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The pricing of European options in a multiperiod binomial model that is characterized by ill-defined states of the world is described. The risk-neutral valuation approach for the pricing methodology is discussed.

The use of a second home may result in different outcomes for households, ranging from financial profit and holiday use to uses that are clearly unprofitable. We contribute to the literature on second homes by exploring the case of second homes that are not let out, representing the least profitable outcome from an economic viewpoint. The empirical investigation relies on the 2002–2012 Bank of Italy Survey on Household Income and Wealth (SHIW), which also provides extensive information on property, including the actual use. Our results highlight: a gender gap, whereby the unprofitable use of second homes tends to be more clearly associated with male decision-makers; a lack of association with the economic characteristics of the household; and a strong association with the specific characteristics of the property, with inherited property more likely to be used unprofitably. In addition to casting doubt on the effectiveness of second homes as an investment vehicle, our results may have important policy or regulatory implications for housing and rental markets. [ABSTRACT FROM PUBLISHER]

We investigate household financial fragility in Italy, providing three main contributions. First, we propose a novel characterization of financial fragility that is not necessarily linked to indebtedness, distinguishes between expected and unexpected expenses, takes portfolio composition into account, and is free of subjectivity bias. Second, we use it to assess the importance of household portfolio composition for determining the difficulties related to coping with unexpected expenditures, besides socio-economic and demographic factors. Third, we test its ability to forecast future conditions of financial distress. The empirical analysis is based on the Bank of Italy Survey on Household Income and Wealth. The results highlight the relevance of portfolio choices as determinants of financial distress, that is, they provide evidence that homeownership increases the likelihood of financial fragility while the presence of a mortgage decreases it. Moreover our measure is shown to act as an early warning indicator of distress. [ABSTRACT FROM AUTHOR]