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# Recovering Stochastic Processes from Option Prices

Type of Publication: | Contribution to a collection |

Publication status: | Published |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-377233 |

Author: | Jackwerth, Jens Carsten; Rubinstein, Mark |

Year of publication: | 2012 |

Published in: | Derivative Securities Pricing and Modelling / Batten, Jonathan A.; Wagner, Niklas (ed.). - Bradford : Emerald, 2012. - (Contemporary Studies in Economic and Financial Analysis ; 94). - pp. 123-154. - ISBN 978-1-78052-616-4 |

DOI (citable link): | https://dx.doi.org/10.1108/S1569-3759(2012)0000094008 |

Summary: |
How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the stock market crash of 1987 and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black-Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-toexpiration, or times. The latter amounts to examining predictions of future implied volatilities.
Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option pricing models might then be limited. |

Subject (DDC): | 330 Economics |

Link to License: | Terms of use |

Bibliography of Konstanz: | Yes |

Checksum:
MD5:02452f1ad47c7d081ce19627b53747b5

JACKWERTH, Jens Carsten, Mark RUBINSTEIN, 2012. Recovering Stochastic Processes from Option Prices. In: BATTEN, Jonathan A., ed., Niklas WAGNER, ed.. Derivative Securities Pricing and Modelling. Bradford:Emerald, pp. 123-154. ISBN 978-1-78052-616-4. Available under: doi: 10.1108/S1569-3759(2012)0000094008

@incollection{Jackwerth2012Recov-36295, title={Recovering Stochastic Processes from Option Prices}, year={2012}, doi={10.1108/S1569-3759(2012)0000094008}, number={94}, isbn={978-1-78052-616-4}, address={Bradford}, publisher={Emerald}, series={Contemporary Studies in Economic and Financial Analysis}, booktitle={Derivative Securities Pricing and Modelling}, pages={123--154}, editor={Batten, Jonathan A. and Wagner, Niklas}, author={Jackwerth, Jens Carsten and Rubinstein, Mark} }

Jackwerth_0-377233.pdf | 538 |