcomes of the game are those corresponding to one of the imputations of the so called main simple solution.Then let us consider the problem faced by an arbiter whose task is to produce a fair but also stable situation.We propose the following method to accomplish this purpose: single out an imputation of the main simple solution, with a random mechanism chosen in such a way that the resulting expected gain (the prospective value to play the game) equals for every player the respective homogeneous weights.We call this procedure a balanced arbitration scheme forn person homogeneous weighted majority games.A crucial problem then concerns the existence of such a random mechanism for a general game of this type, or formally of am-tuple of probabilitiesp1, ...,pm (pj being the probability of choosing the imputationj) which solves a particular system of linear equations.We prove a theorem which guarantees the existence of (at least) a solution to this problem, and so the existence of one balanced arbitration scheme for every homogeneous weighted majority game is assured.

Synthetic portfolio insurance on the Italian stock index: From theory to practice

Abstract We claim here that a practical way to create synthetic portfolio insurance on the Italian stock market index (not currently traded) should be to select a portfolio of a small number of Italian blue chips properly composed so as to be a good proxy of the market index, and to revise proportions between the proxy and the risk-free asset only if the difference between the current composition and the theoretically optimal one exceeds some fixed bound so as to squeeze transaction costs. With reference to a three-year weekly data base of the Milan Stock Exchange, this paper reports results of a test of efficiency of strategies of this type in granting synthetic portfolio insurance.

A managerial approach to risk theory: Some suggestions from the theory of financial decisions

Abstract As suggested by the theory of financial economics, strategic decisions of an insurance company should aim to maximize the market value of the company. This simple idea could be advantageously applied to a key problem of ruin theory; that is, the choice of the optimal level of surplus of an insurance company.

Fibonacci Representations of Homogeneous Weighted Majority Games

Isbell (1956) introduced a class of homogeneous weighted majority games based on the Fibonacci sequence. In our paper, we generalize this approach to other homogeneous representations of weighted majority games in a suitable Fibonacci framework. We provide some properties of such representations.

The influence of correlation and loading on M–V efficient retentions in variable quota share proportional reinsurance

Based on our recent discovery of closed form formulae of efficient Mean Variance retentions in variable quota-share proportional reinsurance under group correlation, we analyzed the influence on the efficient frontier of two key variables, correlation and safety loading levels, in a single period stylized problem. We found a clear separated influence of each variable (given the level of the other) and a surprising joint influence of both on the efficient set.