Option Implied Risk-Neutral Density Estimation: A Robust and Flexible Method

In practice, a reliable and flexible estimation of risk-neutral density from empirical data is a challenging task since it can not be observed directly from the market. In this study, we apply Bernstein polynomial basis to recover the risk-neutral density function from the observed price quotes of European-type option contingent on an underlying asset. More importantly, we perform an extensive simulation study to examine the flexibility and robustness of the proposed method in recovering different shapes of the true risk-neutral density function from noisy option price quotes. Also, we compare the proposed method with other two popular nonparametric methods namely the constrained local linear polynomial smoothing and the smoothed implied volatility smile reported in the literature. Accuracy and stability of the three nonparametric methods are assessed by the root mean integrated square error criterion. The simulation results show that the proposed method is flexible as it exhibits the various shapes of the true risk-neutral density function even when the volatility is high. Moreover, in comparison with the other two methods, the proposed approach is robust and yields more accurate densities even in the presence of noise. Finally, we demonstrate the applicability of the proposed method in recovering a smooth risk-neutral density function from the S&P 500 market index option data.