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  • 1.
    Henderson, Vicky
    et al.
    Department of Statistics, Zeeman Building, University of Warwick, Coventry, UK.
    Kladivko, Kamil
    Norwegian School of Economics, Bergen, Norway.
    Monoyios, Michael
    Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, UK.
    Executive stock option exercise with full and partial information on a drift change point2017Manuscript (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.

  • 2.
    Kladivko, Kamil
    Örebro University, Örebro University School of Business. Norwegian School of Economics, Bergen, Norway.
    Essays on Financial Options: Employee Stock Options and Reinsurance Pricing2016Doctoral thesis, monograph (Other academic)
  • 3.
    Kladivko, Kamil
    et al.
    Norwegian School of Economics, Bergen, Norway.
    Zervos, Mihail
    Department of Mathematics, London School of Economics, London, UK.
    Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging2017Manuscript (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.

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Citation style
  • apa
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  • modern-language-association-8th-edition
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  • Other style
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  • en-GB
  • en-US
  • fi-FI
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