A fractional Black-Scholes model with stochastic volatility and European option pricing
•European option pricing is studied under a FMLS model with stochastic volatility.•We have successfully solved a fractional partial differential equation system.•The derived pricing formula is truly explicit, involving no Fourier inversion. In this paper, we introduce the stochastic volatility into...
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| Published in | Expert systems with applications Vol. 178; p. 114983 |
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| Format | Journal Article |
| Language | English |
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15.09.2021
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| Abstract | •European option pricing is studied under a FMLS model with stochastic volatility.•We have successfully solved a fractional partial differential equation system.•The derived pricing formula is truly explicit, involving no Fourier inversion.
In this paper, we introduce the stochastic volatility into the FMLS (finite moment log-stable) model to capture the effect of both jumps and stochastic volatility. However, this additional stochastic source adds another degree of complexity in seeking for analytical formula when pricing European options, as the involved FPDE (fractional partial differential equation) system governing option prices is now of three dimensions. Albeit difficult, we have still managed to present an analytical solution expressed in terms of Fourier cosine series, after a two-step solution procedure is developed for the target FPDE system. This solution is different from the most literature as it is truly explicit, involving no Fourier inversion. It is also shown through the numerical experiments that it converges very rapidly and has potential to be applied in practice. |
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| AbstractList | In this paper, we introduce the stochastic volatility into the FMLS (finite moment log-stable) model to capture the effect of both jumps and stochastic volatility. However, this additional stochastic source adds another degree of complexity in seeking for analytical formula when pricing European options, as the involved FPDE (fractional partial differential equation) system governing option prices is now of three dimensions. Albeit difficult, we have still managed to present an analytical solution expressed in terms of Fourier cosine series, after a two-step solution procedure is developed for the target FPDE system. This solution is different from the most literature as it is truly explicit, involving no Fourier inversion. It is also shown through the numerical experiments that it converges very rapidly and has potential to be applied in practice. •European option pricing is studied under a FMLS model with stochastic volatility.•We have successfully solved a fractional partial differential equation system.•The derived pricing formula is truly explicit, involving no Fourier inversion. In this paper, we introduce the stochastic volatility into the FMLS (finite moment log-stable) model to capture the effect of both jumps and stochastic volatility. However, this additional stochastic source adds another degree of complexity in seeking for analytical formula when pricing European options, as the involved FPDE (fractional partial differential equation) system governing option prices is now of three dimensions. Albeit difficult, we have still managed to present an analytical solution expressed in terms of Fourier cosine series, after a two-step solution procedure is developed for the target FPDE system. This solution is different from the most literature as it is truly explicit, involving no Fourier inversion. It is also shown through the numerical experiments that it converges very rapidly and has potential to be applied in practice. |
| ArticleNumber | 114983 |
| Author | He, Xin-Jiang Lin, Sha |
| Author_xml | – sequence: 1 givenname: Xin-Jiang surname: He fullname: He, Xin-Jiang email: xinjiang@zjut.edu.cn organization: School of Economics, Zhejiang University of Technology, Hangzhou, China – sequence: 2 givenname: Sha surname: Lin fullname: Lin, Sha email: linsha@mail.zjgsu.edu.cn organization: School of Finance, Zhejiang Gongshang University, Hangzhou, China |
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| Cites_doi | 10.1016/S0370-1573(00)00070-3 10.1007/s00780-011-0157-9 10.1007/s11147-013-9091-7 10.1111/1467-9965.00020 10.1093/rfs/4.4.727 10.1287/mnsc.48.8.1086.166 10.1016/0304-405X(76)90022-2 10.1016/j.ejor.2018.08.033 10.1016/j.physa.2006.08.071 10.1080/15326349708807456 10.2307/2330793 10.1093/rfs/6.2.327 10.2139/ssrn.1941464 10.1016/0304-405X(87)90009-2 10.1023/A:1009703431535 10.1086/338705 10.21314/JCF.1999.043 10.1137/080718061 10.1080/14697688.2012.676208 10.1016/S0378-4266(98)00119-8 10.1080/1350486X.2014.960529 10.1080/14697688.2017.1412494 10.1080/14697688.2020.1741668 10.1086/260062 10.1080/14697688.2016.1149610 10.1017/S0956792515000510 10.1016/j.najef.2017.02.005 10.1111/1540-6261.00544 10.1090/S0033-569X-2014-01373-2 10.1111/j.1540-6261.1987.tb02568.x |
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| Snippet | •European option pricing is studied under a FMLS model with stochastic volatility.•We have successfully solved a fractional partial differential equation... In this paper, we introduce the stochastic volatility into the FMLS (finite moment log-stable) model to capture the effect of both jumps and stochastic... |
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| SubjectTerms | Cosine series Exact solutions Explicit and analytical FMLS model Fourier series Fractional partial differential equation Partial differential equations Pricing Securities prices Stochastic models Stochastic volatility Volatility |
| Title | A fractional Black-Scholes model with stochastic volatility and European option pricing |
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