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.
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
Objectives and Topics
The paper examines the fundamental determinants of European option prices by conducting a simulation study based on S&P 500 stock data. It seeks to identify how variations in stock return means and return volatility influence the pricing of call and put options under ceteris paribus conditions.
- Simulation of stock price paths based on historical return data
- Mathematical modeling of European option payoff and discounting
- Assessment of the impact of return means on option premiums
- Analysis of volatility effects on call and put option values
- Correlation analysis between underlying stock characteristics and option prices
Excerpt from the Book
1 Introduction
When Thales of Miletus in the 6th century B.C. secured himself the right to rent the citys olive presses for a fixed price one year in advance, he may have established the first futures contract in human history. Anticipating an upcoming olive harvest that would greatly surpass the years before, he now was able to buy (rent) low and sell high, when his prediction was correct. The time came around, and the olive harvest was, as foreseen, a great one, making him a rich man. Although anecdotal, this story captures the essence of a common derivative: the forward/future contract. Besides being an interesting object of speculative investing, its technical use is to hedge ones position against the risk of large changes in the value of the underlying asset, by agreeing with the option issuer to a future trade with a fixed price. When the execution of this trade is only optional, the contract is called option.
The price of a future contract can be determined by the current commodity price and the costs of carrying the commodity until the maturity of the contract. The price of an option contract is, generally, determined by the payoff of the option plus a part that prices the risk of the value change of the underlying asset, which are also referred to as the intrinsic and the time value. The valuation of the time value of an option is much more complicated than the valuation of the cost of carry and because of this a huge topic of academic research.
Summary of Chapters
1 Introduction: Provides a historical and theoretical context for derivatives, specifically forward and option contracts, and introduces the research aim of analyzing price determinants.
2 Theoretical Framework and Simulation Methodology: Outlines the mathematical formulas for simulating stock prices and calculating discounted option payoffs, while formulating testable hypotheses.
3 Data: Describes the source and selection criteria for the S&P 500 stock dataset, including statistical observations regarding return distribution and skewness.
4 Results: Presents the simulated stock and option price data, evaluating the impact of return mean and volatility shifts against the formulated hypotheses.
5 Conclusion: Summarizes the findings, noting that while the first hypothesis regarding return means was confirmed, results for volatility remain mixed and dependent on specific distributional assumptions.
Keywords
Option Pricing, Stock Returns, Simulation, Volatility, Return Mean, S&P 500, Derivative Valuation, Financial Modeling, Market Risk, European Options, Call Options, Put Options, Quantitative Finance, Asset Pricing
Frequently Asked Questions
What is the fundamental focus of this assignment?
The assignment explores the relationship between stock returns and European option prices using a simulation approach to isolate the effects of return means and volatility.
Which central topics are addressed?
The study centers on option valuation theory, the impact of market parameters on derivative pricing, and the empirical analysis of S&P 500 constituents.
What is the primary research question?
The research aims to determine how stock return mean and volatility influence option prices, specifically testing whether higher returns and higher volatility lead to predictable price changes in options.
Which scientific methodology is applied?
The author employs a quasi-simulation methodology, using historical daily adjusted prices of 448 S&P 500 stocks to simulate future price paths and calculate hypothetical option premiums.
What is covered in the main body of the text?
The body covers the theoretical derivation of pricing models, the data processing of the stock sample, and the subsequent results of the simulation scenarios regarding stock and option price behavior.
Which keywords best characterize this work?
Key concepts include Option Pricing, Return Volatility, Simulation, European Options, and Asset Pricing.
How does the author test the relationship between return volatility and option prices?
The author varies the volatility parameter in the simulation and compares the resulting option premiums to determine if there is a monotonic relationship across different strike prices.
What is the significance of the simulated return skewness?
The author notes that the negative return skewness found in the sample influences the simulation results, suggesting that stock distribution characteristics are critical for accurate option pricing models.
What conclusion does the author reach regarding the two hypotheses?
The author confirms the first hypothesis (that higher returns lead to higher call prices), but finds only mixed evidence for the second hypothesis concerning volatility, as the observed effects depend heavily on the underlying return distribution.
- Quote paper
- Martin Georg Haas (Author), 2018, Stock Returns and Option Prices. A Simulation Analysis, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/1043527
