# Richter's local limit theorem and Black-Scholes type formulas

Manfred Heinz Denker, Souha Fares

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

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 Richter (1956). The general approach has first been developed in Kan (2005).

Original language English (US) 241-248 8 Statistics and Probability Letters 92 https://doi.org/10.1016/j.spl.2014.06.003 Published - Jan 1 2014

### Fingerprint

Local Limit Theorem
Multinomial Distribution
Black-Scholes
Black-Scholes Formula
Geometric Brownian Motion
Option Pricing
Approximation
Limit theorems
Black-Scholes formula
Option pricing
Geometric Brownian motion

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty

### Cite this

Denker, Manfred Heinz ; Fares, Souha. / Richter's local limit theorem and Black-Scholes type formulas. In: Statistics and Probability Letters. 2014 ; Vol. 92. pp. 241-248.
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Richter's local limit theorem and Black-Scholes type formulas. / Denker, Manfred Heinz; Fares, Souha.

In: Statistics and Probability Letters, Vol. 92, 01.01.2014, p. 241-248.

Research output: Contribution to journalArticle

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