Review of Probability Probability Space Independence and Conditional Probability Random Variables Random Vectors Conditional Distributions Conditional Expectation Classical Limit Theorems Brownian Motion Brownian Motion Running Maximum of Brownian Motion Derivatives and Black-Scholes Prices Multidimensional Brownian Motions Arbitrage Free Pricing Arbitrage Free Principle Asset Pricing with Binomial Trees The Black-Scholes Model Monte Carlo Simulation Basics of Monte Carlo Simulation Standard Error and Confidence Interval Examples of Monte Carlo Simulation Summary Generating Random Variables Inverse Transform Method Acceptance-Rejection Method Sampling from Multivariate Normal Distributions Variance Reduction Techniques Antithetic Sampling Control Variates Stratified Sampling Importance Sampling Basic Ideas of Importance Sampling The Cross-Entropy Method Applications to Risk Analysis Stochastic Calculus Stochastic Integrals Itô Formula Stochastic Differential Equations Risk-Neutral Pricing Black-Scholes Equation Simulation of Diffusions Euler Scheme Eliminating Discretization Error Refinements of Euler Scheme The Lamperti Transform Numerical Examples Sensitivity Analysis Commonly Used Greeks Monte Carlo Simulation of Greeks Appendix A: Multivariate Normal Distributions Appendix B: American Option Pricing Appendix C: Option Pricing Formulas Bibliography Index Exercises appear at the end of each chapter. amples of Monte Carlo Simulation Summary Generating Random Variables Inverse Transform Method Acceptance-Rejection Method Sampling from Multivariate Normal Distributions Variance Reduction Techniques Antithetic Sampling Control Variates Stratified Sampling Importance Sampling Basic Ideas of Importance Sampling The Cross-Entropy Method Applications to Risk Analysis Stochastic Calculus Stochastic Integrals Itô Formula Stochastic Differential Equations Risk-Neutral Pricing Black-Scholes Equation Simulation of Diffusions Euler Scheme Eliminating Discretization Error Refinements of Euler Scheme The Lamperti Transform Numerical Examples Sensitivity Analysis Commonly Used Greeks Monte Carlo Simulation of Greeks Appendix A: Multivariate Normal Distributions Appendix B: American Option Pricing Appendix C: Option Pricing Formulas Bibliography Index Exercises appear at the end of each chapter. Simulation of Diffusions Euler Scheme Eliminating Discretization Error Refinements of Euler Scheme The Lamperti Transform Numerical Examples Sensitivity Analysis Commonly Used Greeks Monte Carlo Simulation of Greeks Appendix A: Multivariate Normal Distributions Appendix B: American Option Pricing Appendix C: Option Pricing Formulas Bibliography Index Exercises appear at the end of each chapter.