This academic paper focuses on breaking down the magic of the Black-Scholes formula, which is used to value options. The author first introduces basic concepts like options, option strategies and the put-call parity to guide the reader through the underlying, basic concepts. To illustrate the use and the power of the Black-Scholes formula, two examples are calculated to better understand the complex steps involved in finding the call value. Finally, a failure case is presented, to show some pitfalls of this mathematical function.

Excerpt

Inhaltsverzeichnis (Table of Contents)

Introduction
From the Basics to the Parity
- Put and Call Options
- Put-Call Parity
Black-Scholes - An Option Pricing Model
- Assumptions of the Model and its Influencing Factors
- The Black-Scholes Formula
- The Black-Scholes Formula in Practice
  - Fictional Example
  - General Electric Example
- Excursion to the Greeks
Conclusion

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This text aims to provide a walkthrough of the Black-Scholes formula, a groundbreaking model in option pricing. It begins with foundational concepts of options and their pricing, progressing to a detailed explanation of the Black-Scholes model, its assumptions, and practical applications. The text also explores related concepts such as put-call parity.

Understanding Put and Call Options
The Black-Scholes Formula and its Derivation
Practical Applications of the Black-Scholes Formula
Put-Call Parity and its Relevance
Underlying Assumptions and Limitations of the Model

Zusammenfassung der Kapitel (Chapter Summaries)

Introduction: This introductory chapter sets the stage by highlighting the significant impact of the Black-Scholes model on financial practice. It traces the historical development of options trading, emphasizing the challenges in accurately pricing options before the advent of the Black-Scholes model. The chapter underscores the significance of the model's contribution to the field of finance and its subsequent widespread adoption by traders and academics alike, referencing key figures such as Robert Merton and Dan French. The inherent difficulty in pricing options due to fluctuating underlying asset prices is discussed, noting early attempts to incorporate various parameters into pricing models before the breakthrough achieved by Black and Scholes.

From the Basics to the Parity: This chapter establishes the fundamental concepts of put and call options, explaining their mechanics and potential for profit or loss based on underlying asset price fluctuations. It defines intrinsic and time value, and distinguishes between American and European options, explaining their exercise features. The chapter then introduces the concept of put-call parity and its importance within option pricing models, connecting this concept to the later presentation of the Black-Scholes formula. Examples of option combinations like covered call and protective put strategies are presented to illustrate practical applications of option trading and how they relate to put-call parity.

Black-Scholes - An Option Pricing Model: This chapter forms the core of the text, delving into the Black-Scholes model itself. It begins by outlining the underlying assumptions of the model, highlighting the factors that influence option pricing within its framework. The chapter then presents the Black-Scholes formula, explaining its components and their mathematical relationships. The practical application of the formula is illustrated through both fictional and real-world examples (General Electric), demonstrating how the model is used to determine option prices. Finally, the chapter provides a brief excursion into the concept of "Greeks" – measures of option sensitivity to various factors. This chapter connects the theoretical underpinnings of the model with practical implementation, establishing its relevance for real-world financial decisions.

Schlüsselwörter (Keywords)

Black-Scholes model, option pricing, put options, call options, put-call parity, financial derivatives, risk management, option valuation, financial modeling.

Frequently Asked Questions: A Comprehensive Guide to the Black-Scholes Option Pricing Model

What is this text about?

This text provides a comprehensive overview of the Black-Scholes option pricing model. It covers fundamental concepts, the model's formula, practical applications, and related topics like put-call parity.

What are the key themes explored in this text?

The main themes include understanding put and call options, deriving and applying the Black-Scholes formula, exploring put-call parity, and analyzing the model's underlying assumptions and limitations.

What topics are covered in the Introduction chapter?

The introduction highlights the Black-Scholes model's impact on financial practice. It discusses the historical context of options trading, the challenges in accurately pricing options before the model, and the contributions of key figures like Robert Merton and Dan French (Note: While Merton is correctly identified, Dan French is not a recognized figure in the development of the Black-Scholes model. This may be an OCR error). The chapter also emphasizes the difficulty in pricing options due to fluctuating asset prices and early attempts to create pricing models.

What does the "From the Basics to the Parity" chapter cover?

This chapter explains the fundamentals of put and call options, including their mechanics, profit/loss potential, intrinsic and time value, and the differences between American and European options. It introduces put-call parity and its significance, illustrating its application through examples of option combinations like covered call and protective put strategies.

What is the focus of the "Black-Scholes - An Option Pricing Model" chapter?

This core chapter details the Black-Scholes model, outlining its assumptions and the factors influencing option pricing. It presents the Black-Scholes formula, explaining its components and their mathematical relationships. Practical applications are shown through fictional and real-world (General Electric) examples. The chapter also briefly introduces "Greeks," which are measures of option sensitivity to various factors.

What is the conclusion of the text?

(The provided HTML does not include a separate Conclusion chapter summary. The conclusion would likely summarize the key findings and reiterate the importance of the Black-Scholes model in option pricing.)

What are the key assumptions of the Black-Scholes model?

(The specific assumptions are not explicitly listed in the provided summaries. However, the text indicates that the chapter on the Black-Scholes model details these assumptions.)

What are the practical applications of the Black-Scholes model?

The model is used to determine option prices. The text provides both fictional and real-world (General Electric) examples to illustrate its practical application.

What is put-call parity?

Put-call parity is a concept in options pricing that describes the relationship between the prices of put and call options with the same strike price and expiration date. The text explains its importance within option pricing models and its connection to the Black-Scholes formula.

What are the key words associated with this text?