Su alcunieffetti dell'adozione di iniziali finitamente additive quando il modello di base appartiene alla classe esponenziale troncata

In questo lavoro si adottano particolari iniziali finitamente additive volte a massimizzare l'associazione tra gli elementi di un processo scambiabile e vengono discussi effetti e significato complessivo di tale adozione (par. 1 e 2).Nell'ipotesi che tali distribuzioni si riferiscano al parametro di un modello appartenente alla classe esponenziale troncata si ottiene (par. 3) la corrispondente espressione per la legge di probabilità congiunta di un vettore di osservazioni (teorema 1).Nel par. 4 si suggerisce un metodo alternativo di prova per risultati di supporto al teorema 1.Nel par. 5, sotto ipotesi assai blande, si ottengono risultati relativi alla previsione in alcuni casi particolari. Interessanti sono le conseguenze sulla distribuzione predittiva e sulla distribuzione finale del parametro di troncamento.

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Summary In this paper we use finitely additive prior distributions with the aim of maximizing the association between the elements of an exchangeable process and we discuss the effects and the meaning of this assumptions (§1 and §2).Applying these distributions to the canonical parameter in elements of truncated exponential family of distributions we obtain (§3) the expression for the joint distribution of a vector of observation (theorem 1).In § 4 a different method of proof is suggested for some results pertaining theorem 1.In § 5, under mild hypotheses, we obtain some results about the expectation of the predictive distribution. We examine some droll consequences of our assumptions on the predictive and posterior distributions.

     

Project Finance Collateralised Debt Obligations: an Empirical Analysis of Spread Determinants

Credit rating is the most important variable in determining tranche spread at issue on collateralised debt obligations (CDOs) issues backed by project finance (PF) loans. Factors that are important for pricing in the case of corporate bonds, such as market liquidity and weighted average maturity, are also relevant for determining spreads for these securities. Furthermore, the nature of the underlying assets has a substantial impact on CDO pricing: Primary market spread is significantly higher when the underlying PF loans bear a higher level of market risk and when the proportion of projects still under construction in the securitised portfolio is larger.     

HEDGING WITH ENERGY

In the setting of diffusion models for price evolution, we suggest an easily implementable approximate evaluation formula for measuring the errors in option pricing and hedging due to volatility misspecification. The main tool we use in this paper is a (suitably modified) classical inequality for the L ² norm of the solution, and the derivatives of the solution, of a partial differential equation (the so-called "energy" inequality). This result allows us to give bounds on the errors implied by the use of approximate models for option valuation and hedging and can be used to justify formally some "folk" belief about the robustness of the Black and Scholes model. Surprisingly enough, the result can also be applied to improve pricing and hedging with an approximate model. When statistical or a priori information is available on the "true" volatility, the error measure given by the energy inequality can be minimized w.r.t. the parameters of the approximating model. The method suggested in this paper can help in conjugating statistical estimation of the volatility function derived from flexible but computationally cumbersome statistical models, with the use of analytically tractable approximate models calibrated using error estimates.