Title: | Nonexpansive maps and option pricing theory (English) |

Author: | Kolokoltsov, Vassili N. |

Language: | English |

Journal: | Kybernetika |

ISSN: | 0023-5954 |

Volume: | 34 |

Issue: | 6 |

Year: | 1998 |

Pages: | [713]-724 |

Summary lang: | English |

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Category: | math |

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Summary: | The famous Black–Sholes (BS) and Cox–Ross–Rubinstein (CRR) formulas are basic results in the modern theory of option pricing in financial mathematics. They are usually deduced by means of stochastic analysis; various generalisations of these formulas were proposed using more sophisticated stochastic models for common stocks pricing evolution. In this paper we develop systematically a deterministic approach to the option pricing that leads to a different type of generalisations of BS and CRR formulas characterised by more rough assumptions on common stocks evolution (which are therefore easier to verify). On the other hand, this approach is more elementary, because it uses neither martingales nor stochastic equations. (English) |

Keyword: | option pricing |

Keyword: | stocks pricing evolution |

Keyword: | Black-Scholes formula |

MSC: | 91B24 |

MSC: | 91B28 |

MSC: | 91B42 |

MSC: | 91G20 |

idZBL: | Zbl 1274.91420 |

idMR: | MR1695373 |

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Date available: | 2009-09-24T19:22:02Z |

Last updated: | 2015-03-28 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/135256 |

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Reference: | [1] Baccelli F., Cohen G., Olsder G., Quadrat J.-P.: Synchronisation and Linearity: An Algebra for Discrete Event Systems.Wiley, New York 1992 MR 1204266 |

Reference: | [2] Cox J. C., Ross S. A., Rubinstein M.: Option pricing: A simplified approach.J. Financial Economics 7 (1979), 229–263 Zbl 1131.91333, 10.1016/0304-405X(79)90015-1 |

Reference: | [3] (Ed.) J. Gunawardena: Proceedings of the International Workshop “Idempotency”, Bristol 1994.Cambridge Univ. Press, Cambridge 1998 MR 1608365 |

Reference: | [4] Kolokoltsov V. N.: A Formula for Option Prices on a Market with Unknown Volatility.Research Report No. 9/96, Dep. Math. Stat. and O. R., Nottingham Trent University 1996 |

Reference: | [5] Kolokoltsov V. N., Maslov V. P.: Idempotent Analysis and its Applications.Kluwer Academic Publishers, Dordrecht 1997 Zbl 0941.93001, MR 1447629 |

Reference: | [6] Lions T.: Uncertain volatility and the risk-free synthesis of derivatives.Appl. Math. Finance 2 (1995), 117–133 10.1080/13504869500000007 |

Reference: | [7] McEneaney W. M.: A robust control framework for option pricing.Math. Oper. Research 22 (1997), 202–221 Zbl 0871.90010, MR 1436580, 10.1287/moor.22.1.202 |

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