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Change of Time Methods in Quantitative Finance

SpringerBriefs in Mathematics

By (author) Anatoliy Swishchuk
Format: Paperback / softback
Publisher: Springer International Publishing AG, Cham, Switzerland
Published: 28th Jul 2016
Dimensions: w 156mm h 234mm d 8mm
Weight: 216g
ISBN-10: 3319324063
ISBN-13: 9783319324067
Barcode No: 9783319324067
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Synopsis
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.

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