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Pricing asset-or-nothing options using Haar wavelet | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 4، شماره 1، مهر 2024، صفحه 19-35 اصل مقاله (562.68 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2024.77996.1120 | ||
| نویسندگان | ||
| Saeed Vahdati* 1؛ Foad Shokrollahi2 | ||
| 1University of Isfahan, Isfahan, Iran | ||
| 2Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, FIN-65101 Vaasa, Finland. | ||
| چکیده | ||
| This article proposes a new numerical technique for pricing asset-or-nothing options using the Black-Scholes partial differential equation (PDE). We first use the θ−weighted method to discretize the time domain, and then use Haar wavelets to approximate the functions and derivatives with respect to the asset price variable. By using some vector and matrix calculations, we reduce the PDE to a system of linear equations that can be solved at each time step for different asset prices. We perform an error analysis to show the convergence of our technique. We also provide some numerical examples to compare our technique with some existing methods and to demonstrate its efficiency and accuracy. | ||
| کلیدواژهها | ||
| Option pricing؛ Asset-or-Nothing Options؛ Haar Wavelets؛ Black-Scholes Model؛ Error analysis | ||
| مراجع | ||
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