In: Mathematical finance, 2008, vol. 18, no. 1, p. 23-54
In this paper we propose a model of financial markets in which agents have limited ability to trade and no probability is given from the outset. In the absence of arbitrage opportunities, assets are priced according to a probability measure that lacks countable additivity. Despite finite additivity, we obtain an explicit representation of the expected value with respect to the pricing measure,...
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In: Statistics & probability letters, 2007, vol. 77, no. 8, p. 795-802
We prove a version of the Doob Meyer decomposition for supermartingales with a linearly ordered index set.
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In: Journal of Theoretical Probability, 2008, vol. 21, no. 3, p. 586-603
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In: Journal of theoretical probability, 2008, vol. 21, no. 3, p. 586-603
The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob–Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no...
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In: International review of financial analysis, 2006, vol. 15, no. 2, p. 145-178
We analyze the volatility surface vs. moneyness and time to expiration implied by MIBO options written on the MIB30, the most important Italian stock index. We specify and fit a number of models of the implied volatility surface and find that it has a rich and interesting structure that strongly departs from a constant volatility, Black-Scholes benchmark. This result is robust to alternative...
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In: International journal of theoretical and applied finance, 2005, vol. 8, no. 4, p. 523-536
In this paper we propose a model of asset prices consistent with the no-arbitrage principle but allowing for the existence of "bubbles". The structure of bubbles is explicitly characterized and we show that, for example, they may be of either sign. Furthermore, we discuss the existence of bubbles under alternative definitions of absence of arbitrage opportunities.
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We analyze the pricing and informational effciency of the Italian market for options written on the most important stock index, the MIB30. We find several indications inconsistent with the hypothesis that the Italian MIBO is an effcient market. We report that a striking percentage of the data consists of option prices violating basic no-arbitrage conditions. This percentage declines but never...
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In: Economic notes, 2004, vol. 33, no. 2, p. 275-321
We analyze the pricing and informational efficiency of the Italian market for options written on the most important stock index, the MIB30. We report that a striking percentage of the data consists of option prices violating basic no-arbitrage conditions. This percentage declines when we relax the no-arbitrage restrictions to accommodate for the presence of bid/ask spreads and other...
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In: Statistics & probability letters, 2010, vol. 80, no. 5-6, p. 421-426
We consider quasi-martingales indexed by a linearly order set. We show that such processes are isomorphic to a given class of (finitely additive) measures. From this result we easily derive the classical theorem of Stricker as well as the decompositions of Riesz, Rao and the supermartingale decomposition of Doob and Meyer.
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In: Stochastic processes and their applications, 2010, vol. 120, no. 7, p. 1060-1073
We prove results on the existence of Doléans-Dade measures and of the Doob-Meyer decomposition for supermartingales indexed by a general index set.
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