Table of Contents:
  • IntroductionIntroduction to financial derivatives Financial derivativeswhats the big deal? Stylized factsOverview
  • Fundamentals Interest rates Cash flows Continuously compounded interest rates Interest rate options: caps and floors
  • Discrete-Time Finance The binomial one period model The one period model The multi period model
  • Linear Time Series Models Introduction Linear systems in the time domain Linear stochastic processes Linear processes with a rational transfer functionAutocovariance functions Prediction in linear processes
  • Non-Linear Time Series Models Introduction The aim of model buildingQualitative properties of the models Parameter estimationParametric models Model identification Prediction in non-linear models Applications of non-linear models
  • Kernel Estimators in Time Series Analysis Non-parametric estimation Kernel estimators for time series Kernel estimation for regression Applications of kernel estimators-- Stochastic Calculus Dynamical systems The Wiener process Stochastic Integrals It stochastic calculus Extensions to jump processes
  • Stochastic Differential Equations Stochastic differential equations Analytical solution methods FeynmanKac representation Girsanov measure transformation
  • Continuous-Time Security Markets From discrete to continuous time Classical arbitrage theoryModern approach using martingale measures Pricing Model extensions Computational methods
  • Stochastic Interest Rate Models Gaussian one-factor models A general class of one-factor models Time-dependent models Multifactor and stochastic volatility models
  • The Term Structure of Interest Rates Basic concepts The classical approach The term structure for specific models HeathJarrowMorton framework Credit models Estimation of the term structurecurve-fitting
  • Discrete-Time Approximations Stochastic Taylor expansionConvergence Discretization schemes Multilevel Monte Carlo Simulation of SDEs
  • Parameter Estimation in Discretely Observed SDEsIntroduction High frequency methods Approximate methods for linear and non-linear modelsState dependent diffusion term MLE for non-linear diffusionsGeneralized method of moments (GMM) Model validation for discretely observed SDEs
  • Inference in Partially Observed Processes IntroductionThe model Exact filtering Conditional moment estimators Kalman filter Approximate filters State filtering and predictionThe unscented Kalman filter A maximum likelihood method Sequential Monte Carlo filters Application of non-linear filters
  • Appendix A: Projections in Hilbert Spaces Appendix B: Probability Theory
  • Bibliography-- Problems appear at the end of each chapter.