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created by Gianluca Fusai
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Brownian Motion
Simulating the BM
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Brownian Motion in Excel
Total and Quadratic Variation
Stochastic Integral
Important SDEs
Arithmetic Brownian Motion
Model Simulation
Geometric Brownian Motion
Model Simulation
Mean Reverting Models
What is mean reversion
Understanding Mean Reversion
Vasicek Model
Simulating the Vasicek Model
Cox-Ingersoll-Ross Model
Simulating the CIR model
The CIR PDF
Constant Elasticity of Variance Model (CEV)
Density and option pricing
Brownian Bridge Model
Model Simulation
Heston Model
Moments in the Heston Model
The density function
Option Pricing
Simulating log-asset prices
The simulated distribution of the variance
Issues in simulating the variance
Variance mean-reversion
Jump Diffusion Models
Simulating JD models
Gamma Process
Variance Gamma Model
Main Properties
Option Pricing
Numerical Integration
Rectangle Rule
Mid-Point Rule
Trapezium Rule
A comparison
Gaussian Quadrature
Characteristic Functions
FFT
COS method
Numerical Integration
Important Distributions
Gaussian Distribution
Lognormal Distribution
Properties
Chi2 Distribution
Non-Central Chi2 Distribution
Bivariate Gaussian Distribution
Multivariate Gaussian Distribution
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created by Gianluca Fusai
The simulated distributions of log-asset returns and variance
A courtesy of
Ioannis Kyriakou
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