Shape constrained risk-neutral density estimation by support vector regression

• We propose a nonparametric method for estimating the risk-neutral density based on support vector regression.
• The method does not need preprocessing of the data and is robust to the bid-ask spread.
• The estimated density is arbitrage-free and contains full tails.
• The accuracy and stability of the method are very well.
• We demonstrate the effect of the method by Monte-Carlo simulations and empirical tests.

Options are believed to have the function of reflecting market expectations on future underlying movements through its implicit risk-neutral density (RND). However, it is not easy to obtain a well-behaved RND due to the data limitations, the complex constraints and the ill-posedness of the problem. In this paper, we propose a more effective nonparametric method for estimating the RND from a set of European option bid-ask quotes based on a Linear Programming Support Vector Regression (LPSVR). The method allows us to fit beyond the range of data and to incorporate all the shape constraints, and it thus always gives an arbitrage-free density with full tails. In addition, the method does not need preprocessing of the data and is robust to the bid-ask spread. The Monte-Carlo simulations and the empirical tests have been carried out to demonstrate the excellent accuracy and stability of the method. The results show that the LPSVR method is a promising alternative for estimating the RND.