A TAYLOR FORMULA TO PRICE AND HEDGE EUROPEAN CONTINGENT CLAIMS

Maria Elvira Mancino

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 04, 603-620

Abstract: We present the no-arbitrage price and the hedging strategy of an European contingent claim through a representation formula which is an extension of the Clark-Ocone formula. Our formula can be interpreted as a second order Taylor formula of the no arbitrage price of a contingent claim. The zero order term is given by the mean of the contingent claim payoff, the first order term by the stochastic integral of the mean of its Malliavin derivative and the second order term by the stochastic integral of the conditional expectation of the second Malliavin derivative. A Taylor series expansion is also provided together with a bound to the approximation error obtained by neglecting the second order term in the Taylor formula.

Keywords: European options; Taylor formula; hedging strategy (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S021902490100119X

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