Abstract
During the 1920s, Francesco P. Cantelli wrote that the price of a good or asset is the product of an indefinite number of independent causes that oblige us to shift our attention from the causes themselves to the possible laws driving the changes in price. The prediction of changes in prices also lay at the heart of Bachelier’s Theory of Speculation (1900). Despite Cantelli’s acute observation, Italian economists of his time seemed rather skeptical about whether it was possible to forecast prices. They dealt with prices, of both financial assets and real goods, but linked them to the market’s behavior rather than searching for a law to explain their trends. Their work on financial assets consequently failed to follow the path indicated by Cantelli, and already investigated by Bachelier—despite the fact that Bachelier’s Theory was known in Italy. Although the approaches presented in this chapter differ analytically, they reflect a common tendency of authors during the period considered to look at market dynamics in order to understand price trends, and hopefully support their stability.
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Notes
- 1.
Bachelier’s Theory of Speculation is cited nine times in De Pietri-Tonelli’s book of 1921. At the time, Bachelier’s other book, Calcul de probabilités (1912), was probably quoted more often in the Italian economic literature, by De Pietri-Tonelli (1921a), but also by other Italian economists, including Bordin (1935a) and Martello (1913), among others.
- 2.
The notion of “mental variables” comes from Giocoli (2003, p. 175), who included expectations, conjectures, and beliefs among them. We add “habits”.
- 3.
Assuming that St = Tt + 1, we can rewrite the two equations in a system as follows: \( {S}_t=a+{v}^2{P}_t^{\prime}\kern0.75em {P}_t=b-{n}^2{S}_t^{\prime } \). We then deduce \( {P}_t=b-{n}^2{v}^2{P}_t^{{\prime\prime} } \) and, setting λ = 1/nv, we have \( {P}_t^{{\prime\prime} }=-{\lambda}^2{P}_t+\lambda b \). Integrating this second-order differential equation with the Euler-MacLaurin formula, we obtain Pt = Acosλt + Bsenλt + b and St = Ccosλt + Dsenλt + a, where A, B, C, and D are constants. Then it is easy to obtain the equation system P (.), T (.) given in the main text (see Palomba 1966, pp. 594–595).
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Tusset, G. (2018). Asset Pricing Dynamics. In: From Galileo to Modern Economics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-95612-1_6
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