Financial Economics and Stochastic Calculus

Abstract

In Chap. 2, the theory of financial economics is used to show that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure under the discrete securities models. This important result is coined as the Fundamental Theorem of Asset Pricing. This leads to the risk neutral valuation principle, which states that the price of an attainable contingent claim is given by the expectation of the discounted value of the claim under a risk neutral measure. The concepts of attainable contingent claims, absence of arbitrage and risk neutrality form the cornerstones of the modern option pricing theory. Brownian processes and basic analytic tools in stochastic calculus are introduced. In particular, we discuss the Feynman-Kac representation, Radon–Nikodym derivative between two probability measures and the Girsanov Theorem that effects the change of measure on an Ito process.