Numerical simulation for European and American option of risks in climate change of Three Gorges Reservoir Area. (English) Zbl 1493.91143
The authors first establish a real option model with sea level and temperature as the target assets to evaluate the potential opportunities in the risk management of sea level rising. By using Itô’s lemma and the non-arbitrage pricing principle, the real option model depending on time independent two-dimensional linear parabolic variational inequalities is obtained. In view of European and American real options, the issue switched into a parabolic variational inequalities. Subsequently, a power penalty approach is proposed to transform it into a nonlinear parabolic equation. It is shown that the solutions of the nonlinear parabolic equation is unique and it converges to the solution of the parabolic variational inequalities. A fitted finite volume method is developed to solve the nonlinear parabolic equation in the case of European and American options, and the convergence of the nonlinear parabolic equation is obtained. Some numerical tests are presented to support the theoretical results.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 91G50 | Corporate finance (dividends, real options, etc.) |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 65M22 | Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65K10 | Numerical optimization and variational techniques |
| 35K55 | Nonlinear parabolic equations |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 35R35 | Free boundary problems for PDEs |
| 91-10 | Mathematical modeling or simulation for problems pertaining to game theory, economics, and finance |
Keywords:
risks in climate change; Three Gorges Reservoir Area; power penalty approach; fitted finite volume method; European and American real optionReferences:
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