A European option general first-order error formula

Guillaume Leduc


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 \(\mathcal{O}(n^{3/2})\).



European options, approximation scheme, error formula, Black–Scholes

DOI: http://dx.doi.org/10.21914/anziamj.v54i0.6224

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.