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A European option general first-order error formula. (English) Zbl 1282.91337

Author’s abstract: “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 \(\mathcal O ({n}^{-3/2})\).”
All results are carefully proved.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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