Equilibrium Pricing of Options in a Fractional Brownian Market

19 Pages Posted: 4 Nov 2010

See all articles by Stefan Rostek

Stefan Rostek

University of Tuebingen - Faculty of Economics and Business Administration

Rainer Schoebel

University of Tuebingen - Faculty of Economics and Social Sciences

Date Written: September 8, 2010

Abstract

We derive European option prices when the underlying security dynamics are driven by geometric fractional Brownian motion. The latter is a parsimonious way to capture serial correlation within financial time series. Though being incompatible with the assumption of dynamic complete markets, we suggest fractional Brownian motion as a favorable candidate whenever incompleteness enters the scene. Following Brennan (1979), we discuss a model where market participants have constant relative risk aversion and trade in discrete time. Moreover, investors' wealth and the underlying stock are assumed to be of fractional Brownian motion type and follow a bivariate lognormal distribution. We introduce an equilibrium condition and provide closed-form solutions for European options. The derived results are an extension of the Black-Scholes pricing formulae and contain the latter as a special case.

Keywords: Fractional Brownian Motion, Closed-Form Solution, Conditional Expectation, Pricing Equilibrium, Risk Aversion

JEL Classification: G12, G13

Suggested Citation

Rostek, Stefan and Schoebel, Rainer, Equilibrium Pricing of Options in a Fractional Brownian Market (September 8, 2010). Available at SSRN: https://ssrn.com/abstract=1701596 or http://dx.doi.org/10.2139/ssrn.1701596

Stefan Rostek (Contact Author)

University of Tuebingen - Faculty of Economics and Business Administration ( email )

Mohlstrasse 36
D-72074 Tuebingen, 72074
Germany

Rainer Schoebel

University of Tuebingen - Faculty of Economics and Social Sciences ( email )

Mohlstrasse 36
D-72074 Tuebingen
Germany
+49 7071 2977088 (Phone)

Register to save articles to
your library

Register

Paper statistics

Downloads
188
Abstract Views
1,344
rank
162,114
PlumX Metrics