Change of Time Methods in Quantitative Finance
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Beschreibung
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.
New approach in quantitative finance-change of time method (for standard diffusion and Levy-based finance models), which is different from a traditional one using subordinators Contains the solutions of new problems in quantitative finance such as pricing of variance and volatility swaps in energy markets and hedging of volatility swaps (with hedge ratio), to name a few Contains new financial models such as delayed Heston model that improves the volatility surface fitting Includes supplementary material: sn.pub/extras
Autor*in
Anatoliy Swishchuk
Themen in »Change of Time Methods in Quantitative Finance«
Change of Time Method Geometric Brownian Motion Mean-reverting Asset Multi-factor Levy Models Stochastic Differential Equations quantitative finance