Computational Methods in Finance (Hardcover)

I Pricing and Valuation
Stochastic Processes and Risk-Neutral Pricing
Characteristic Function
Stochastic Models of Asset Prices
Valuing Derivatives under Various Measures
Types of Derivatives

Derivatives Pricing via Transform Techniques
Derivatives Pricing via the Fast Fourier Transform
Fractional Fast Fourier Transform
Derivatives Pricing via the Fourier-Cosine (COS) Method
Cosine Method for Path-Dependent Options
Saddlepoint Method

Introduction to Finite Differences
Taylor Expansion
Finite Difference Method
Stability Analysis
Derivative Approximation by Finite Differences: A Generic Approach
Matrix Equations Solver

Derivative Pricing via Numerical Solutions of PDEs
Option Pricing under the Generalized Black-Scholes PDE
Boundary Conditions and Critical Points
Nonuniform Grid Points
Dimension Reduction
Pricing Path-Dependent Options in a Diffusion Framework
Forward PDEs
Finite Differences in Higher Dimensions

Derivative Pricing via Numerical Solutions of PIDEs
Numerical Solution of PIDEs (a Generic Example)
American Options
PIDE Solutions for Levy Processes
Forward PIDEs
Calculation of g₁ and g₂

Simulation Methods for Derivatives Pricing
Random Number Generation
Samples from Various Distributions
Models of Dependence
Brownian Bridge
Monte Carlo Integration
Numerical Integration of Stochastic Differential Equations
Simulating SDEs under Different Models
Output/Simulation Analysis
Variance Reduction Techniques

II Calibration and Estimation
Model Calibration
Calibration Formulation
Calibration of a Single Underlier Model
Interest Rate Models
Model Risk
Optimization and Optimization Methodology
Construction of the Discount Curve
Arbitrage Restrictions on Option Premiums
Interest Rate Definitions

Filtering and Parameter Estimation
Filtering
The Likelihood Function
Kalman Filter
Non-Linear Filters
Extended Kalman Filter
Unscented Kalman Filter
Square Root Unscented Kalman Filter (SR UKF)
Particle Filter
Markov Chain Monte Carlo (MCMC)