Dissertations, Theses, and Capstone Projects

Date of Degree

6-2021

Document Type

Dissertation

Degree Name

Ph.D.

Program

Business

Advisor

Liuren Wu

Committee Members

Jun Wang

Xi Dong

Yuzhao Zhang

Subject Categories

Finance and Financial Management

Keywords

option implied volatility skew, option returns, delta hedging, term structure, variance risk premium, machine learning

Abstract

This dissertation consists of three chapters that examine the cross-sectional behaviors of option implied volatility skew and option risk premiums/returns as well as their term structures, using the structural factor model approach as well as the machine learning techniques.

Chapter 1: The introduction discusses the motivation of this dissertation, interlinks and the main findings of the three chapters.

Chapter 2: The slope of the option implied volatility plot against the strike reflects the risk-neutral skewness of the underlying security's conditional return distribution. We identify two principal risk sources that contribute to the cross-sectional variation of individual stock options' implied volatility skew: the market risk exposure of the stock's return and the company's default risk. Once controlled for these two risk exposures and the implied volatility level, the remaining idiosyncratic variation of the implied volatility skew reflects more of investor expectation and sentiment on the stock's future price movement and can be used to predict future stock returns with more consistency.

Chapter 3: Classic option pricing theory shows that the risk of underwriting an option can be completely removed via dynamic delta hedging when the underlying security can be traded frictionlessly without cost and the security price moves diffusively with known volatility. In such an idealistic environment, the option is redundant security and underwriting it does not earn any extra risk premium other than the risk premium embedded in the underlying security investment. In practice, there are limits to the dynamic hedging strategy that prevent the option underwriters from fully removing their risk exposure. These limits include the non-zero cost associated with trading the underlying security and other hedging instruments, uncertainty about the security return's volatility level and its variation, and random security price jumps that cannot be effectively hedged by the delta hedging strategy. To the extent that delta hedging can be costly and cannot fully remove all the risks, investors require a premium for the remaining risk in underwriting an option. In this paper, we examine the cross-sectional variation of investment returns from underwriting options on different individual stocks, and attribute the cross-sectional variation to variations in limits to dynamic hedging.

Chapter 4: This paper adopts a data driven approach using the machine learning technology to conduct a comprehensive study of option return predictability based on a rich set of firm fundamental characteristics. Firstly, we use the classical OLS regressions with Fama French three factors as the baseline model and find that the common risk factors, book-to-market, size and momentum factors do not work very well collectively in predicting individual option returns, as evidenced by the negativity of out-of-sample performance. Then we include the elastic net, random forest and gradient boosted regression trees as typical machine learning methods to address the multi dimensional challenge when simultaneously considering a large number of features. We find that different models agree on a set of predominant factors: momentum, illiquidity, financial statement health, and volatility risk factors. Next we classify the features and gauge how investors' concerns and investment style change through our sample years. We show that as time goes by, the market style concentrates more on risk and liquidity factors. On the model level, the comparison of the performance of trees models with the linear models reveals that the tree model does not enhance the option return predictability by a great amount, but is much computationally expensive and hard to interpret the results. The option return predictability does not gain too much from the higher nonlinearities. Lastly, we investigate the complexity of the machine learning models and find that the option investors focus on fewer features, reflecting that firm characteristics carry partially redundant and fundamentally noisy signals.

Chapter 5 concludes the dissertation.

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