A1628
Title: Risk neutral density estimation through Hermite polynomials
Authors: Rui Pascoal - University of Coimbra, Faculty of Economics (Portugal) [presenting]
Ana Monteiro - University of Coimbra (Portugal)
Abstract: The focus is on ascertaining the robustness of Hermite polynomials in estimating risk-neutral densities (RND) with simulated data from the Black-Scholes-Merton (BSM) model, and market data from S\&P500 (SPX) index, Arch Resources (ARCH) and Cassava (SAVA) companies. Hermite polynomials are an expansion method within the family of semi-nonparametric approaches for estimating risk-neutral densities, introduced in a prior study. Through comparative analysis, the deviation of estimated risk-neutral densities from the theoretical ones is analyzed. Furthermore, in order to extract important information regarding market sentiment, skewness and kurtosis are retrieved for the estimated risk-neutral density functions obtained from the BSM simulated data and market data. With this information, it is concluded that as skewness increases, kurtosis decreases, and since leptokurtic distributions are obtained, a higher risk is expected. It is observed that for simulated data from the BSM model, the obtained estimates, when noise is introduced, only deviate from the theoretical densities for longer maturities. Also, when maturity increases, apparently, the quality of the estimation decreases, as expected. In addition, higher open interest is a possible criterion for strike selection. Finally, Hermite polynomials seem to be effective in obtaining proper RND estimates. Investors seem more pessimistic regarding the S\&P500 index and more confident about SAVA and ARCH companies.
