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Estimating the parameters of 3/2 stochastic volatility model with jump | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 3، شماره 1، آذر 2023، صفحه 137-143 اصل مقاله (1.17 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2023.75272.1101 | ||
| نویسندگان | ||
| Ali Safdari-Vaighani* 1؛ Pooya Garshasebi2 | ||
| 1Department of mathematics, Allameh Tabataba’i University, Tehran, Iran | ||
| 2Department of Mathematics, Allameh Tabataba'i University, Tehran, Iran. | ||
| چکیده | ||
| The financial markets reveal stylized facts that could not be captured by Black-Scholes partial differential equations (PDEs). In this research, we investigate 3/2 stochastic volatility to pricing options which is more compatible with the interpretation of implied volatility. Numerical study and calibrations show that the 3/2 model incorporating jumps effectively encompasses key market characteristics attributed. However, it requires more estimating parameters in comparison to the pure diffusion model. Stochastic volatility models with jumps describe the log return features of the financial market although more parameters are involved in estimations. | ||
| کلیدواژهها | ||
| Black-Scholes model؛ Stochastic volatility models؛ 3/2 model؛ 3/2 plus jump model | ||
| مراجع | ||
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[1] G. G. Drimus, Options on realized variance by transform methods: A non-affine stochastic volatility model, Quantitative Finance., 11 (2009), 1679–1694. [2] J. Baldeaux, A. Badran, Consistent modelling of VIX and equity derivatives using a 3/2 plus jump model, Research Paper Series 306, Quantitative Finance Research Center, University of Technology, Sydney, 2012. [3] P. Carr, J. Sun A new approach for option pricing under stochastic volatility, Review of Derivatives Research, 10 (2007), 87–150. [4] R. Cont, P. Tankov, Financial modelling with jump processes, CRC Press LLC, London, 2004. [5] S. G. Kou, J. Jump-diffusion models for asset pricing on financial engineering, Handbooks in Operations Research and Management Science, 15 (2007), 73–116. | ||
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