Monte Carlo simulation and finance

Abstract

Chapter 1. Introduction. Chapter 2. Some Basic Theory of Finance. Introduction to Pricing: Single PeriodModels. Multiperiod Models. Determining the Process Bt. Minimum Variance Portfolios and the Capital Asset Pricing Model. Entropy: choosing a Q measure. Models in Continuous Time. Problems. Chapter 3. Basic Monte Carlo Methods. Uniform Random Number Generation. Apparent Randomness of Pseudo--Random Number Generators. Generating Random Numbers from Non--Uniform Continuous Distributions. Generating Random Numbers from Discrete Distributions. Random Samples Associated with Markov Chains. Simulating Stochastic Partial Differential Equations. Problems. Chapter 4. Variance Reduction Techniques. Introduction. Variance reduction for one--dimensional Monte--Carlo Integration. Problems. Chapter 5. Simulating the value of Options. Asian Options. Pricing a Call option under stochastic interest rates. Simulating Barrier and lookback options. Survivorship Bias. Problems. Chapter 6. Quasi-- Monte Carlo Multiple Integration. Introduction. Theory of Low discrepancy sequences. Examples of low discrepancy sequences. Problems. Chapter 7. Estimation and Calibration. Introduction. Finding a Root. Maximization of Functions. MaximumLikelihood Estimation. Using Historical Data to estimate the parameters in Diffusion Models. Estimating Volatility. Estimating Hedge ratios and Correlation Coefficients. Problems. Chapter 8. Sensitivity Analysis, Estimating Derivatives and the Greeks. Estimating Derivatives. Infinitesimal Perturbation Analysis: Pathwise differentiation. Calibrating aModel using simulations. Problems. Chapter 9. Other Directions and Conclusions. Alternative Models. ARCH and GARCH. Conclusions. Notes. References. Index.

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