The value of an american basket call with dividends increases with the basket volatility

Abstract

We show the American Call on a basket (i.e., a weighted sum of assets) and with dividends increases with the basket volatility in a large class of multivariate continuous diffusion models. In case of a flat yield curve the same result holds for the American Put on a basket. The proof of our result is based on extensions of Hajek’s mean stochastic comparison results to stochastic sums. We provide a simple proof of Hajek’s result and show why the argument is much more involved in case of our extensions. We provide the main ideas of the proofs of our extensions based on heat kernel expansions.