43 - The dynamics of asset prices

Abstract

This chapter reviews the basic principles of the dynamics of asset prices that looks at the Black–Scholes model. The main principles are considered in the context of yield curve modelling. The first property that asset prices are assumed to follow is that they are part of a continuous process. This means that the value of any asset can and does change at any time and from one point in time to another and can assume any fraction of a unit of measurement. The price processes of shares and bonds, as well as interest rate processes, are stochastic processes. That is, they exhibit a random change over time. The first step in asset pricing theory builds on the assumption that prices follow a Brownian motion. Continuous time asset pricing is an important part of finance theory and involves some quite advanced mathematics. A martingale is an important type of stochastic process and the concept of a martingale is fundamental to asset pricing theory. A process that is a martingale is one in which the expected future value, based on what is known up to now, is the same as today's value.