Contents
Introduction to the Techniques of Derivative Modeling
1.2.3 Two Initial Methods for Modeling Derivatives
1.2.5 The Archetypal Security Process: Normal Returns
Preliminary Mathematical Tools
2.2 n-Dimensional Jacobians and n-Form Algebra
2.3 Functional Analysis and Fourier Transforms
2.4 Normal (Central) Limit Theorem
2.7 Functions of Two/More Variables: Path Integrals
3.3 Variable Changes to Get the Martingale
3.4 Other Processes: Multivariable Correlations
Applications of Stochastic Calculus to Finance
4.2 Analytic Formula for the Expected Payoff of a European Option
From Stochastic Processes Formalism to Differential Equation Formalism
5.1 Backward and Forward Kolmogorov Equations
5.2 Derivation of Black-Scholes Equation, Risk-Neutral Pricing
5.3 Risks and Trading Strategies
Understanding the Black-Scholes Equation
6.1 Black-Scholes Equation: A Type of Backward Kolmogorov Equation
6.2 Black-Scholes Equation: Risk-Neutral Pricing
6.3 Black-Scholes Equation: Relation to Risk Premium Definition
6.4 Black-Scholes Equation Applies to Currency Options: Hidden Symmetry ...