Computation and analysis for a constrained entropy optimization problem in finance

作者:

Highlights:

摘要

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.

论文关键词:35K55,54C70,65M06,65M12,Nonlinear PDE,Entropy minimization,Viscosity solution,Uncertain volatility model,Option pricing,Model calibration

论文评审过程:Received 30 May 2006, Revised 19 January 2007, Available online 22 October 2007.

论文官网地址:https://doi.org/10.1016/j.cam.2007.10.016