Essays in asset pricing and financial econometrics
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The objective of this dissertation is to develop and test new theoretical and empirical pricing models for assets such as American-styled derivatives, exotic (non-standard) hybrid debts and oil-related securities. In Chapter 1, we develop a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early exercise premium representation of the American option price. The advantages of the proposed approach are threefold. First, our approach does not require the transition density and characteristic functions of the underlying asset dynamics to be attainable in closed form. Second, our approach is fast and accurate, while the prices and exercise policy can be jointly produced. Third, our approach has a wide range of applications. We show theoretically that the proposed approximations of the price and optimal exercise boundary converge to the true ones. A efficiency study between popular methods and the presented method is constructed. We also provide a numerical method based on a step function to implement our proposed approach. Applications to nonlinear mean-reverting models, double mean-reverting models, Merton’s and Kou’s jump-diffusion models are discussed. In Chapter 2, we focus on the pricing of one specific asset called contingent convertible bonds (CoCos). CoCos become popular since late 2000s due to the change of regulations in the banking sectors and are viewed as important instruments to fulfill regulatory capitals. We propose a valuation approach for CoCo based on its issuing bank’s bad debt ratio, which is commonly accepted as an indicator of the bank’s current solvency and triggers the default of the CoCo as soon as it breaches some predetermined threshold. We formulate models for the bank’s bad debt ratio and stock price using a jump-diffusion structure with correlated jump risk, which takes into account the typical negative influence of the bad debt ratio on the share price. Both write-down and equity-convertible CoCos are considered, and for the latter we also propose a class of new power mechanisms of conversion that generalize traditional conversion ratios while still remaining analytically tractable. A novel computational algorithm is also proposed. A set of valuation formulas are derived for the CoCos in semi-closed form, and their performance is further illustrated with a case study. In Chapter 3, I develop an empirical framework to provide a precursory analysis on the nexus between prices of oil-related securities, Covid-19 and risk neutral higher moments (RNM). Using daily data of oil future options, I calculate the option-implied RNM and moment contract prices. I then conduct regression analysis between moment prices, daily Covid-19 cases, oil returns and oil future option returns, together with a series of other regressors. Major findings are: 1) the spread of Covid-19 made the risk-neutral skewness more negative, implying an increase in risk aversion in the oil market; 2) return predictability of RNMs increased during the period when the pandemic was severe; and 3) the structure of oil option prices recovers as vaccination popularizes.