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Optimal Exercise Of An Executive Stock Option By An Insider

Author

Listed:
  • MICHAEL MONOYIOS

    (Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford, OX1 3LB, UK)

  • ANDREW NG

    (Mathematical Institute, University of Oxford, 24–29 St Giles', Oxford, OX1 3LB, UK)

Abstract

We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a time-inhomogeneous diffusion and a call-type reward. We establish conditions under which the option value exhibits time decay, and derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward, and derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. Hence we show that early exercise may arise due to the agent having inside information on the future stock price.

Suggested Citation

  • Michael Monoyios & Andrew Ng, 2011. "Optimal Exercise Of An Executive Stock Option By An Insider," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 83-106.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:n:s0219024911006279
    DOI: 10.1142/S0219024911006279
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    Cited by:

    1. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios & Christoph Reisinger, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Jul 2020.
    2. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
    3. Yukihiro Tsuzuki, 2023. "Pitman's Theorem, Black-Scholes Equation, and Derivative Pricing for Fundraisers," Papers 2303.13956, arXiv.org.

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