Essays on Option Pricing

Abstract

Derivative contracts play a fundamental role in the financial system since they provide unique flexibility and precision in financial strategies, which are not possible with other instruments. Among these contracts, options are the most traded derivative contracts worldwide, with a volume of 108.2 billion contracts in 2023 and, in the first four months of 2024, their trading volume increased by 104 percent.1 The use of options has driven major innovations in financial markets, enabling the development of instruments such as contingent claims, structured and volatility derivatives. By replicating the pay-off of other financial assets, options contribute to market efficiency through synthetic positions that take advantage of price inefficiencies across different assets and markets. Furthermore, synthetic positions enhance market liquidity. For investors, options are essential tools in risk and portfolio management, allowing them to hedge against asset volatility and leverage their positions. Option pricing facilitates future estimates of the underlying asset volatility and reflects market expectations. The concept of implied volatility2 which captures market uncertainty, serves as a robust measure for future volatility forecasting. To sum up,options are a critical component of modern finance, and their role in the financial markets is crucial for maintaining stability. The Black and Scholes (1973) model revolutionized options pricing by providing a closed-form solution to value options. Since then, extensive research has built on the theoretical framework of option pricing, price and return dynamics, empirical analysis, and forecasting. This cumulative dissertation comprises four papers that contribute to this ongoing research by applying option pricing to company valuation, exploring options rates of return dynamics from multiple perspectives, and analyzing options in the rapidly evolving decentralized finance ecosystem. The Merton (1973) model significantly transformed company valuation by representing equity and debt as options on company’s assets. The first paper extends the computaion of the cost of capital within the Merton (1973) and Modigliani and Miller (1958) frameworks incorporating credit risk. This framework also enables the calculation of the value of the tax shield under credit risk. The paper critically discusses the debt beta approach where, under the Capital Asset Pricing Model, the debt beta is calculated with respect to a combined market portfolio of stocks and corporate bonds, which does not exist. Therefore, the first paper proposes an option-based and combined option- factor sensitivities approach that integrates credit risk into the Weighted Average Cost of Capital computations. The paper also compares the data requirements of the discussed approach and conducts a peer-group valuation of Apple Inc. assuming it were not a publicly traded company. Since the major research on options has been conducted for the US market, in the second and third papers, this dissertation empirically analyzes options rates of return dynamics and compares the results on the US and the EU markets. The second paper builds on Aretz et al. (2023) study and explores the relationship between equity option rates of return and underlying volatility. The empirical study employs the Fama-French-Carhart and expo- nential GARCH models to decompose the underlying volatility into systematic and idiosyncratic components and examines their impact on option rates of return across different moneyness levels, including nonlinear relationship. The paper provides detail discussion of systematic and idiosyncratic volatility slopes conditional on moneyness. The results contribute to the literature by disclosing the nuanced impact of underlying systematic volatility on option rates of return. The third paper extends the second by investigating the cross-section of index option rates of return again on both the US and EU markets. It employs the ARIMA-GJR-GARCH model to estimate the underlying index volatility and deploys two mixed effect panel regressions. The regression analysis focuses, first, on the cross-section of option rates of return with respect to underlying volatility, volatility of volatility, leverage, moneyness, and elasticity. Second, the analysis compares the elasticity sensitivities to its components, i.e., delta and leverage, and discusses the elasticity dynamics across options and markets with respect to volatility and moneyness bins. These papers contribute to the literature by providing empirical evidence on options market dynamics and highlighting differences that should be taken into consideration for region-specific risk management. Concluding this dissertation and with regard to a relatively new but rapidly growing financial market, the fourth paper explores the pricing of cryptocurrency options on-chain as a part of a decentralized finance ecosystem. This is the first empirical study in its field and investigates the pricing of wrapped Bitcoin and Ethereum options in the Hegic protocol. It utilizes the two regimes Markov Switching Autoregression (GJR) GARCH model to estimate the underlying volatility and the feasible GLS regression to examine the discrepancies between the Hegic and the benchmark prices. The regression analysis includes the rate of return, volume, and volatility of the underlying and options’ amount, strike, and moneyness. The paper also discusses the difference between implied and market volatility, indicating potential mispricing exploitation. This paper contributes to volatility forecasting and opens a discussion on a sophisticated automated market maker for pricing options in decentralized finance ecosystem. Overall, this dissertation shows a manifold contribution to scientific research on option pricing. It covers both the theoretical and empirical perspectives of option pricing, and the traditional and decentralized financial markets. The results are practically relevant for risk assessment and management, investment strategies optimization, and financial modeling.