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 different equilibrium distributions depending on the form of transition probabilities. In the...

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

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...