Kwok Y. Pricing Models of Volatility Products...Derivatives 2022

Textbook in PDF format

Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods.
Features
Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives
Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products
Can be used as a university textbook in a topic course on pricing variance derivatives

Dedication
Contents
Preface
Volatility Trading and Variance Derivatives
Implied volatility and local volatility
Volatility trading using options
Taking volatility position using straddles and strangles
Volatility exposure generated by delta hedging options
Derivatives on discrete realized variance
Swaps and options on realized variance and volatility
Generalized variance swaps
Timer options
Target volatility options
Replication of variance swaps
Replication of continuous variance swaps
Practical implementation of replication: Finite strikes and discrete monitoring
Continuously sampled realized variance replicated by options of finite strikes
VIX: Extracting model-free volatility from S&P 500 index options
Replication of swaps on discrete realized variance
Appendix
Lévy Processes and Stochastic Volatility Models
Compound Poisson process
Poisson process
Random jump sizes
Stochastic integration
Jump measure and Lévy measure
Jump-diffusion models
Itô’s formula
Asset price process: Geometric Brownian motion with compound Poisson jumps
Merton’s model with Gaussian jumps
Kou’s model with exponential jumps
Lévy processes
Definition
Infinite divisibility
Characteristic exponent and Lévy-Khintchine representation
Lévy-Itô decomposition theorem
CGMY model: Dampened power law as Lévy measure
Generalized Hyperbolic model
Martingale condition on drift under risk neutral measure
Time-changed Lévy processes
Time-change techniques: Subordinators and activity rates
Variance Gamma model
Normal Inverse Gaussian model
Barndorff-Nielsen and Shephard model
Stochastic volatility models with jumps
Distribution formulas of instantaneous variance of CIR type
Pricing of swap on continuous realized variance
Affine jump-diffusion stochastic volatility models
Joint moment generating function of the affine model
Numerical valuation of complex algorithms and Heston trap
Schobel-Zhu model
/2 stochastic volatility model
Model formulation
ial Fourier transform of the triple joint density
ial Fourier transform of the joint density function of (X,V)
Joint characteristic function of (X,I)
Appendix
VIX Derivatives under Consistent Models and Direct Models
VIX, variance swap rate and VIX derivatives
Relation between variance swap rate and VIX2 under jumps
VIX derivatives
Pricing VIX derivatives under consistent models
Affine stochastic volatility models
/2-model with jumps in index value
Barndorff-Nielsen and Shephard model
GARCH type models
Direct modeling of VIX
Multifactor affine jump-diffusion models
/2 plus models
Appendix
Swap Products on Discrete Variance and Volatility
Direct expectation of square of log return
Nested expectation via partial integro-differential equation
Vanilla variance swaps under the Heston stochastic volatility model
Variance swaps under the 3/2-model
Moment generating function methods
Variance swap and gamma swap
Corridor type swaps
Numerical tests of the convergence for discretely monitored variance swaps
Volatility swaps
Variance swaps under time-changed Lévy processes
Multiple of log contract for pricing swaps on continuous realized variance
Swaps on discrete realized variance
Generalized variance swaps
Convergence of fair strikes
Conditions on convergence in expectation
Appendix
Options on Discrete Realized Variance
Adjustment for discretization effect via lognormal approximation
Discrete realized variance under the lognormal model
Approximation formulas for moment generating function
Normal approximation to conditional distribution of discrete realized variance
Conditional normal approximation pricing scheme
Simplified conditional pricing schemes
Non-simulation asymptotic approximation pricing scheme
ially exact and bounded approximation for options on discrete realized variance
Lower bound with known characteristic function
ially exact and bounded approximation
Numerical calculations of partially exact and bounded approximation
Small time asymptotic approximation
Small time asymptotics under Lévy models
Small time asymptotics under the semimartingale models
Option pricing using small time asymptotic approximation
Timer Options
Model formulation
Governing partial differential equation
Pricing perpetual timer options
Conditional expectation based on Black-Scholes type formula
Integral price formulas under the Heston model
Perturbation approximation
Finite maturity discrete timer options
Fourier inversion integral price formula
Fourier space time stepping numerical algorithm
Appendix
Bibliography
Index