About this book
Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic
Volatilities is devoted to the modeling and pricing of various kinds of swaps,
such as those for variance, volatility, covariance, correlation, for financial
and energy markets with different stochastic volatilities, which include CIR
process, regime-switching, delayed, mean-reverting, multi-factor, fractional,
Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this
book is change of time method. The book outlines how the change of time method
works for different kinds of models and problems arising in financial and energy
markets and the associated problems in modeling and pricing of a variety of
swaps. The book also contains a study of a new model, the delayed Heston model,
which improves the volatility surface fitting as compared with the classical
Heston model. The author calculates variance and volatility swaps for this model
and provides hedging techniques. The book considers content on the pricing of
variance and volatility swaps and option pricing formula for mean-reverting
models in energy markets. Some topics such as forward and futures in energy
markets priced by multi-factor Levy models and generalization of Black-76
formula with Markov-modulated volatility are part of the book as well, and it
includes many numerical examples such as S&P60 Canada Index, S&P500 Index and
AECO Natural Gas Index.
Contents:
Stochastic Volatility
Stochastic Volatility Models
Swaps
Change of Time Methods
Black-Scholes Formula by Change of Time Method
Modeling and Pricing of Swaps for Heston Model
Modeling and Pricing of Variance Swaps for Stochastic Volatilities with Delay
Modeling and Pricing of Variance Swaps for Multi-Factor Stochastic
Volatilities with Delay
Pricing Variance Swaps for Stochastic Volatilities with Delay and Jumps
Variance Swap for Local L谷vy-Based Stochastic Volatility with Delay
Delayed Heston Model: Improvement of the Volatility Surface Fitting
Pricing and Hedging of Volatility Swap in the Delayed Heston Model
Pricing of Variance and Volatility Swaps with Semi-Markov Volatilities
Covariance and Correlation Swaps for Markov-Modulated Volatilities
Volatility and Variance Swaps for the COGARCH(1,1) Model
Variance and Volatility Swaps for Volatilities Driven by Fractional Brownian
Motion
Variance and Volatility Swaps in Energy Markets
Explicit Option Pricing Formula for a Mean-Reverting Asset in Energy Markets
Forward and Futures in Energy Markets: Multi-Factor L谷vy Models
Generalization of Black-76 Formula: Markov-Modulated Volatility
Readership: Post-graduate level
researchers and professionals with interest in the modeling and pricing of swaps
for energy and financial markets.
Živorad Tomovski,
Trifce Sandev,
Ralf Metzler,
Johan Dubbeldam
Publication information:Živorad Tomovski,
Trifce Sandev,
Ralf Metzler,
Johan Dubbeldam,
Generalized space每time fractional diffusion equation with composite fractional
time derivative,
Physica A,
391(8), 2012,
2527每2542.
http://www.sciencedirect.com/science/article/pii/S037843711100971X
Abstract
We investigate the solution of space每time fractional diffusion equations with a
generalized Riemann每Liouville time fractional derivative and Riesz每Feller space
fractional derivative. The Laplace and Fourier transform methods are applied to
solve the proposed fractional diffusion equation. The results are represented by
using the Mittag-Leffler functions and the Fox
H-function.
Special cases of the initial and boundary conditions are considered. Numerical
scheme and Gr邦nwald每Letnikov approximation are also used to solve the space每time
fractional diffusion equation. The fractional moments of the fundamental
solution of the considered space每time fractional diffusion equation are
obtained. Many known results are special cases of those obtained in this paper.
We investigate also the solution of a space每time fractional diffusion equations
with a singular term of the form.
Bashir Ahmad,
Juan J. Nieto,
Ahmed Alsaedi,
Moustafa El-Shahed
Publication
information:
Bashir Ahmad,
Juan J. Nieto,
Ahmed Alsaedi,
Moustafa El-Shahed.
A study of nonlinear Langevin equation involving two fractional orders in
different intervals.
Nonlinear Analysis: Real
World Applications,
Nonlinear Analysis: Real
World Applications,
13(2), 2012,
599每606.
http://www.sciencedirect.com/science/article/pii/S1468121811002215
Abstract.
This paper studies a nonlinear Langevin equation involving two fractional orders
汐﹋(0,1]
and 汕﹋(1,2] with three-point boundary
conditions. The contraction mapping principle and Krasnoselskii＊s fixed point
theorem are applied to prove the existence of solutions for the problem. The
existence results for a three-point third-order nonlocal boundary value problem
of nonlinear ordinary differential equations follow as a special case of our
results. Some illustrative examples are also discussed.
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