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Change of Time Methods in Quantitative Finance
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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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