A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A...

In this paper, we explore a dynamical version of by Aoki and Yoshikawa model (AYM) for an economy driven by demand. We show that when an appropriate Markovian dynamics is taken into account, AYM has di¤erent equilibrium distributions depending on the form of transition probabilities. In the...