Essays on Option Hedging and Application of the Black-Scholes Model

Abstract

This dissertation is composed of three essays related to hedging and application of the Black-Scholes model. The first essay is motivated by the short-lived arbitrage model, which has been shown to significantly improve in-sample option pricing fit relative to the Black-Scholes model. We imply both volatility and virtual interest rates to adjust minimum variance hedge ratios. Using several error metrics, we find that the hedging model significantly outperforms the traditional delta hedge and a current bench-mark hedge based on the practitioner Black-Scholes model. Our applications include hedges of index options, individual stock options and commodity futures options. Hedges on gold and silver are especially sensitive to virtual interest rates. The second essay analyzes the optimal capital structure of a nation from a corporate finance perspective. In particular, we draw an analogy between a nation's fiat money and corporate equity following Bolton and Huang (2018). Based on dynamic capital structure theory, we develop a stochastic model to determine the optimal combination of fiat money and foreign-currency debt used by a nation to fund its investments. The optimal capital structure of a nation depends on the trade-off between the inflation risk of fiat money and the default risk of foreign-currency debt. Introducing outstanding debt to our model sheds light on how a nation dynamically adjusts its capital structure over time. Based on an analysis of 22 emerging economies, the empirical results support our theoretical model of the capital structure of a nation. The third essay studies the impact of changes in the Federal funds rate target on option prices. I find that, on average, an unanticipated 25-basis-point cut in the Federal funds rate target is associated with an 18.5% increase in S&P 500 index call options prices and an 18.6% decrease in the put options prices. However, the result is reversed in the 2008 financial crisis, during which an unexpected cut in the Federal funds rate target raises market concerns. I conduct a quantitative analysis of the transmission channels in terms of underlying security price, volatility and interest rates. Evidence shows that FOMC monetary policy has more influence on the options market during the 2008 financial crisis. Bank equity options are more sensitive to the changes in the Federal funds rate target than S&P 500 index options.