Option pricing and hedging with temporal correlations

5 November 2000

Social sharing

Share via Twitter Share via LinkedIn Share via Email

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 Δ-hedge. We introduce a compact notation which eases the computations and could be of use to deal with more complicated models.


Lorenzo Cornalba , Marc Potters , Adam Rej

Related articles