Introduction to Stochastic Calculus for Finance A New Didactic Approach 1st Edition by Dieter Sondermann ISBN 3540348360 9783540348368

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Product details:
ISBN 10: 3540348360
ISBN 13: 9783540348368
Author: Dieter Sondermann

Introduction to Stochastic Calculus for Finance A New Didactic Approach 1st Edition Table of contents:

Part I: Introduction to Stochastic Processes and Finance

1. Introduction to Financial Markets and Derivatives

   • Overview of Financial Markets
   • Basic Concepts in Derivatives: Options, Futures, and Swaps
   • The Role of Stochastic Processes in Financial Modeling
   • Importance of Stochastic Calculus in Modern Finance

2. Fundamentals of Stochastic Processes

   • Definition and Types of Stochastic Processes
   • Random Walks and Brownian Motion
   • Markov Processes in Finance
   • Poisson Processes and Their Applications

3. Probability Theory Basics for Finance

   • Review of Probability and Random Variables
   • Conditional Probability and Expectation
   • Joint and Marginal Distributions
   • Laws of Large Numbers and Central Limit Theorem

Part II: Stochastic Calculus and Financial Applications

4. Brownian Motion and Its Properties

   • Definition and Properties of Brownian Motion
   • Applications of Brownian Motion in Financial Models
   • The Wiener Process: Mathematical Foundations
   • The Role of Brownian Motion in Asset Pricing

5. Ito Calculus and Its Basic Principles

   • Introduction to Stochastic Integration
   • Ito’s Lemma and Its Financial Significance
   • Stochastic Differential Equations (SDEs)
   • Solving SDEs in Finance: Methods and Techniques

6. Applications of Ito’s Lemma in Option Pricing

   • Deriving Option Pricing Models Using Ito’s Lemma
   • The Black-Scholes Model and Its Derivation
   • Properties of the Black-Scholes Model
   • Sensitivity Analysis of Option Prices (Greeks)

Part III: Advanced Topics in Stochastic Calculus for Finance

7. Stochastic Differential Equations in Finance

   • Introduction to SDEs in Finance
   • Types of SDEs: Linear and Nonlinear Models
   • Numerical Solutions to SDEs: Monte Carlo and Finite Difference Methods
   • Applications to Interest Rates and Fixed Income Markets

8. The Term Structure of Interest Rates

   • Modeling the Evolution of Interest Rates
   • The Heath-Jarrow-Morton Model
   • Affine Term Structure Models
   • Calibration and Estimation of Interest Rate Models

9. Advanced Option Pricing Models

   • Stochastic Volatility Models: Heston and SABR Models
   • Jump Diffusion Models and Lévy Processes
   • Modeling Credit Risk and Counterparty Risk
   • Multi-Asset and Exotic Option Pricing

Part IV: Numerical Methods and Computational Techniques

10. Numerical Methods for Stochastic Processes

    • Monte Carlo Simulation in Financial Modeling
    • Finite Difference Methods for Solving SDEs
    • The Crank-Nicolson Scheme
    • Techniques for Model Calibration and Parameter Estimation

11. Computational Methods for Option Pricing

    • Binomial Tree Models and Lattice Methods
    • Efficient Computation of Greeks
    • Stochastic Differential Equation Solvers
    • Optimizing Computation for Large-Scale Financial Models

12. Risk Management and Stochastic Calculus

    • Value at Risk (VaR) and Its Applications
    • Stress Testing and Scenario Analysis
    • Hedging Strategies with Stochastic Models
    • Managing Portfolio Risk Using Stochastic Calculus

Part V: Conclusion and Further Directions

13. Recent Developments and Future Directions in Stochastic Finance

    • Advances in Stochastic Process Theory and Its Financial Applications
    • The Role of Machine Learning in Stochastic Finance
    • The Future of Computational Finance: Big Data and AI
    • Challenges and Opportunities in Financial Modeling

14. Conclusion and Summary

    • Recap of Key Concepts in Stochastic Calculus for Finance
    • Practical Applications and Real-World Implications
    • Final Remarks and Further Reading

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