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Option convergence rate with geometric random walks approximations. (English) Zbl 1410.91456

Summary: We describe a broad setting under which, for European options, if the underlying asset form a geometric random walk then, the error with respect to the Black-Scholes model converges to zero at a speed of \(1/n\) for continuous payoffs functions, and at a speed of \(1/\sqrt{n}\) for discontinuous payoffs functions.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60G50 Sums of independent random variables; random walks
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