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© 2016

Change of Time Methods in Quantitative Finance

Book

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

About this book

Introduction

This book is devoted to the history of Change of Time Methods (CTM), the connections of CTM to stochastic volatilities and finance, fundamental aspects of the theory of CTM, basic concepts, and its properties. An emphasis is given on many applications of CTM in financial and energy markets, and the presented numerical examples are based on real data. The change of time method is applied to derive the well-known Black-Scholes formula for European call options, and to derive an explicit option pricing formula for a European call option for a mean-reverting model for commodity prices. Explicit formulas are also derived for variance and volatility swaps for financial markets with a stochastic volatility following a classical and delayed Heston model. The CTM is applied to price financial and energy derivatives for one-factor and multi-factor alpha-stable Levy-based models.

Readers should have a basic knowledge of probability and statistics, and some familiarity with stochastic processes, such as Brownian motion, Levy process and martingale.

Keywords

Change of Time Method Geometric Brownian Motion Mean-reverting Asset Multi-factor Levy Models Stochastic Differential Equations

Authors and affiliations

  1. 1.Dept. of Mathematics & StatisticsUniversity of CalgaryCalgaryCanada

Bibliographic information

  • Book Title Change of Time Methods in Quantitative Finance
  • Authors Anatoliy Swishchuk
  • Series Title SpringerBriefs in Mathematics
  • Series Abbreviated Title SpringerBriefs in Mathematics
  • DOI https://doi.org/10.1007/978-3-319-32408-1
  • Copyright Information The Author 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-32406-7
  • eBook ISBN 978-3-319-32408-1
  • Series ISSN 2191-8198
  • Series E-ISSN 2191-8201
  • Edition Number 1
  • Number of Pages XV, 128
  • Number of Illustrations 1 b/w illustrations, 10 illustrations in colour
  • Topics Quantitative Finance
  • Buy this book on publisher's site
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