This paper is concerned with analyzing the basic determinants of option prices. These are the information derived from the underlying stock, namely the mean and the volatility of its returns. Therefore, this paper aims at answering the question, what influence stock return mean and volatility have on the respective option prices. This can be important to option traders trying to identify the stocks for which to trade options, by providing an understanding for the foundations of the option pricing and the information those prices provide.
To isolate these basic determinants from the other influences, described above as structural and institutional factors, a simulation study is conducted. Section 2 will provide the theoretical framework and simulation methodology for the study. Section 3 describes the used dataset and section 4 presents and discusses the results of the simulation.
Inhaltsverzeichnis (Table of Contents)
- 1 Introduction
- 2 Theoretical Framework and Simulation Methodology
- 2.1 Stock Price Simulation
- 2.2 Option Price Calculation
- 2.3 Simulation Implementation
- 2.4 Hypotheses
- 3 Data
- 4 Results
- 4.1 Simulated Stock Prices
- 4.2 Simulated Option Prices
- 5 Conclusion
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This paper aims to analyze the fundamental determinants of option prices, specifically the influence of stock return mean and volatility on option prices. It seeks to understand how these factors impact option pricing, providing insights for traders looking to identify suitable stocks for options trading. A simulation study is employed to isolate these core determinants from other structural and institutional market influences.
- The relationship between stock return characteristics (mean and volatility) and option prices.
- The use of simulation to isolate the effects of stock returns from other market factors on option pricing.
- Application of option pricing models and their underlying assumptions.
- Analysis of simulated stock and option price distributions.
- Implications for option traders in identifying suitable trading opportunities.
Zusammenfassung der Kapitel (Chapter Summaries)
1 Introduction: This chapter introduces the concept of options and futures contracts, highlighting their differences and relative popularity. It discusses the complexities of option pricing, emphasizing the importance of the underlying asset's price and volatility. The chapter establishes the paper's objective: to analyze the influence of stock return mean and volatility on option prices using a simulation study, isolating these factors from other market influences. The historical context of option trading is presented through the anecdote of Thales of Miletus, while the limitations of existing models, such as the Black-Scholes model, are also discussed. The introduction serves to provide both a practical and theoretical framework for the study.
2 Theoretical Framework and Simulation Methodology: This chapter details the simulation methodology employed to analyze the relationship between stock returns and option prices. It outlines the mathematical models used for simulating stock prices (Equation 1) and calculating option prices for both put and call options (Equations 2 and 3). The chapter explains the implementation of the simulation, involving the generation of 1000 simulated stock prices based on real stock return data, and using these to calculate option prices for various strike prices. The use of a fixed risk-free rate is also detailed. This section lays the groundwork for the empirical analysis presented in subsequent chapters. The methodology centers on using characteristics of a real stock sample to simulate option price behavior under controlled conditions, avoiding strong distributional assumptions.
3 Data: [Note: The provided text lacks a detailed description of the data used in the study. This section would typically describe the source, selection criteria, and characteristics of the stock data used in the simulations. This information is crucial for assessing the validity and reliability of the results.]
4 Results: [Note: The provided text only mentions the presentation and discussion of simulation results in this section. A complete summary would require details on the findings regarding the relationship between simulated stock prices, option prices, and the manipulated parameters (mean and volatility). The summary would explain the observed correlations and their significance within the context of the research question.]
Schlüsselwörter (Keywords)
Option pricing, stock returns, volatility, simulation, implied volatility, Black-Scholes model, futures contracts, hedging, risk management, quantitative finance.
Frequently Asked Questions: Comprehensive Language Preview of Option Pricing Simulation
What is the main objective of this research paper?
The primary goal is to analyze how the average return and volatility of a stock affect its option prices. The study uses a simulation to isolate these key factors from other market influences, providing insights for traders seeking suitable options trading opportunities.
What methodology is used in this study?
The research employs a simulation study. Stock prices are simulated using a specific mathematical model (Equation 1), and these simulated prices are then used to calculate option prices for both call and put options (Equations 2 and 3). The simulation generates 1000 simulated stock prices based on real stock return data, allowing for the analysis of option prices at various strike prices under controlled conditions, without making strong assumptions about the distribution of returns. A fixed risk-free interest rate is utilized.
What are the key themes explored in the paper?
The key themes revolve around the relationship between stock return characteristics (mean and volatility) and option prices; the use of simulation to isolate the effects of stock returns; the application of option pricing models; the analysis of simulated stock and option price distributions; and the implications for option traders in identifying suitable trading opportunities.
What are the limitations of this study?
The provided text lacks detail on the data used (source, selection criteria, characteristics). This omission limits the ability to fully assess the validity and reliability of the results. Additionally, while the chapter summaries introduce the methodology and research question, specific details on the simulation results (Chapter 4) are missing. Without these details, the overall findings and conclusions cannot be thoroughly evaluated.
What are the key chapters and their contents?
The paper includes: an introduction outlining the context of options trading, a chapter detailing the theoretical framework and simulation methodology used, a chapter (lacking detail) on the data employed, a results chapter (lacking details on the findings), and a concluding chapter. The introduction specifically mentions the limitations of existing option pricing models, such as the Black-Scholes model, and uses the historical example of Thales of Miletus to provide context.
What are the keywords associated with this research?
Keywords include: Option pricing, stock returns, volatility, simulation, implied volatility, Black-Scholes model, futures contracts, hedging, risk management, and quantitative finance.
What kind of options are discussed?
The research discusses both call and put options.
Where can I find more information on the data used?
The provided text lacks detailed information on the data source and characteristics. This information is crucial for evaluating the study's validity and reliability.
What are the specific findings of the simulation?
The provided text does not offer specific results from the simulation study. Details on the relationships between simulated stock prices, option prices, and the manipulated parameters (mean and volatility) are missing.
What are the implications of the research for option traders?
The research aims to provide insights for traders seeking to identify suitable stocks for options trading by highlighting the relationship between stock return characteristics and option prices. However, without the detailed results, the specific implications for traders remain unclear.
- Quote paper
- Martin Georg Haas (Author), 2018, Stock Returns and Option Prices. A Simulation Analysis, Munich, GRIN Verlag, https://www.grin.com/document/1043527
