January 25th, 2005, 12:11 pm
sure,here is a non-final version of the table of contents, sorry it is rather awkward but it is all in laTex ...------------------------------------------------------------------------------------------------Introduction Summary Contributions and Further Research Data and Programs The Volatility Problem Introduction The Stock Market--- The Stock Price Process--- Historic Volatility The Derivatives Market--- The Black Scholes Approach--- The Cox Ross Rubinstein Approach Jump Diffusion and Level Dependent Volatility--- Jump Diffusion------ Link to Credit Spread--- Level Dependent Volatility------ The Constant Elasticity Variance Approach------ The Bensoussan Crouhy Galai Approach Local Volatility--- The Dupire Approach------ The Breeden \& Litzenberger Identity------ The Dupire Identity------ Local Volatility vs Instantaneous Volatility--- The Derman Kani Approach--- Stability Issues--- Calibration Frequency Stochastic Volatility--- Stochastic Volatility Processes--- GARCH and Diffusion Limits The Pricing PDE under Stochastic Volatility--- The Market Price of Volatility Risk--- The Two Factor PDE The Generalized Fourier Transform--- The Transform Technique--- Special Cases The Mixing Solution--- The Romano Touzi Approach--- A One Factor Monte-Carlo Technique The Long Term Asymptotic Case--- The Deterministic Case--- The Stochastic Case--- A Series Expansion on Volatility-of-Volatility Pure-Jump Models--- Variance Gamma------ Remark on the Gamma Distribution------ Stochastic Volatility vs Time-Changed processes--- Variance Gamma with Stochastic Arrival------ Option Pricing under VGSA------ The Characteristic Function--- Variance Gamma with Gamma Arrival RateThe Inference Problem Introduction Using Option Prices--- Direction Set (Powell) Method--- Numeric Tests--- The Distribution of the Errors Using Stock Prices--- The Likelihood Function------ The Justification for the MLE------ Likelihood Evaluation and Filtering--- Filtering------ Interpretation of the Kalman Gain--- The Simple and Extended Kalman Filters------ Another Interpretation of the Kalman Gain------ Residuals, MPE and RMSE--- The Unscented Kalman Filter--- Kushner's Non-Linear Filter------ Details of the Kushner algorithm--- Parameter Learning------ An Illustration------ Joint Filtering Examples------ Observability------ The One-Dimensional State within the Joint Filter------ Joint Filters and Time Interval--- Parameter Estimation via MLE------ An Illustration------ Stochastic Volatility Examples------ Optimization-Constraints for the Square-Root Model------ An Alternative Implementation------ The One-Dimensional State------ Other stochastic volatility models--- Diagnostics------ Chi-Square Test------ Box-Ljung Test------ Test Results------ Variogram--- Particle Filtering------ Underlying Theory------ Resampling------ Implementation------ An Illustration------ Application to the Heston Model------ Test Results------ Error Size------ The MH Enhancement--- Comparing Heston with other Models------ The Models------ The Results------ Parameter Learning Revisited--- The Performance of the Inference Tools------ Sample Size------ Joint Estimation of the Parameters------ Error Size revisited------ High Frequency Data------ The Frequency of the Observations------ Sampling Distribution--- The Bayesian Approach------ The Gibbs Sampler------ A Simple Illustration------ The Metropolis-Hastings Algorithm------ Illustration------ A Few Distributions------ Regression Analysis------ Application to Gaussian SV Models (Heston)--- Using the Characteristic Function--- Introducing Jumps------ The Model------ The Generic Particle Filter------ Extended/ Unscented Particle Filters------ The Srivastava Approach------ Numeric results------ The Optimization Algorithm--- Pure-Jump Models------ VG------ VGSA------ The Filtering Algorithm------ Parameter Estimation------ A More Efficient Algorithm------ An Extended/ Unscented Particle Filter------ Numeric Results------ Diagnostics------ VGG------ A Bayesian Approach for VGSA Recapitulation--- Model Identification--- Convergence Issues and SolutionsThe Consistency Problem Introduction The Consistency Test--- The Setting--- The Cross-Sectional Results------ Robustness Issues for the Cross-Sectional Method--- Time-Series Results------ Robustness Issues for the Time-Series Method--- Financial Interpretation The ``Peso'' Theory--- Background--- Numeric Results Trading Strategies--- Skewness Trades--- Kurtosis Trades--- Directional Risks------ Skewness vs Kurtosis--- An Exact Replication--- The Mirror Trades--- An Example of the Skewness Trade------ The Options Bid-Ask Spread------ Early Termination------ Implied Volatility Term-Structure------ Which Hedge-Ratio should we use?--- Multiple Trades--- High Volatility-of-Volatility and High Correlation Non-Gaussian Case--- VGSA------ VGSA vs VG------ Cross-Sectional vs Time-Series VGSA A Word of Caution Foreign Exchange, Fixed Income and Other Markets--- Foreign Exchange--- Fixed Income------ The Time-Series------ The Cross-Section Bibliography
Last edited by
reza on January 24th, 2005, 11:00 pm, edited 1 time in total.