Book Description

There are many measures to price an option. This dissertation investigates a risk-adjusted measure to price the option with an alternative numeraire that retains the expected return of the underlying in the pricing equation. This model is consistent with the Black-Scholes model when their assumptions are imposed and is consistent with the standard capital asset pricing model. Unlike many asset pricing models that rely on historical data, we provide a forward-looking approach for extracting the ex ante return distribution parameters of the underlying from option prices. Using this framework and observing the market prices of options, we jointly extract implied return and implied volatility of the underlying assets for different days-to-maturity using a grid search method of global optima. Our approach does not use a preference structure or information about the market such as the market risk premium to estimate the expected return of the underlying asset. We find that when there are not many near-the-money traded options available our approach provides a better solution to forecast future volatility than the Black-Scholes implied volatility. Further, our results show that option prices reflect a higher expectation of stock return in the short-term, but a lower expectation of stock return in the long-term that is robust to many alternative tests. We further find that ex ante expected returns have a positive and significant cross-sectional relation with ex ante betas even in the presence of firm size, book-to-market, and momentum. The cross-sectional regression estimate of ex ante market risk premium has a statistical significance as well as an economic significance in that it contains significant forward-looking information on future macroeconomic conditions. Furthermore, in an ex ante world, firm size is still negatively significant, but book-to-market is also negatively significant, which is the opposite of the ex post results. Our risk-adjusted approach provides a framework for extraction of ex ante information from option prices with alternative assumptions of stochastic processes. In this vein, we provide a risk-adjusted stochastic volatility pricing model and discuss its estimation process.