A Fitted Finite-Volume Method Combined with the Lagrangian Derivative for the Weather Option Pricing Model
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Shuhua Chang
Abstract
The purpose of weather option is to allow companies to insure themselves against fluctuations in the weather. However, the valuation of weather option is complex, since the underlying process has no negotiable price. Under the assumption of mean-self-financing, by hedging with a correlated asset which follows a geometric Brownian motion with a jump diffusion process, this paper presents a new weather option pricing model on a stochastic underlying temperature following a mean-reverting Brownian motion. Consequently, a two-dimensional partial differential equation is derived to value the weather option. The numerical method applied in this paper is based on a fitted finite-volume technique combined with the Lagrangian derivative. In addition, the monotonicity, stability, and the convergence of the discrete scheme are also derived. Lastly, some numerical examples are provided to value a series of European HDD-based weather put options, and the effects of some parameters on weather option prices are discussed.
Funding source: National Basic Research Program
Award Identifier / Grant number: 2012CB955804
Funding source: Major Research Plan of the National Natural Science Foundation of China
Award Identifier / Grant number: 91430108
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11171251
Funding source: Major Program of Tianjin University of Finance and Economics
Award Identifier / Grant number: ZD1302
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Dual-Dual Formulation for a Contact Problem with Friction
- A Fitted Finite-Volume Method Combined with the Lagrangian Derivative for the Weather Option Pricing Model
- Comparison of the Analytical Approximation Formula and Newton's Method for Solving a Class of Nonlinear Black–Scholes Parabolic Equations
- Mollification in Strongly Lipschitz Domains with Application to Continuous and Discrete De Rham Complexes
- Numerical Methods for Genetic Regulatory Network Identification Based on a Variational Approach
- On the Numerical Solution of Some Non-Linear Stochastic Differential Equations Using the Semi-Discrete Method
- Numerical Computation of the Inverse Born Approximation for the Nonlinear Schrödinger Equation in Two Dimensions
- Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation
- A Splitting Scheme to Solve an Equation for Fractional Powers of Elliptic Operators
- Predictor-Corrector Balance Method for the Worst-Case 1D Option Pricing
Articles in the same Issue
- Frontmatter
- Dual-Dual Formulation for a Contact Problem with Friction
- A Fitted Finite-Volume Method Combined with the Lagrangian Derivative for the Weather Option Pricing Model
- Comparison of the Analytical Approximation Formula and Newton's Method for Solving a Class of Nonlinear Black–Scholes Parabolic Equations
- Mollification in Strongly Lipschitz Domains with Application to Continuous and Discrete De Rham Complexes
- Numerical Methods for Genetic Regulatory Network Identification Based on a Variational Approach
- On the Numerical Solution of Some Non-Linear Stochastic Differential Equations Using the Semi-Discrete Method
- Numerical Computation of the Inverse Born Approximation for the Nonlinear Schrödinger Equation in Two Dimensions
- Efficient Computation of Highly Oscillatory Integrals by Using QTT Tensor Approximation
- A Splitting Scheme to Solve an Equation for Fractional Powers of Elliptic Operators
- Predictor-Corrector Balance Method for the Worst-Case 1D Option Pricing
