2000/11/29 by Lorenzo Cornalba, Jean-Philippe Bouchaud, Marc Potters
Physics and Astronomy · #cond-mat
published as International Journal of Theoretical and Applied Finance 5 (3) (2002) 307-320 · LaTeX, 15 pp, no figure
arxiv created 2000/11/29 · arxiv updated 2009/11/30
We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for Gaussian price increments, the correlations are irrelevant, and the Black-Scholes formula holds with the volatility of the price increments on the scale of the re-hedging. For non-Gaussian processes, further non trivial corrections to the `smile' are brought about by the correlations, even when the hedge is the Black-Scholes Delta-hedge. We introduce a compact notation which eases the computations and could be of use to deal with more complicated models.