Computation and analysis for a constrained entropy optimization problem in finance |
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Authors: | Changhong He Thomas F Coleman Yuying Li |
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Institution: | 1. J.P. Morgan Securities Inc., 270 Park Ave, Floor 6, New York, NY, 10017-2070, United States;2. Faculty of Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1;3. School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1 |
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Abstract: | In T. Coleman, C. He, Y. Li, Calibrating volatility function bounds for an uncertain volatility model, Journal of Computational Finance (2006) (submitted for publication)], an entropy minimization formulation has been proposed to calibrate an uncertain volatility option pricing model (UVM) from market bid and ask prices. To avoid potential infeasibility due to numerical error, a quadratic penalty function approach is applied. In this paper, we show that the solution to the quadratic penalty problem can be obtained by minimizing an objective function which can be evaluated via solving a Hamilton–Jacobian–Bellman (HJB) equation. We prove that the implicit finite difference solution of this HJB equation converges to its viscosity solution. In addition, we provide computational examples illustrating accuracy of calibration. |
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Keywords: | 35K55 54C70 65M06 65M12 |
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