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Henderson, V., Kladivko, K. & Monoyios, M. (2017). Executive stock option exercise with full and partial information on a drift change point. , Article ID 1709.10141.
Open this publication in new window or tab >>Executive stock option exercise with full and partial information on a drift change point
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.

Publisher
p. 31
Keywords
Optimal stopping, executive stock options, insider information, American options, Wonham lter
National Category
Economics
Identifiers
urn:nbn:se:oru:diva-69638 (URN)
Note

ArXiv:1210.2071

Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2018-11-09Bibliographically approved
Kladivko, K. & Zervos, M. (2017). Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging. , Article ID 1710.00897.
Open this publication in new window or tab >>Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging
2017 (English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider the problem of ESO valuation in continuous time. In particular, we consider models that assume that an appropriate random time serves as a proxy for anything that causes the ESO's holder to exercise the option early, namely, reflects the ESO holder's job termination risk as well as early exercise behaviour. In this context, we study the problem of ESO valuation by means of mean-variance hedging. Our analysis is based on dynamic programming and uses PDE techniques. We also express the ESO's value that we derive as the expected discounted payoff that the ESO yields with respect to an equivalent martingale measure, which does not coincide with the minimal martingale measure or the variance-optimal measure. Furthermore, we present a numerical study that illustrates aspects or our theoretical results.

Publisher
p. 27
Keywords
Employee stock options, mean-variance hedging, classical solutions of PDEs
National Category
Economics
Identifiers
urn:nbn:se:oru:diva-69639 (URN)
Note

ArXiv: 1710.00987

Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2018-11-09Bibliographically approved
Kladivko, K. (2016). Essays on Financial Options: Employee Stock Options and Reinsurance Pricing. (Doctoral dissertation). Bergen, Norway: Department of Finance, Norwegian School of Economics
Open this publication in new window or tab >>Essays on Financial Options: Employee Stock Options and Reinsurance Pricing
2016 (English)Doctoral thesis, monograph (Other academic)
Place, publisher, year, edition, pages
Bergen, Norway: Department of Finance, Norwegian School of Economics, 2016. p. 85
National Category
Economics
Identifiers
urn:nbn:se:oru:diva-69637 (URN)978-82-405-0333-8 (ISBN)
Supervisors
Available from: 2018-11-07 Created: 2018-10-17 Last updated: 2018-11-07Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9024-3054

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