Robust numerical algorithm to the European option with illiquid markets
| Autor: | Davood Ahmadian, O. Farkhondeh Rouz, Ali Safdari-Vaighani, Karim Ivaz |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Applied Mathematics Mathematics::Optimization and Control 020206 networking & telecommunications 02 engineering and technology Computational Mathematics symbols.namesake Nonlinear system 020901 industrial engineering & automation Kantorovich theorem Convergence (routing) 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics Call option Newton's method Linear equation Mathematics |
| Zdroj: | Applied Mathematics and Computation. 366:124693 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2019.124693 |
| Popis: | In this paper, we consider illiquid European call option which is arisen in nonlinear Black–Scholes equation. In this respect, we apply the Newton’s method to linearize it. Based on the obtained linear equation, we obtain the approximate solutions recursively in two steps. Finally, based on the conditions of Kantorovich theorem, we investigate the convergence analysis of the Newton’s method on the proposed problem. Finally the positivity of the solution is discussed. |
| Databáze: | OpenAIRE |
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