On the pricing of exotic options: A new closed-form valuation approach

Abstract

Abstract We provide a novel method to estimate in a closed-form solution the option prices of various exotic options, using techniques based on Laplace–Beltrami operator for estimating diffusion boundary times. We estimate exit times and their expectations, the hitting probabilities, boundary local times until the first hitting and other probabilistic quantities and moment generating functions related to local hitting times. Our findings maybe of paramount importance for traders, investors, speculators and more broadly speaking for financial institutions.