Data-Driven Stochastic Pricing and Application to Electricity Market

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.

[1]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[2]  Risk Premia in Electricity Forward Prices , 2006 .

[3]  V. A. Epanechnikov Non-Parametric Estimation of a Multivariate Probability Density , 1969 .

[4]  Pin T. Ng,et al.  Quantile smoothing splines , 1994 .

[5]  James W. Taylor A Quantile Regression Neural Network Approach to Estimating the Conditional Density of Multiperiod Returns , 2000 .

[6]  R. Koenker Quantile Regression: Name Index , 2005 .

[7]  J. Rosenberg Nonparametric Pricing of Multivariate Contingent Claims , 2000 .

[8]  Xuming He Quantile Curves without Crossing , 1997 .

[9]  M. Stutzer A Simple Nonparametric Approach to Derivative Security Valuation , 1996 .

[10]  J. Corcoran Modelling Extremal Events for Insurance and Finance , 2002 .

[11]  Hans Byström,et al.  Extreme Value Theory and Extremely Large Electricity Price Changes , 2005 .

[12]  M. Rosenblatt Remarks on a Multivariate Transformation , 1952 .

[13]  W. Härdle,et al.  Quantile Regression in Risk Calibration , 2012 .

[14]  Andrew W. Lo,et al.  Nonparametric estimation of state-price densities implicit in financial asset prices , 1995, Proceedings of 1995 Conference on Computational Intelligence for Financial Engineering (CIFEr).

[15]  A. McNeil Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory , 1997, ASTIN Bulletin.

[16]  Saahil Shenoy,et al.  Stochastic optimization of power market forecast using non-parametric regression models , 2015, 2015 IEEE Power & Energy Society General Meeting.

[17]  S. Poon,et al.  Financial Modeling Under Non-Gaussian Distributions , 2006 .

[18]  Estimation of VAR Using Copula and Extreme Value Theory , 2006 .

[19]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[20]  Ivor W. Tsang,et al.  A Family of Simple Non-Parametric Kernel Learning Algorithms , 2011, J. Mach. Learn. Res..

[21]  A. Conejo,et al.  A Stochastic Programming Approach to Electric Energy Procurement for Large Consumers , 2007, IEEE Transactions on Power Systems.

[22]  Saahil Shenoy,et al.  Estimating Long Tail Models for Risk Trends , 2015, IEEE Signal Processing Letters.

[23]  Sunder Kekre,et al.  Optimal Energy Procurement in Spot and Forward Markets , 2014, Manuf. Serv. Oper. Manag..

[24]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[25]  René Carmona,et al.  Pricing and Hedging Spread Options , 2003, SIAM Rev..

[26]  Rob J. Hyndman,et al.  Forecasting Uncertainty in Electricity Smart Meter Data by Boosting Additive Quantile Regression , 2016, IEEE Transactions on Smart Grid.

[27]  Alexander J. Smola,et al.  Nonparametric Quantile Estimation , 2006, J. Mach. Learn. Res..

[28]  Stephen P. Boyd,et al.  Block splitting for distributed optimization , 2013, Mathematical Programming Computation.

[29]  I. Tsai The relationship between stock price index and exchange rate in Asian markets: A quantile regression approach , 2012 .

[30]  Cheng-Few Lee,et al.  Handbook of Financial Econometrics and Statistics , 2015 .

[31]  Ioannis D. Vrontos,et al.  Quantile Regression Analysis of Hedge Fund Strategies , 2007 .

[32]  Keming Yu,et al.  Quantile regression: applications and current research areas , 2003 .

[33]  Saahil Shenoy,et al.  Risk adjusted forecasting of electric power load , 2014, 2014 American Control Conference.

[34]  Federica Asnicar Optimization of Electricity Reserved Capacity , 2006 .

[35]  Lixing Zhu,et al.  Composite Quantile Regression for the Single-Index Model , 2013 .

[36]  Takafumi Kanamori,et al.  Nonparametric Conditional Density Estimation Using Piecewise-Linear Solution Path of Kernel Quantile Regression , 2009, Neural Computation.

[37]  A. McNeil Extreme Value Theory for Risk Managers , 1999 .

[38]  Mauro Bernardi,et al.  Bayesian Tail Risk Interdependence Using Quantile Regression , 2015 .

[39]  Anthony W. Hughes,et al.  A Quantile Regression Analysis of the Cross Section of Stock Market Returns , 2002 .

[40]  Erik Hjalmarsson Does the Black-Scholes formula work for electricity markets? A nonparametric approach , 2003 .

[41]  Kush R. Varshney,et al.  Business Analytics Based on Financial Time Series , 2011, IEEE Signal Processing Magazine.

[42]  J. Geweke,et al.  Comparing and Evaluating Bayesian Predictive Distributions of Asset Returns , 2008 .

[43]  Siddharth Arora,et al.  Forecasting electricity smart meter data using conditional kernel density estimation , 2014, 1409.2856.