A Multifractal Model of Assets Returns

An important determinant of option prices is the elasticity of the pricing kernel used to price all decline in the economy. In this paper, we first show that for a given forward price of the underlying asset, option prices are higher when the elasticity of pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the stochastic process followed by the underlying asset. Given that the underlying information process follows a geometric Brownlan motion, we demonstrate that constant elasticity of the pricing kernel is equivalent to a Brownlan motion for the forward price of the underlying asset, so that the Black-Scholes formula correctly prices option on the asset. In contrast, declining elasticity implies that he forward price process is no longer a Brownlan motion. It has higher volatility and exhibits autocorrelation. In this case, the Black-Scholes formula and underprices all options.