An algorithm to generate samples with approximate first-, second-, and third-order moments is presented extending the Cholesky matrix decomposition to a Cholesky tensor decomposition of an arbitrary order. The tensor decomposition of the first-, second-, and third-order objective moments...

The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied...

We derived a model-free analytical approximation of the price of a multi-asset option defined over an arbitrary multivariate process, applying a semi-parametric expansion of the unknown risk-neutral density with the moments. The analytical expansion termed as the Multivariate Generalised...