Equilibrium Pricing of Options in a Fractional Brownian Market
19 Pages Posted: 4 Nov 2010
Date Written: September 8, 2010
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
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