About the IATACF

Module 1: Fundamentals of Finance

Module one will commence with an introduction to the principles of applied Itô calculus as a modeling framework. You will be equipped with the ability to construct essential tools utilizing stochastic calculus and martingale theory. This module will also familiarize you with the application of straightforward stochastic differential equations and their corresponding Fokker-Planck and Kolmogorov equations.

Asset Price Volatility

Various Approaches to Financial Analysis
Analyzing Time-Series Data for Return Modeling
Unpredictable Behavior of Asset Prices
Necessity of Probability-Based Models
Wiener Process: A Mathematical Representation of Randomness
Lognormal Random Walk: A Key Model for Equities, Currencies, Commodities, and Indices

Binomial Pricing Model

A basic representation of the random walk of asset prices.
The practice of delta hedging.
The absence of arbitrage opportunities.
Fundamental principles underlying the binomial option pricing method.
The concept of risk neutrality.

Partial Differential Equations (PDEs) and Probability Density Functions for State Transitions.

Taylor series
Trinomial random walk
Functions for transition density
Introduction to stochastic differential equations
Utilizing similarity reduction for partial differential equation solutions
Fokker-Planck and Kolmogorov equations

Introduction to Stochastic Calculus 1 in Practice

Generating Moments Function
Building Brownian Motion (Wiener Process)
Stochastic Variable Functions and Itô’s Lemma
Practical Applications of Itô’s Calculus
Integrating Stochastic Processes
Understanding the Itô Integral
Illustrative Examples of Common Stochastic Differential Equations

Introduction to Stochastic Calculus 2 in Practice

Expansions of Itō’s Lemma
Key Scenarios – Equities and Interest Rates
Generating Standardized Normal Random Variables
The Equilibrium Distribution

Stochastic Processes With Certain Properties

Expanding the Binomial Model
Understanding the Probabilistic Framework: Sample Space, Filtration, and Measures
Expectation Concepts: Conditional and Unconditional
Transitioning Measures: Change of Measure and the Radon-Nikodym Derivative
Delving into Martingales and Itô Calculus
Exploring Additional Aspects of Itô Calculus
Exponential Martingales, Girsanov Transformation, and Measure Change