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Fixed Income Modelling$
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Claus Munk

Print publication date: 2011

Print ISBN-13: 9780199575084

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199575084.001.0001

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Stochastic Processes and Stochastic Calculus

Stochastic Processes and Stochastic Calculus

Chapter:
(p.38) 3 Stochastic Processes and Stochastic Calculus
Source:
Fixed Income Modelling
Author(s):

Claus Munk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199575084.003.0003

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

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