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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 | |