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| Contents | |
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| Preface | |
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| Introduction to Probability | |
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| Intuitive Explanation | |
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| Axiomatic Definition | |
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| Introduction to Random Variables | |
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| Random Variables | |
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| Random Vectors | |
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| Transformation of Random Variables | |
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| Transformation of Random Vectors | |
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| Approximation of the Standard Normal Cumulative Distribution Function | |
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| Random Sequences | |
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| Sum of Independent Random Variables | |
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| Law of Large Numbers | |
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| Central Limit Theorem | |
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| Convergence of Sequences of Random Variables | |
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| Introduction to Computer Simulation of Random Variables | |
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| Uniform Random Variable Generator | |
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| Generating Discrete Random Variables | |
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| Simulation of Continuous Random Variables | |
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| Simulation of Random Vectors | |
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| Acceptance-Rejection Method | |
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| Markov Chain Monte Carlo Method (MCMC) | |
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| Foundations of Monte Carlo Simulations | |
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| Basic Idea | |
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| Introduction to the Concept of Precision | |
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| Quality of Monte Carlo Simulations Results | |
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| Improvement of the Quality of Monte Carlo Simulations or Variance Reduction Techniques | |
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| Application Cases of Random Variables Simulations | |
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| Fundamentals of Quasi Monte Carlo (QMC) Simulations | |
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| Van Der Corput Sequence (Basic Sequence) | |
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| Halton Sequence | |
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| Faure Sequence | |
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| Sobol Sequence | |
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| Latin Hypercube Sampling | |
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| Comparison of the Different Sequences | |
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| Introduction to Random Processes | |
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| Characterization | |
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| Notion of Continuity, Differentiability and Integrability | |
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| Examples of Random Processes | |
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| Solution of Stochastic Differential Equations | |
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| Introduction to Stochastic Calculus | |
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| Introduction to Stochastic Differential Equations | |
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| Introduction to Stochastic Processes with Jump | |
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| Numerical Solutions of some Stochastic Differential Equations (SDE) | |
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| Application case: Generation of a Stochastic Differential Equation using the Euler and Milstein Schemes | |
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| Application Case: Simulation of a Stochastic Differential Equation with Control and Antithetic Variables | |
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| Application Case: Generation of a Stochastic Differential Equation with Jumps | |
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| General Approach to the Valuation of Contingent Claims | |
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| The Cox, Ross and Rubinstein (1979) Binomial Model of Option Pricing | |
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| Black and Scholes (1973) and Merton (1973) Option Pricing Model | |
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| Derivation of the Black-Scholes Formula using the Risk-Neutral Valuation Principle | |
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| Pricing Options using Monte Carlo Simulations | |
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| Plain Vanilla Options: European put and Call | |
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| American options | |
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| Asian options | |
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| Barrier options | |
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| Estimation Methods for the Sensitivity Coefficients or Greeks | |
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| Term Structure of Interest Rates and Interest Rate Derivatives | |
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| General Approach and the Vasicek (1977) Model | |
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| The General Equilibrium Approach: The Cox, Ingersoll and Ross (CIR, 1985) model | |
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| The Affine Model of the Term Structure | |
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| Market Models | |
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| Credit Risk and the Valuation of Corporate Securities | |
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| Valuation of Corporate Risky Debts: The Merton (197 | |