dc.contributor.author | Chechelnytska, Kateryna | |

dc.date.accessioned | 2020-06-23T11:51:01Z | |

dc.date.available | 2020-06-23T11:51:01Z | |

dc.date.issued | 2020-06-23 | |

dc.identifier.uri | http://hdl.handle.net/2077/64922 | |

dc.description.abstract | The graph of the implied volatility of call options as a function of the strike price
is called volatility curve. If the options market were perfectly described by the
Black-Scholes model, the implied volatility would be independent of the strike price
and thus the volatility curve would be a
at horizontal line. However the volatility
curve of real markets is often found to have recurrent convex shapes called volatility
smile and volatility skew. The common approach to explain this phenomena is by
assuming that the volatility of the underlying stock is a stochastic process (while in
Black-Scholes it is assumed to be a deterministic constant). The main purpose of this
project is to propose and explore the idea that the occurrence of non-
at volatility
curves is the result of market incompleteness. A market is incomplete if it admits
more than one risk-neutral probability. In other words, within an incomplete market,
investors do not necessarily agree on the market price of risk. The hypothesis that
volatility curves are linked to market incompleteness is, at least from a qualitative
perspective, reasonable and justified, since the convex shape of volatility curves
indicates that investors demand an extra premium for call options which are out of
the money, that is to say, they assume that out-of-the money options are more risky
than predicted by Black- Scholes. Mathematically this means that investors use a
different risk-neutral probability to price call options with different strikes. This
hypothesis will be tested quantitatively by using the trinomial model, which is the
simplest example of one- dimensional incomplete market. | sv |

dc.language.iso | eng | sv |

dc.subject | Implied volatility, Incomplete markets, Trinomial option pricing model, Black-Scholes option pricing model, Risk-neutral probability | sv |

dc.title | Volatility Curves of Incomplete Markets | sv |

dc.type | text | |

dc.setspec.uppsok | PhysicsChemistryMaths | |

dc.type.uppsok | H2 | |

dc.contributor.department | University of Gothenburg/Department of Mathematical Science | eng |

dc.contributor.department | Göteborgs universitet/Institutionen för matematiska vetenskaper | swe |

dc.type.degree | Student essay | |