1. Introduction The purpose of this paper is to prove various geometric inequalities in option pricing using familiar inequalities of the Brunn-Minkowski type in Gauss space. To begin with, recall that a European (American) call [putJ option is defined as the right to buy [sellJ one share of stock at a specified price on (or before) a specified date. The specified price is referred to as the exercise price and the terminal date of the contract is called the expiration date or maturity date. In fact, already the early paper [20J by Merton treats a variety of convexity properties of puts and calls, sometimes without any distributional assumptions on the underlying stock prices. Here, however, it will always be assumed that the price process X(t) = (X1 (t), …,Xm(t)), t ≥ 0, of the underlying risky assets X l, … , Xm is governed by a so called joint geometric Brownian motion. Furthermore, all options will be of European type and so, from now on, option will always mean option of European type.