Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications
In this paper, we first investigate the stochastic representation of the modified advection-dispersion equation, which is proved to be a subordinated stochastic process. Taking advantage of this result, we get the analytical solution and mean square displacement for the equation. Then, applying the...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/7168571 |
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| _version_ | 1832547716927848448 |
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| author | Longjin Lv Luna Wang |
| author_facet | Longjin Lv Luna Wang |
| author_sort | Longjin Lv |
| collection | DOAJ |
| description | In this paper, we first investigate the stochastic representation of the modified advection-dispersion equation, which is proved to be a subordinated stochastic process. Taking advantage of this result, we get the analytical solution and mean square displacement for the equation. Then, applying the subordinated Brownian motion into the option pricing problem, we obtain the closed-form pricing formula for the European option, when the underlying of the option contract is supposed to be driven by the subordinated geometric Brownian motion. At last, we compare the obtained option pricing models with the classical Black–Scholes ones. |
| format | Article |
| id | doaj-art-8b5255d365024b7ea438061eb6d63b1a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8b5255d365024b7ea438061eb6d63b1a2025-02-03T06:43:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/71685717168571Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and ApplicationsLongjin Lv0Luna Wang1School of Finance and Information, Ningbo University of Finance and Economics, Ningbo 315000, ChinaSchool of Finance and Information, Ningbo University of Finance and Economics, Ningbo 315000, ChinaIn this paper, we first investigate the stochastic representation of the modified advection-dispersion equation, which is proved to be a subordinated stochastic process. Taking advantage of this result, we get the analytical solution and mean square displacement for the equation. Then, applying the subordinated Brownian motion into the option pricing problem, we obtain the closed-form pricing formula for the European option, when the underlying of the option contract is supposed to be driven by the subordinated geometric Brownian motion. At last, we compare the obtained option pricing models with the classical Black–Scholes ones.http://dx.doi.org/10.1155/2020/7168571 |
| spellingShingle | Longjin Lv Luna Wang Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications Discrete Dynamics in Nature and Society |
| title | Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications |
| title_full | Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications |
| title_fullStr | Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications |
| title_full_unstemmed | Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications |
| title_short | Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications |
| title_sort | option pricing based on modified advection dispersion equation stochastic representation and applications |
| url | http://dx.doi.org/10.1155/2020/7168571 |
| work_keys_str_mv | AT longjinlv optionpricingbasedonmodifiedadvectiondispersionequationstochasticrepresentationandapplications AT lunawang optionpricingbasedonmodifiedadvectiondispersionequationstochasticrepresentationandapplications |