Richter’s local limit theorem and Black-Scholes type formulas. (English) Zbl 1298.91162
Summary: We prove a Black-Scholes type formula when the geometric Brownian motion originates from approximations by multinomial distributions. It is shown that the variance appearing in the Black-Scholes formula for option pricing can be structured according to occurrences of different types of events at each time instance using a local limit theorem for multinomial distributions in [H. Richter, Wahrscheinlichkeitstheorie. Berlin-Göttingen-Heidelberg: Springer-Verlag (1956; Zbl 0074.33605)]. The general approach has first been developed in [N. Kan-Dobrosky, Generalized multinomial CRR option pricing model and its Black-Scholes type limit. Göttingen: Univ. Göttingen (Diss.) (2006; Zbl 1140.91394)].
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60J65 | Brownian motion |
| 60F05 | Central limit and other weak theorems |
References:
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