Analysing and Interpreting the Yield Curve, 2nd Edition

CHAPTER 4Interest Rate Modelling II: The Dynamic of Asset Prices

The pricing of derivative instruments such as options is a function of the movement in the price of the underlying asset over the lifetime of the option, and valuation models describe an environment where the price of an option is related to the behaviour process of the variables that drive asset prices. This process is described as a stochastic process, and pricing models describe the stochastic dynamics of asset price changes, whether this is a change in share prices, interest rates, foreign exchange rates or bond prices. To understand the mechanics of interest rate modelling therefore, we must familiarise ourselves with the behaviour of functions of stochastic variables. The concept of a stochastic process is a vital concept in finance theory. It describes random phenomena that evolve over time, and these include asset prices. For this reason, an alternative title for this chapter could be An Introduction to Stochastic Processes.

In this chapter, we review the basic principles of the dynamics of asset prices, which are then put into context in the following chapters, which look at term structure models.

THE BEHAVIOUR OF ASSET PRICES

The first property that asset prices, which can be taken to include interest rates, 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 ...