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Option prices for risk‐neutral density estimation using nonparametric methods through big data and large‐scale problems

Ana M. Monteiro and António A. F. Santos

Journal of Futures Markets, 2022, vol. 42, issue 1, 152-171

Abstract: Option pricing theory determines the structure of call and put option pricing functions. In nonparametric risk‐neutral density estimation based on kernel functions, local constraints cannot induce a second derivative function that must integrate one. Convexity and monotonicity of pricing functions also cannot be enforced. A large‐scale (optimization) approach is proposed for the risk‐neutral density estimation, imposing an enlarged set of no‐arbitrage constraints. We considered simulations using Heston's model and hypergeometric functions. The method is applied to samples of intraday data from VIX and S&P500 indexes.

Date: 2022
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