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Convergence rate of regime-switching trees. (English) Zbl 1358.41009

Summary: Considering a general class of regime-switching geometric random walks and a broad class of piecewise twice differentiable payoff functions, we show that convergence of option prices occurs at a speed of order \(\mathcal{O}(n^{- \beta})\), where \(\beta = 1/2\) when the payoff is discontinuous and \(\beta = 1\) otherwise.

MSC:

41A25 Rate of convergence, degree of approximation
65C50 Other computational problems in probability (MSC2010)
65C20 Probabilistic models, generic numerical methods in probability and statistics
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