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Estimating option implied risk-neutral densities using spline and hypergeometric functions



Summary  We examine the ability of two recent methods – the smoothed implied volatility smile method (SML) and the density functionals based on confluent hypergeometric functions (DFCH) – for estimating implied risk-neutral densities (RNDs) from European-style options. Two complementary Monte Carlo experiments are conducted and the performance of the two RND estimators is evaluated by the root mean integrated squared error (RMISE) criterion. Results from both experiments show that the DFCH method outperforms the SML method for the overall quality of the estimated RNDs concerning both accuracy and stability. An application of the two methods to the OTC currency options market is also presented.