Asset prices are Brownian motion: Only in business time (Q2725577)

The authors question the validity of diffusions as an appropriate model for the underlying uncertainties. Instead, they represent the price process as instantaneously and continuously adjusting to exogeneous demand and supply shocks. They model a price process by a Lévy process, which is decomposed into the difference of two increasing random processes of finite variations, representing respectively the up and down moves of the market.NEWLINENEWLINE In the presence of local uncertainty such processes are generally purely discontinuous.NEWLINENEWLINE In the paper under review, the result of \textit{P. K. Clark} [Econometrica 41, 135--155 (1973; Zbl 0308.90011)] is generalized and it is shown that such processes are continuous and normal after a time change, which is related to a measure of economic activity. In many cases the characteristic functions of the log price relative are given in the closed form. Such expressions can be used to obtain option prices.NEWLINENEWLINE Thus the paper provides a new class of operational models for continuous-time processes in economics, for which estimation and derivative pricing are feasible.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00019].