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Executive stock option exercise with full and partial information on a drift change point
Department of Statistics, Zeeman Building, University of Warwick, Coventry, UK.
Norwegian School of Economics, Bergen, Norway.ORCID iD: 0000-0001-9024-3054
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, UK.
2017 (English)Manuscript (preprint) (Other academic)
Abstract [en]

We analyse the valuation and exercise of an American executive call option written on a stock whose drift parameter falls to a lower value at a change point given by an exponential random time, independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the change point, and seek to optimally exercise the option by maximising its discounted payoff under the physical measure. The first agent has full information, and observes the change point. The second agent has partial information and filters the change point from price observations. Our setup captures the position of an executive (insider) and employee (outsider), who receive executive stock options. The latter yields a model under the observation filtration $\widehat{\mathbb F}$ where the drift process becomes a diffusion driven by the innovations process, an $\widehat{\mathbb F}$-Brownian motion also driving the stock under $\widehat{\mathbb F}$, and the partial information optimal stopping problem has two spatial dimensions. We analyse and numerically solve to value the option for both agents and illustrate that the additional information of the insider can result in exercise patterns which exploit the information on the change point.

Place, publisher, year, edition, pages
2017. , p. 31article id 1709.10141
Keywords [en]
Optimal stopping, executive stock options, insider information, American options, Wonham lter
National Category
Economics
Identifiers
URN: urn:nbn:se:oru:diva-69638OAI: oai:DiVA.org:oru-69638DiVA, id: diva2:1256445
Note

ArXiv:1210.2071

Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2018-11-09Bibliographically approved

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Executive stock option exercise with full and partial information on a drift change point(891 kB)132 downloads
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Executive stock option exercise with full and partial information on a drift change point

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Kladivko, Kamil

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf