Costanza Torricelli

A multiperiod binomial model for pricing options in a vague world

Abstract The aim of this paper is the pricing of European options in a multiperiod binomial model characterised by ill-defined states of the world. The pricing methodology is still the risk-neutral valuation approach. However, the vagueness in the stock price movements implies that both the risk-neutral probabilities and the stock price are weighted intervals. An empirical validation of the model with DAX-index option data is also provided.

On the no-arbitrage condition in option implied trees

The aim of this paper is to discuss the no-arbitrage condition in option implied trees based on forward induction and to propose a no-arbitrage test that rules out the negative probabilities problem and hence enhances the pricing performance. The no-arbitrage condition takes into account two main features: the position of the node in the tree and the relation between the dividend yield and the risk-free rate. The proposed methodology is tested in and out of sample with Italian index options data and findings support a good pricing performance.

Marriage and other risky assets: a portfolio approach

We study the joint impact of gender and marital status on financial decisions. First, we test the hypothesis that marriage represents - in a portfolio framework - a sort of safe asset, and that this effect is stronger for women. Controlling for a number of observable characteristics, we show that single women have a lower propensity to invest in risky assets than married females and males. Second, we show that the differential behavior of single women evolves over time, reflecting the increasing incidence of divorce and the expansion of female labor market participation. In particular, towards the end of our sample period, we observe a reduction in the gap between women with different family status, which can be attributed to the gradual erosion of the perception of marriage as a sort of safe asset. Our results therefore suggest that the differential behavior of single vs. married women can be explained by the evolution of gender roles in society, even after controlling for differential risk attitudes. Our empirical investigation is based on a dataset drawn from the 1989-2006 Bank of Italy Survey of Household Income and Wealth.

Economic activity and recession probabilities: information content and predictive power of the term spread in Italy

The aim of the present article is to examine the information content of the Italian term spread as for real economic growth rates and recession probabilities and to test its predictive power in forecasting regime probabilities. To this end the relationship between the term spread and economic growth rates is modelled as a nonlinear one and specifically the Logistic Smooth Transition model is used, while a probit model is implemented to forecast recession probabilities. Specific to this article is the use of the OECD business cycle chronology, which was never used before to this end for the Italian case. Overall evidence supports the informative content of the spread in Italy over the whole period (1984–2005) although results are more satisfactory as from 1992. In particular, recession forecasts are generally better than those obtained with other chronologies previously adopted for the Italian case (ISAE and ECRI).

The information in the term structure of German interest rates

This paper tests the Expectations Hypothesis (EH) of the term structure of interest rates using new data for Germany. The German term structure appears to forecast future short-term interest rates surprisingly well, compared with previous studies with US data, while it has lower predictive power for long-term interest rates. However, the direction suggested by the coefficient estimates is consistent with that implied by the EH, that is when the term spread widens, long rates increase. The use of instrumental variables to deal with possible measurement errors in the data significantly improves regressions for the long rates. Moreover, re-estimation with proxy variables to account for the possibility of time-varying term premia confirms that the evolution of both short and long rates corresponds to the predictions of the EH and that most of the information is in the term spread. These results are important as they suggest that monetary policy in Germany could be guided by the slope of the term structure.

A comparative evaluation of alternative models of the term structure of interest rates

Abstract In the paper alternative models of the term structure of interest rates are classified in two different approaches: the no-arbitrage and the general equilibrium approach. It is maintained that the general equilibrium approach is superior on a theoretical ground for two main reasons: first, relevant variables, such as the spot interest rate and the interest risk-premium, are endogenous; second, the relationship between the real and the financial side of the economy becomes a clear and important element in the understanding of the term structure. As regards the applications, however, the advantages of the general equilibrium over the no-arbitrage approach are not so clear: the major role in the empiricil performance of alternative models is played by their ability to capture volatility. At the current state of the literature, there is no model that outperforms others, in particular on the empirical side.

Population age structure and household portfolio choices in Italy

Based on the exceptional ageing of the Italian population, this paper aims to contribute to the current debate on population ageing and financial markets. To this end, we use the data taken by the Bank of Italy Survey of Household Income and Wealth over the period 1995–2006, and we analyse the average household portfolios in relation to age and net wealth (NW). Our analysis rests on a clustering of assets according to risk, which is different from the one used in Guiso and Jappelli (Guiso, L., and T. Jappelli. 2002. The portfolio of Italian households. In Household portfolios, eds. L. Guiso, M. Haliassos, and T. Jappelli. Cambridge: MIT Press). We find that age has affected financial choices of Italian households over the whole decade, but the portfolio age profile has significantly evolved over time with important differences across wealth quartiles. Overall, our analysis highlights a tendency towards a hump-shaped age profile of the allocation in risky assets for the most NW levels.

Is it Money or Brains? The Determinants of Intra-Family Decision Power

We empirically study the determinants of intra-household decision power with respect to economic and financial choices using a suitable direct measure provided in the 1989-2010 Bank of Italy Survey of Household Income and Wealth. Focusing on a sample of couples, we evaluate the effect of each spouses characteristics, household characteristics, and background variables. We find that the probability that the wife is in charge is affected by household characteristics such as family size and total income and wealth, but more importantly that it increases with the difference between hers and her husbands characteristics in terms of age, education, and income. The main conclusion is that decision-making power over family economics is not only determined by strictly economic differences, as suggested by previous studies, but also by differences in human capital and experience. Finally, exploiting the time dimension of our dataset, we show that this pattern is increasing over time.

Implied trees in illiquid markets: A Choquet pricing approach

Implied trees are necessary to implement the risk neutral valuation approach, and standard methodologies for their derivation are based on the validity of the put call parity. However, in illiquid markets the put call parity fails to hold, and the uniqueness of the artificial probabilities leaves room for an interval. The contribution of this article is twofold. First we propose a methodology for the derivation of implied trees in illiquid markets. Such a methodology, by contrast with standard ones, takes into account the information stemming both from call and put prices. Second, we set up a framework for pricing derivatives written on an underlying asset traded on an illiquid market. To this end we have extended the Choquet integral definition to account for interval payoffs of the underlying asset. The price interval we obtain may be interpreted as a bid‐ask price quoted by the intermediary issuing the derivative security.

The pricing of options on an interval binomial tree. An application to the DAX-index option market

Abstract This paper implements a model setup in Muzzioli and Torricelli [Int. J. Intell. Syst. 17 (6) (2002) 577–594] for deriving implied trees and pricing options when the put–call parity is not fulfilled. The model basically extends Derman and Kani’s [Risk 7 (2) (1994) 32–39], whereby call (put) prices are also used in the lower (upper) part of the tree thus exploiting the information content of both call and put prices. The DAX-index option market is chosen for this application because it is a relatively new European market where short-selling restrictions may induce put–call parity violations and the nature of the option (European) and of the underlying (dividends reinvested in the index) avoid some estimation problems. In order to test the pricing fit of the model, a non-linear optimisation procedure is proposed to estimate a unique implied tree which allows a comparison between the model prices, Derman and Kani’s and market prices. The results suggest that the MT model improves the pricing.