This dissertation develops two new parametric and nonparametric methods for estimating risk-neutral measures (RNM) which embody important information about market participants’ sentiments concerning prices of the underlying asset in the future, and investigates empirical performance of parametric RNM estimation methods.
The first essay, “Estimation of Risk Neutral Measures using the Generalized Two-Factor Log-Stable Option Pricing Model”, constructs a simple representative agent model to provide a theoretical framework for the log-stable option pricing model and then implements a new parametric method for estimating the RNM using a generalized two-factor log-stable option pricing model. Under the generalized two-factor log-stable uncertainty assumption, the RNM for the log of price is a convolution of two exponentially tilted stable distributions. The generalized two-factor log-stable RNM provides a sufficiently accurate tool for estimating the RNM from observed option prices even if the log-stable assumption might not be satisfied. I estimate the RNM using the S&P 500 index options and find that the generalized two-factor log-stable model gives better performance than alternative models in fitting the observed option prices.
The second essay, “Parametric Risk Neutral Measure Estimation Methods: A Horse Race”, implements 12 parametric RNM estimation methods by means of the closed-form or characteristic function of RNM distributions and then compares the empirical performance under three criteria – the root mean squared error (RMSE), likelihood ratio (LR), and the root mean integrated squared error (RMISE). The empirical results show that the generalized two-factor log-stable model outperforms other alternative parametric RNM estimation methods.
The third essay, “Nonparametric Estimation of Risk-Neutral Measures using Quartic B-Spline CDFs with Power Tails”, proposes a new nonparametric (BSP) method. I model a RNM cumulative distribution function (CDF) using quartic B-splines with power tails so that the resulting RNM probability density function (PDF) has continuity C2 and arbitrage-free properties. Since the number of knots is selected optimally in constructing the quartic B-spline RNM CDF, my method avoids both overfitting and oversmoothing. To improve computational efficiency and accuracy I introduce a 3-step RNM estimation procedure that transforms a nonlinear optimization problem into a convex quadratic program, which is efficiently solved by numerical optimization software.