Linearizing Option Returns for Portfolio and Risk Management: A Tetranomial Approach

This paper proposes a method to deduce the first four moments and the co-moments (with any other asset) of an option return. We consider the dynamics of an option-replicating portfolio of four basic assets: the underlying, two long-term options and a zero coupon bond. This approach allows us to capture the moments up to order four of the underlying and to linearize the option return. A numerical example illustrates some of the features and applications of this model.