Risk-Neutral Densities and Their Application in the Piterbarg Framework

In this paper, we consider two well-known interpolation schemes for the construction of the JSE ShareholderWeighted Top 40 implied volatility surface. We extend the Breeden and Litzenberger formula to the derivative pricing framework developed by Piterbarg post the 2007 financial crisis. Our results show that the statistical moments of the constructed risk-neutral densities are highly dependent on the choice of interpolation scheme. We show how the risk-neutral density surface can be used to price options and briefly describe how the statistical moments can be used to inform trading strategies.