Essays on the Econometrics of Option Prices
This dissertation develops new econometric techniques for use in estimating and conducting inference on parameters that can be identified from option prices. The techniques in question extend the existing literature in financial econometrics along several directions.
The first essay considers the problem of estimating and conducting inference on the term structures of a class of economically interesting option portfolios. The option portfolios of interest play the role of functionals on an infinite-dimensional parameter (the option surface indexed by the term structure of state-price densities) that is well-known to be identified from option prices. Admissible functionals in the essay are generalizations of the VIX volatility index, which represent weighted integrals of options prices at a fixed maturity. By forming portfolios for various maturities, one can study their term structure. However, an important econometric difficulty that must be addressed is the illiquidity of options at longer maturities, which the essay overcomes by proposing a new nonparametric framework that takes advantage of asset pricing restrictions to estimate a shape-conforming option surface. In a second stage, the option portfolios of interest are cast as functionals of the estimated option surface, which then gives rise to a new, asymptotic distribution theory for option portfolios. The distribution theory is used to quantify the estimation error induced by computing integrated option portfolios from a sample of noisy option data. Moreover, by relying on the method of sieves, the framework is nonparametric, adheres to economic shape restrictions for arbitrary maturities, yields closed-form option prices, and is easy to compute. The framework also permits the extraction of the entire term structure of risk-neutral distributions in closed-form. Monte Carlo simulations confirm the framework's performance in finite samples. An application to the term structure of the synthetic variance swap portfolio finds sizeable uncertainty around the swap's true fair value, particularly when the variance swap is synthesized from noisy long-maturity options. A nonparametric investigation into the term structure of the variance risk premium finds growing compensation for variance risk at long maturities.
The second essay, which represents joint work with Jia Li, proposes an econometric framework for inference on parametric option pricing models with two novel features. First, point identification is not assumed. The lack of identification arises naturally when a researcher only has interval observations on option quotes rather than on the efficient option price itself, which implies that the parameters of interest are only partially identified by observed option prices. This issue is solved by adopting a moment inequality approach. Second, the essay imposes no-arbitrage restrictions between the risk-neutral and the physical measures by nonparametrically estimating quantities that are invariant to changes of measures using high-frequency returns data. Theoretical justification for this framework is provided and is based on an asymptotic setting in which the sampling interval of high frequency returns goes to zero as the sampling span goes to infinity. Empirically, the essay shows that inference on risk-neutral parameters becomes much more conservative once the assumption of identification is relaxed. At the same time, however, the conservative inference approach yields new and interesting insights into how option model parameters are related. Finally, the essay shows how the informativeness of the inference can be restored with the use of high frequency observations on the underlying.
The third essay applies the sieve estimation framework developed in this dissertation to estimate a weekly time series of the risk-neutral return distribution's quantiles. Analogous quantiles for the objective-measure distribution are estimated using available methods in the literature for forecasting conditional quantiles from historical data. The essay documents the time-series properties for a range of return quantiles under each measure and further compares the difference between matching return quantiles. This difference is shown to correspond to a risk premium on binary options that pay off when the underlying asset moves below a given quantile. A brief empirical study shows asymmetric compensation for these return risk premia across different quantiles of the conditional return distribution.
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