Call warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion

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dc.citation.epage897
dc.citation.issue4
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage892
dc.contributor.affiliationУніверситет Путра Малайзія
dc.contributor.affiliationUniversiti Putra Malaysia
dc.contributor.authorІбрагім, С. Н. І.
dc.contributor.authorЛахам, М. Ф.
dc.contributor.authorIbrahim, S. N. I.
dc.contributor.authorLaham, M. F.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-24T09:14:06Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractЗмішаний дробовий броунівський рух (ЗДБР) — це лінійна комбінація броунівського руху та незалежного дробового броунівського руху, яка може вирішити проблему арбітражу, тоді як стрибковий процес у часових рядах є ще однією проблемою, яку слід вирішити під час моделювання цін на акції. Це дослідження спрямоване на моделювання варантів за допомогою ЗДБР і включення стрибкоподібного процесу в його динаміку. Формула ціноутворення для варанта зі змішаним дробовим броунівським рухом і стрибком отримана за допомогою квазіумовного очікування та нейтральної до ризику оцінки.
dc.description.abstractMixed fractional Brownian motion (MFBM) is a linear combination of a Brownian motion and an independent fractional Brownian motion which may overcome the problem of arbitrage, while a jump process in time series is another problem to be address in modeling stock prices. This study models call warrants with MFBM and includes the jump process in its dynamics. The pricing formula for a warrant with mixed-fractional Brownian motion and jump, is obtained via quasi-conditional expectation and risk-neutral valuation.
dc.format.extent892-897
dc.format.pages6
dc.identifier.citationIbrahim S. N. I. Call warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion / S. N. I. Ibrahim, M. F. Laham // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 892–897.
dc.identifier.citationenIbrahim S. N. I. Call warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion / S. N. I. Ibrahim, M. F. Laham // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 892–897.
dc.identifier.doidoi.org/10.23939/mmc2022.04.892
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/64226
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 4 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 4 (9), 2022
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dc.relation.referencesen[1] Black F., Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy. 81 (3), 637–654 (1973).
dc.relation.referencesen[2] Cont R. Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance. 1 (2), 223–236 (2010).
dc.relation.referencesen[3] Cajueiro D. O., Tabak B. M. Long-range dependence and multifractality in the term structure of LIBOR interest rates. Physica A. 373, 603–614 (2007).
dc.relation.referencesen[4] Huang T.-C., Tu Y.-C., Chou H.-C. Long memory and the relation between options and stock prices. Finance Research Letters. 12, 77–91 (2015).
dc.relation.referencesen[5] Rogers L. C. G. Arbitrage with fractional Brownian motion. Mathematical Finance. 7 (1), 95–105 (1997).
dc.relation.referencesen[6] Cheridito P. Arbitrage in fractional Brownian motion models. Finance and Stochastics. 7, 533–553 (2003).
dc.relation.referencesen[7] Li J., Xiang K., Luo C. Pricing study on two kinds of power options in jump-diffusion models with fractional Brownian motion and stochastic rate. Applied Mathematics. 5 (16), 2426–2441 (2014).
dc.relation.referencesen[8] Wang C., Zhou S., Yang J. The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment. Discrete Dynamics in Nature and Society. 2015, 579213 (2015).
dc.relation.referencesen[9] El-Nouty C. The fractional mixed fractional Brownian motion. Statistics & Probability Letters. 65 (2), 111–120 (2003).
dc.relation.referencesen[10] Mishura Y. S. Stochastic calculus for fractional Brownian motions and related processes. Springer Berlin, Heidelberg (2008).
dc.relation.referencesen[11] Kuznetsov Yu. A. The absence of arbitrage in a model with fractal Brownian motion. Russian Mathematical Surveys. 54 (4), 847 (1999).
dc.relation.referencesen[12] Bj¨ork T., Hult H. A note on Wick products and the fractional Black–Scholes model. Finance and Stochastics. 9, 197–209 (2005).
dc.relation.referencesen[13] Cheridito P. Mixed Fractional Brownian Motion. Bernoulli. 7 (6), 913–934 (2001).
dc.relation.referencesen[14] Dominique C. R., Rivera–Solis L. E. S. Mixed fractional Brownian motion, short and long-term dependence and economic conditions: The case of the S&P-500 Index. International Business and Management. 3 (2), 1–6 (2011).
dc.relation.referencesen[15] Prakasa Rao B. L. S. Pricing geometric Asian power options under mixed fractional Brownian motion environment. Physica A. 446, 92–99 (2016).
dc.relation.referencesen[16] Zhang W.-G., Li Z., Liu Y.-J. Analytical pricing of geometric Asian power options on an underlying driven by mixed fractional Brownian motion. Physica A. 490, 402–418 (2018).
dc.relation.referencesen[17] Chen W., Yan B., Lian G., Zhang Y. Numerically pricing American options under the generalized mixed fractional Brownian motion model. Physica A. 451, 180–189 (2016).
dc.relation.referencesen[18] Shokrollahi F., Kili¸cman A. Pricing currency option in a mixed fractional Brownian motion with jumps environment. Mathematical Problems in Engineering. 2014, 858210 (2014).
dc.relation.referencesen[19] Shokrollahi F. Pricing compound and extendible options under mixed fractional Brownian motion with jumps. Axioms. 8 (2), 39 (2019).
dc.relation.referencesen[20] Shokrollahi F., Ahmadian D., Ballestra L. Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps. Preprint arXiv:2105.06999 (2021).
dc.relation.referencesen[21] Xiao W.-L., Zhang W.-G., Zhang X., Zhang X. Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm. Physica A. 391 (24), 6418–6431 (2012).
dc.relation.referencesen[22] Merton R. C. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics. 3 (1–2), 125–144 (1976).
dc.relation.referencesen[23] Biagini F., Hu Y., Øksendal B., Zhang T. Stochastic Calculus for Fractional Brownian Motion and Applications. Springer London (2008).
dc.relation.referencesen[24] Miao J., Yang X. Pricing Model for Convertible Bonds: A Mixed Fractional Brownian Motion with Jumps. East Asian Journal on Applied Mathematics. 5 (3), 222–237 (2015).
dc.relation.referencesen[25] Schulz G. U., Trautmann S. Robustness of option-like warrant valuation. Journal of Banking & Finance. 18 (5), 841–859 (1994).
dc.relation.referencesen[26] Yanishevskyi V. S., Nodzhak L. S. The path integral method in interest rate models. Mathematical Modeling and Computing. 8 (1), 125–136 (2021).
dc.relation.referencesen[27] Yanishevskyi V. S., Baranovska S. P. Path integral method for stochastic equations of financial engineering. Mathematical Modeling and Computing. 9 (1), 166–177 (2022).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectзмішано-дробовий броунівський рух
dc.subjectстрибкоподібна дифузія Мертона
dc.subjectколл–варант
dc.subjectmixed-fractional Brownian motion
dc.subjectMerton jump diffusion
dc.subjectcall warrant
dc.titleCall warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion
dc.title.alternativeФормула ціноутворення колл-варантів за змішано-дробового броунівського руху зі стрибкоподібною дифузією Мертона
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 4