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Title: High-frequency options data in estimating time-varying risk-neutral densities using kernel-type estimators Authors:  Antonio Santos - University of Coimbra (Portugal)
Ana Monteiro - University of Coimbra (Portugal) [presenting]
Abstract: High-frequency data allow developing new models and methods to analyze financial risk. The extraction of risk-neutral densities through option prices has been extensively treated in the literature. The best methods to extract such densities are still not fully established, and only recently, high-frequency data constituted an innovative factor. The risk-neutral density is associated with the second derivative of the option pricing function. We propose a nonparametric-based technique to estimate risk-neutral densities in a static environment and allowing extensions to dynamic ones. We define a criterion function used in nonparametric regression that includes calls, puts, and weights in a constrained optimization problem. The problem's constraints represent the no-arbitrage ones, which results in a large scale convex quadratic programming problem. Two of the main elements influencing option pricing function is the strike and the time to maturity. The former allows the definition of the risk-neutral density (second derivative). The latter allows a dynamic view of the risk-neutral density, which, compared with the ``physical'' density, permits a better understanding of economic-agents risk-aversion evolution. We developed an optimization problem inserted in a nonparametric estimation framework that allows through high-frequency option price data to estimate time-varying risk-neutral densities. We tested the methods using options contracts on the S\&P500 futures.