Conditional risk-neutral density from option prices by local polynomial kernel smoothing with no-arbitrage constraints

Abstract

A new approach is considered to estimate risk-neutral densities (RND) within a kernel regression framework, through local cubic polynomial estimation using intraday data. There is a new strategy for the definition of a criterion function used in nonparametric regression that includes calls, puts, and weights in the optimization problem associated with parameters estimation. No-arbitrage constraints are incorporated into the problem through equality and bound constraints. The approach considered yields directly density functions of interest with minimum requirements needed. Within a simulation framework, it is demonstrated the robustness of proposed procedures. Additionally, RNDs are estimated through option prices associated with two indices, S&P500 and VIX.