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Lecture 5-2: Variance Reduction Techniques

• Principles and rationale. • Control Variates

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Lecture 1 - Principles of Monte Carlo

Crude Monte Carlo: central limit theorem and law of large numbers. Methods for the generation of random variables: inverse transform, rejection sam- pling. Examples: simulation from the exponential…

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Lecture 4: Application of Malliavin calculus to exact and approximate option pricing under stochastic volatility

Introduction Model of asset price and payoff function: additional assumptions, auxiliary properties Elements of Malliavin calculus and application to option pricing The rate of convergence of…

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Lectures 65-66: discretization and Monte Carlo errors

Discretization error and Monte Carlo error. Acceleration techniques. Introduction to MATLAB. Pricing of an Asian option: a horse-race among VBA, MATLAB and parallelized MATLAB codes.

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Lectures 53-54: variance reduction techniques

Variance reduction techniques: control variables, antithetic variables,importance sampling. Implementation in VBA.

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Lecture 48: the Monte Carlo method

The Monte Carlo method. Monte Carlo estimator and error.

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