Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden’s and Schubert’s methods are applied as a modification to Newton’s method in the case of nonlinearity in the equation. An alternating direction explicit method with second-order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods.
['Vera N. Egorova', 'S.-H. Tan', 'C.-H. Lai', 'Lucas Jódar']
I am writing a research paper on a idea Moving boundary transformation for American call options with transaction cost: finite difference methods and computing
[{"from": "human", "value": "I am writing a research paper on a idea Moving boundary transformation for American call options with transaction cost: finite difference methods and computing"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden\u2019s and Schubert\u2019s methods are applied as a modification to Newton\u2019s method in the case of nonlinearity in the equation. An alternating direction explicit method with second-order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods."}]