Abstract
This paper develops a novel approach to computation of the probability integrals encountered in derivative pricing using stochastic models estimated from historical data. First, nonparametric probability distribution models are built directly from the data as a solution of a convex optimization problem scalable to very big datasets. Second, these models are used for numerical calculus of probability integrals, where the quadrature includes long tails of the probability distributions. The application example is the procurement contract in the day-ahead bulk market for electricity. The data for PJM utility loads and prices in the day-ahead and spot markets were used to estimate the risk and to price the contract. The data-driven forward contract pricing allows to optimize the contract cost and reduce it by 2% compared to the baseline; this corresponds to about $0.6B/year in potential utility savings.
Published Version
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