On the Minimal Entropy Martingale Measure and Multinomial Lattices with Cumulants

Abstract

In this article, we describe with relevant examples based on empirical data how to use the minimal entropy martingale measure (MEMM) to price European and American Options in multinomial lattices which take into account cumulants information. For trinomial lattices, we show that minimal entropy prices are close to results obtained using the Black and Scholes option pricing formula. For pentanomial lattices, minimal entropy prices are close to results obtained under the mean-correcting martingale measure using the discrete Fourier transform. The MEMM is very easy to compute and is therefore a good candidate for option pricing in multinomial lattices.