Option pricing and hedging with temporal correlations
AbstractWe 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.
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Bibliographic InfoPaper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500030.
Date of creation: Nov 2000
Date of revision:
Publication status: Published in International Journal of Theoretical and Applied Finance 5 (3) (2002) 307-320
Find related papers by JEL classification:
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-02-13 (All new papers)
- NEP-CFN-2005-02-13 (Corporate Finance)
- NEP-FIN-2005-02-13 (Finance)
- NEP-RMG-2005-02-13 (Risk Management)
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