(A) study on the information content of option prices: estimation of implied probability distributions and its applications

Abstract

This thesis investigates some issues on the estimation of implied probability density functions (PDF) from option cross-sectional prices and their applications. In the former half part of this thesis, alternative measures for assessing the stability of implied PDFs from option prices are developed and applied. Once an implied PDF is recovered from option prices, I extend the methodology for deriving investors’ risk preferences in the latter part of this thesis. Using the KOSPI 200-, S&P 500-, FTSE 100- index options, it is found that the investors’ risk aversion functions are generally decreasing rather than constant across wealth. First, to assess the stability of PDFs implied by option prices, I develop and apply alternative measures other than distributional characteristics. The alternative measures are related to the stability of empirical results in the applications of implied PDFs such as pricing thinly traded options and recovering the risk aversion of investors. Using the KOSPI 200 index options in the Korean market, the performance between the double lognormal approximating function (DLN) method and the smoothed implied volatility smile (SMIV) method which are most widely used for estimating implied PDFs is compared. Empirical results show that while the SMIV method can produce a PDF with more stable summary statistics as in most previous researches, it cannot outperform the DLN method in terms of other measures. The sensitivity analysis by using the randomly perturbed prices increases the validity of these findings. Second, the methodology for deriving investors’ risk preferences from option prices is extended. Instead of assuming a well-behaved functional form for the underlying utility functions such as the power or the exponential, I assume (1) more flexible functional forms for RRA functions and for pricing kernels and (2) wider classes of utility functions. In the former case, the simple monomials for RRA functions and Chebyshev polynomials f...