### Abstract

Bilateral Laplace transform is known for its capability on taking Laplace transform over all real numbers. This paper provides a different approach by using inverse bilateral Laplace transform on deriving analytic solution of European option price formula, both call option and put option. Case of uncorrelated processes between asset price and volatility of Black-Scholes model of asset pricing with stochastic volatility driven by Ornstein-Uhlenbeck process is used to portray price of a risky asset in the market. This paper also provides proof for required formulations to derive the analytic solutions and reference for alternative forms of inverse bilateral Laplace transform.

Original language | English |
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Title of host publication | Proceedings of the 4th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2018 |

Editors | Terry Mart, Djoko Triyono, Ivandini T. Anggraningrum |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735419155 |

DOIs | |

Publication status | Published - 4 Nov 2019 |

Event | 4th International Symposium on Current Progress in Mathematics and Sciences 2018, ISCPMS 2018 - Depok, Indonesia Duration: 30 Oct 2018 → 31 Oct 2018 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2168 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 4th International Symposium on Current Progress in Mathematics and Sciences 2018, ISCPMS 2018 |
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Country | Indonesia |

City | Depok |

Period | 30/10/18 → 31/10/18 |

### Keywords

- Black-Scholes model
- inverse bilateral Laplace transform
- Ornstein-Uhlenbeck process
- stochastic volatility

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## Cite this

*Proceedings of the 4th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2018*[020025] (AIP Conference Proceedings; Vol. 2168). American Institute of Physics Inc.. https://doi.org/10.1063/1.5132452