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

Manfred Denker; Souha Fares

doi:10.1016/j.spl.2014.06.003

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

Manfred Denker
, Souha Fares

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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)
Pages (from-to)	241-248
Number of pages	8
Journal	Statistics and Probability Letters
Volume	92
DOIs	https://doi.org/10.1016/j.spl.2014.06.003
State	Published - Sep 2014

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2014.06.003

Cite this

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title = "Richter's local limit theorem and Black-Scholes type formulas",

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).",

author = "Manfred Denker and Souha Fares",

note = "Funding Information: The first author was supported by the National Science Foundation under Grant Number DMS-1008538 . He also would like to thank Natalia Kan and Brian Nowakowski for many helpful discussions on the topic of this work.",

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journal = "Statistics and Probability Letters",

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AU - Fares, Souha

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PY - 2014/9

Y1 - 2014/9

N2 - 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).

AB - 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).

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DO - 10.1016/j.spl.2014.06.003

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AN - SCOPUS:84902952528

SN - 0167-7152

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SP - 241

EP - 248

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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