Parallel computing in finance for estimating risk-neutral densities through option prices

Abstract

Option pricing is one of the most active Financial Economics research fields. Black-Scholes-Merton option pricing theory states that risk-neutral density is lognormal. However, markets' pieces of evidence do not support that assumption. More realistic assumptions impose substantial computational burdens to calculate option pricing functions. Risk-neutral density is a pivotal element to price derivative assets, which can be estimated through nonparametric kernel methods. A significant computational challenge exists for determining optimal kernel bandwidths, addressed in this study through a parallel computing algorithm performed using Graphical Processing Units. The paper proposes a tailor-made Cross-Validation criterion function used to define optimal bandwidths. The selection of optimal bandwidths is crucial for nonparametric estimation and is also the most computationally intensive. We tested the developed algorithms through two data sets related to intraday data for VIX and S&P500 indexes.