Closed Form Option Pricing Formulas based on a non-Gaussian Stock Price Model with Statistical Feedback

Preprint

4 May 2002

preprint
Published by arXiv in arXiv

Abstract

A closed form option pricing formula is obtained, based on a stochastic model with statistical feedback. The fluctuations evolve according to a Tsallis distribution which fits empirical data for stock returns. A generalized form of the Black-Scholes PDE is derived, parametrized by the Tsallis entropic index q. We also derive a martingale representation which allows us to use concepts of risk-free asset pricing theory to explicitly solve the case of European options. Exact solutions are found which qualitatively capture features found in real option prices such as the volatility smile.

Keywords

MODEL WITH STATISTICAL
OPTION PRICING FORMULA
STOCHASTIC MODEL
PRICING FORMULAS
OPTION PRICES
STATISTICAL
FORM OPTION
FEEDBACK
STOCK

All Related Versions

Version 1, 2002-04-15, ArXiv
Version 2, 2002-04-17, ArXiv
Version 3, 2002-05-04, ArXiv
Version 4, 2002-05-09, ArXiv
Version 5, 2002-06-19, ArXiv
Published version: Physical Review Letters, 89 (9), 098701.

This publication has 0 references indexed in Scilit: