Chapter

Stochastic Processes and Stochastic Calculus

Claus Munk

in Fixed Income Modelling

Published in print June 2011 | ISBN: 9780199575084
Published online September 2011 | e-ISBN: 9780191728648 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575084.003.0003
Stochastic Processes and Stochastic Calculus

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The price of an asset at a future point in time will typically be unknown, i.e. a random variable. In order to describe the uncertain evolution in the price of the asset over time, we need a collection of random variables, namely one random variable for each point in time. Such a collection of random variables is called a stochastic process. Modern finance models therefore apply stochastic processes to represent the evolution in prices — as well as interest rates and other relevant quantities — over time. This is also the case for the dynamic interest rate models presented in this book. This chapter gives an introduction to stochastic processes and the mathematical tools needed to do calculations with stochastic processes, the so-called stochastic calculus, focusing on processes and results that will become important in later chapters.

Keywords: random variables; prices; stochastic process; Brownian motion; diffusion; Ito's Lemma; stochastic calculus

Chapter.  24275 words.  Illustrated.

Subjects: Financial Markets

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