Читать книгу Random Motions in Markov and Semi-Markov Random Environments 2 - Anatoliy Swishchuk - Страница 2
ОглавлениеTable of Contents
1 Cover
4 Preface
6 Introduction I.1. Overview I.2. Description of the book
7 PART 1: Higher-dimensional Random Motions and Interactive Particles 1 Random Motions in Higher Dimensions 1.1. Random motion at finite speed with semi-Markov switching directions process 1.2. Random motion with uniformly distributed directions and random velocity 1.3. The distribution of random motion at non-constant velocity in semi-Markov media 1.4. Goldstein–Kac telegraph equations and random flights in higher dimensions 1.5. The jump telegraph process in Rn 2 System of Interactive Particles with Markov and Semi-Markov Switching 2.1. Description of the Markov model 2.2. Interaction of particles governed by generalized integrated telegraph processes: a semi-Markov case
8 PART 2: Financial Applications 3 Asymptotic Estimation for Application of the Telegraph Process as an Alternative to the Diffusion Process in the Black–Scholes Formula 3.1. Asymptotic expansion for the singularly perturbed random evolution in Markov media in the case of disbalance 3.2. Application: Black–Scholes formula 4 Variance, Volatility, Covariance and Correlation Swaps for Financial Markets with Markov-modulated Volatilities 4.1. Volatility derivatives 4.2. Martingale representation of a Markov process 4.3. Variance and volatility swaps for financial markets with Markov-modulated stochastic volatilities 4.4. Covariance and correlation swaps for two risky assets for financial markets with Markov-modulated stochastic volatilities 4.5. Example: variance, volatility, covariance and correlation swaps for stochastic volatility driven by two state continuous Markov chain 4.6. Numerical example 4.7. Appendix 1 5 Modeling and Pricing of Variance, Volatility, Covariance and Correlation Swaps for Financial Markets with Semi-Markov Volatilities 5.1. Introduction 5.2. Martingale representation of semi-Markov processes 5.3. Variance and volatility swaps for financial markets with semi-Markov stochastic volatilities 5.4. Covariance and correlation swaps for two risky assets in financial markets with semi-Markov stochastic volatilities 5.5. Numerical evaluation of covariance and correlation swaps with semi-Markov stochastic volatility 5.6. Appendices
10 Index
List of Tables
1 Chapter 4Table 4.1. One-step transition probability matrixTable 4.2. One-step transition probability matrix
List of Illustrations
1 Chapter 1Figure 1.1. Approximated probability density function f3(t, x) − r(t, x) for λ =...Figure 1.2. f(t, x) for λ = 2 and v = 3, according to Garra and Orsingher (2014)...Figure 1.3. Integration of f3(t, x) − r(t, x) and f(t, x) for λ = 2 and v = 2. T...Figure 1.4. Integration of f3(t, x) − r(t, x) and f(t, x) for λ = 0.2 and v = 2....Figure 1.5. Integration of f3(t, x) − r(t, x) and f(t, x) for λ = 2 and v = 0.2....Figure 1.6. Integration of f3(t, x) and f(t, x) for λ = 0.2 and v = 0.2. The sin...
2 Chapter 3Figure 3.1. Dependence of European call option price on v (left) and λ (right)Figure 3.2. Dependence of European call option price on v and λ. For a color ver...
3 Chapter 4Figure 4.1. Variance and volatility swap prices. For a color version of this fig...Figure 4.2. Variance and volatility swap prices. For a color version of this fig...
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