A0292
Title: Parallel computations for nonparametric estimation of risk-neutral densities through option prices
Authors: Antonio Santos - University of Coimbra (Portugal) [presenting]
Ana Monteiro - University of Coimbra (Portugal)
Abstract: The risk-neutral density is one of the key objects in option contracts pricing. One of the most flexible ways to estimate that object, especially within big data environments through intraday data available nowadays, is using nonparametric estimation methods. In this context, two main challenges need to be addressed. First, implementing estimation procedures through large-scale constrained convex optimization problems, more robust when compared with simpler estimators, benchmarked by the Nadaraya-Watson estimator. Second, there is the computational challenge associated with nonparametric estimators for choosing the model's complexity done by defining an optimal bandwidth. The state-of-the-art method for choosing the optimal bandwidth is Cross-Validation, a problem that can be parallelized. The paradigm to implement such procedures is using Graphics Processing Units computational capabilities. We demonstrate the use of such capabilities for defining optimal bandwidths in the nonparametric estimation of risk-neutral densities, where thousands of convex optimization problems are solved in parallel. The application of these computational methods is considered in the estimation of risk-neutral densities associated with option contracts for S\&P500 and VIX indexes.
