Option pricing impact of alternative continuous-time dynamics for discretely-observed stock prices

Abstract.

In the present paper we construct stock-price processes with the same marginal lognormal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid.

We then illustrate how option prices based on such processes differ from Black and Scholes', in that option prices can assume any value in-between the no-arbitrage lower and upper bounds.

We also explain that this is due to the particular way one models the stock-price process in between the grid time instants that are relevant for trading.

The findings of the paper are inspired by a theoretical result, linking density-evolution of diffusion processes to exponential families. Such result is briefly reviewed in an appendix.