About the IATACF

Module 3 – Stocks and Foreign Exchange

Module two of the course will delve into the foundations of portfolio theory, specifically Module three delves into the significance of the Black-Scholes theory as both a theoretical and practical pricing model rooted in the concepts of delta hedging and the absence of arbitrage. This module will provide you with insights into the theory’s implications, focusing on equities and currencies, and employing a variety of mathematical techniques to acquaint you with contemporary methods in use.

Black-Scholes Pricing Model

Assumptions Underlying the Black-Scholes Equation
Core Principles of Options Theory: Delta Hedging and Arbitrage-Free Pricing
Understanding the Black-Scholes Partial Differential Equation
Adapting the Model for Commodity and Currency Options
Black-Scholes Formulas for Calls, Puts, and Simple Digital Options
Significance and Role of the Greeks: Delta, Gamma, Theta, Vega, and Rho
American Options and Early Exercise Considerations
Linking Option Values to Market Expectations
Applying Martingale Theory to Option Pricing
Martingales and Their Connection to Partial Differential Equations: Selection, Timing, and Rationale
Introduction to Computational Methods in Option Valuation
Exploring Strategies with Exotic Options
Grasping the Concept of Volatility in Financial Markets
Advanced Computational Techniques for Quantitative Finance
Real-World Applications in Derivatives Trading
Mastery of the Greeks: Advanced Sensitivity Analysis
Cutting-Edge Volatility Modeling in Efficient Markets
Navigating the World of Foreign Exchange (FX) Options

Applying Martingale Theory to Option Valuation

Comprehensive Examination of the Greeks
Delta, Gamma, Theta, Vega, and Rho Explained
Exploring Higher-Order Greeks
Practical Applications of the Greek Letters in Trading

Martingales and Partial Differential Equations: Selection, Timing, and Rationale

Evaluating derivative prices through an expectation approach
Utilizing Girsanov’s theorem and measure transformations
Understanding the foundational asset pricing equation
Applying the Black-Scholes Formula
Implementing the Feynman-Kac formula
Exploring extensions to the Black-Scholes model, considering dividends and time-varying parameters
Employing Black’s formula for options on futures
Employing Greek values for risk assessment in trading

Introduction to Computational Methods

Rationale behind employing Monte Carlo simulation for pricing
Approaches for discretizing derivatives through grids
Application of the explicit finite-difference technique

Exotic Option Strategies

Exotic Options: Describing unique features and attributes
Time Dynamics (Bermudian Options): Examining time-related aspects, particularly in Bermudian options
Path-Dependent Nature and Inherent Choices: Analyzing how options are influenced by their historical paths and associated decision points
Asian Options: Exploring the characteristics and attributes specific to Asian options

Grasping the Concept of Volatility

Various Forms of Volatility
Information on Volatility from Options Market Prices
The Volatility Curve
Volatility Skews and Smiles
Volatility Arbitrage: Choosing Between Implied and Historical Volatility for Hedging

Advanced Computational Techniques

Numerical approaches with implicit finite-difference techniques, such as Crank-Nicolson schemes
Douglas schemes for solving differential equations
Utilizing Richardson extrapolation for enhanced accuracy
Handling American-style options exercise methods
Employing explicit finite-difference techniques for two-factor models
Application of ADI (Alternating Direction Implicit) and Hopscotch methods

Real-world Applications in Derivatives Trading

Periodic Occurrence of Option Traders
Emergence of Put-Call Parity in the Early 1900s
Early 20th Century Options Arbitrage Between London and New York (Nelson, 1904)
The Practice of Delta Hedging
Arbitrage Concepts in the Early 1900s
The Presence of Fat Tails in Price Data
Key Concepts in Finance
The Dynamic Nature of Delta Hedging
Understanding Bates Jump-Diffusion Models

Mastering Greeks: Advanced Sensitivity Analysis

Identification of exotic option types along with their associated contract details
Classification of exotic options based on key characteristics
Comparison and differentiation of various contract types
Valuation of exotic options through Monte Carlo simulation
Exotic option pricing through the utilization of partial differential equations and subsequent finite difference methods

Cutting-edge Volatility Modeling in Efficient Markets

Examining the correlation between implied volatility and realized volatility in a deterministic setting.
Distinguishing between ‘random’ and ‘uncertain’ factors.
Valuing contracts in the presence of uncertain variables like volatility, interest rates, and dividends.
Dealing with non-linear pricing equations.
Implementing optimal static hedging strategies using traded options.
Illustrating how calibration efforts are challenged by non-linear equations.

Navigating the World of Foreign Exchange (FX) Options

Gain insights into the historical evolution of the FX market, exploring its journey to become the largest global market.
Familiarize yourself with the current practices and conventions within the FX market.
Recognize the magnitude and significance of the FX option market, including its development and contemporary applications.
Comprehend the influence of volatility on options, along with key concepts like “out of the money” and the “volatility surface.”
Acquire the ability to price straightforward FX options, both standalone and those structured from a combination of put and call options.
Grasp the pricing mechanisms for other path-dependent FX options, encompassing American and Bermudan options.
Understand the principles of risk management for FX options and gain proficiency in basic Delta hedging strategies.
Develop the skills to conduct historical back-testing and appreciate its role in formulating trading and hedging strategies, such as carry trades, option selling, and hedging various asset classes.

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