### 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 | |

State | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Statistics and Probability Letters*,

*92*, 241-248. https://doi.org/10.1016/j.spl.2014.06.003

}

*Statistics and Probability Letters*, vol. 92, pp. 241-248. https://doi.org/10.1016/j.spl.2014.06.003

**Richter's local limit theorem and Black-Scholes type formulas.** / Denker, Manfred Heinz; Fares, Souha.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Richter's local limit theorem and Black-Scholes type formulas

AU - Denker, Manfred Heinz

AU - Fares, Souha

PY - 2014/1/1

Y1 - 2014/1/1

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).

UR - http://www.scopus.com/inward/record.url?scp=84902952528&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902952528&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2014.06.003

DO - 10.1016/j.spl.2014.06.003

M3 - Article

AN - SCOPUS:84902952528

VL - 92

SP - 241

EP - 248

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -