Pricing Alternatives in Incomplete Markets: An Application for Carbon Allowances

Abstract

n this paper, we bring a new econometric perspective for CO2 emission prices modelling and we provide with an innovative methodological approach to compute option prices in incomplete markets. We apply our methodology to carbon derivative. We calibrate several Generalized Hyperbolic and GARCH models with various innovations, using the CO2 European Union Allowances (EUA) daily prices from 2005 to 2010. The issue of probability changing is handled with a generalization of Duan's [1995] theoretical concept of local risk neutrality. Thus we use some modellings features under the historical measure to derive a valuation model for options implemented through an empirical martingale correction approach with variance rescaling. We compare this approach, with one followed by Gerber and Siu [1994] using a stochastic discount factor exponential affine and with another one recently developed by Chorro, Guegan and Ielpo [2010] considering a pure empirical martingale correction technique. Option prices computed through different techniques for different maturities and moneyness show promising results for Normal Inverse Gaussian distribution.