Estimating Option-Implied Risk-Neutral Densities: A Novel Parametric Approach

The author proposes a novel parametric approach to extract the implied risk-neutral density function from a cross-section of call option prices. By choosing a proper functional form, he shows that well-behaved risk-neutral densities can be generated by imposing restrictions on the parameters of the model. The results of the numerical experiments demonstrate that the method is capable of extracting risk-neutral densities with complex characteristics. Moreover, this study demonstrates the pricing performance of this method by generating arbitrage-free call option prices that can be used to produce well-behaved densities from S&P 500 Index options over a period of 10 years. Additionally, the empirical results indicate that the model is capable of extracting information from the right tail of call option prices. Finally, the author points out that the model is extremely easy to implement and calibrate and further extensions are straightforward. In particular, he illustrates how the model can be modified to incorporate a positive probability of default.