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A EUROPEAN OPTION GENERAL FIRST-ORDER ERROR FORMULA
Published online by Cambridge University Press: 04 September 2013
Abstract
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We study the value of European security derivatives in the Black–Scholes model when the underlying asset 
$\xi $ is approximated by random walks 
${\xi }^{(n)} $. We obtain an explicit error formula, up to a term of order 
$ \mathcal{O} ({n}^{- 3/ 2} )$, which is valid for general approximating schemes and general payoff functions. We show how this error formula can be used to find random walks 
${\xi }^{(n)} $ for which option values converge at a speed of 
$ \mathcal{O} ({n}^{- 3/ 2} )$.
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