A unified entropic pricing framework of option : Using Cressie-Read family of divergences

The entropy valuation of option (Stutzer, 1996) provides a risk-neutral probability distribution (RND, an equivalent martingale measure) as the pricing measure by minimizing the Kullback–Leibler (KL) divergence between the empirical probability distribution and its risk-neutral counterpart. This article establishes a unified entropic pricing framework by developing a class of generalized entropy pricing models based upon Cressie-Read (CR) family of divergences (nesting KL). The main contributions lie in: (1) this unified framework can readily incorporate a set of informative risk-neutral moments (RNMs) of underlying return from the option market which can accurately capture the characteristics of the underlying distribution; (2) the classic KL-based entropy pricing model is extended and a unified (entropic) pricing framework is constructed upon a family of CR divergences. For each of the proposed family of models under the unified framework, the optimal RND is derived by employing the dual method. Simulations show that, compared to the true price, each model of the proposed family can produce high accuracy for European option pricing. Meanwhile, the pricing biases among the models are different, and we hence conduct theoretical analysis and experimental investigations to explore the driving causes