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  • Xingchun Wang (a1), Zhiwei Su (a2) and Guangli Xu (a3)

In this paper, we investigate executive stock options with endogenous departure and time-varying variances. We use a “Generalized Autoregressive Conditional Heteroskedasticity” process to capture the variance process of the log stock price. In addition, we take into consideration the departure risk of the executive and assume that the probability of remaining employed has a power form of stock price ratios. After deriving the closed-form pricing formulae of executive stock options, we illustrate the effects of the departure risk on the values of executive stock options.

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1. Albrecher, H., Mayer, P., Schoutens, W., & Tistaert, J. (2007). The little Heston trap. Wilmott Magazine, pp. 8392.
2. Carmona, J., León, A., & Vaello-Sebastià, A. (2011). Pricing executive stock options under employment shocks. Journal of Economic Dynamics and Control 35: 97114.
3. Carpenter, J. (1998). The exercise and valuation of executive stock options. Journal of Financial Economics 48: 127158.
4. Carr, P. & Linetsky, V. (2000). The valuation of executive stock options in an intensity-based framework. European Finance Review 4: 211230.
5. Chong, T., Ding, Y., & Li, Y. (2015). Executive stock option pricing in China under stochastic volatility. Journal of Futures Markets 35: 953960.
6. Christoffersen, P., Jacobs, K., & Ornthanalai, C. (2012). Dynamic jump intensities and risk premiums: evidence from S&P500 returns and options. Journal of Financial Economics 106: 447472.
7. Cuny, C. & Jorion, P. (1995). Valuing executive stock options with endogenous departure. Journal of Accounting and Economics 20: 193205.
8. Duan, J. & Wei, J. (2005). Executive stock options and incentive effects due to systematic risk. Journal of Banking and Finance 29: 11851211.
9. Engle, R. & Ng, V. (1993). Measuring and testing the impact of news on volatility. Journal of Finance 43: 17491778.
10. Heston, S. & Nandi, S. (2000). A closed-form GARCH option valuation model. Review of Financial Studies 13: 585625.
11. Hull, J. (2015). Options, futures, and other derivatives. New Jersey: Prentice-Hall.
12. Johnson, S. & Tian, Y. (2000). Indexed executive stock options. Journal of Financial Economics 57: 3564.
13. Kendall, M. & Stuart, A. (1977). The advanced theory of statistics, vol. 1. New York: Macmillan.
14. Laux, V. (2012). Stock option vesting conditions, CEO turnover, and myopic investment. Journal of Financial Economics 106: 513526.
15. Shephard, N. (1991). From characteristic function to a distribution function: a simple framework for theory. Econometric Theory 7: 519529.
16. Sircar, R. & Xiong, W. (2007). A general framework for evaluating executive stock options. Journal of Economic Dynamics and Control 31: 23172349.
17. Tzang, S., Wang, C., & Yu, M. (2016). Systematic risk and volatility skew. International Review of Economics and Finance 43: 7287.
18. Wang, X. (2017a). Pricing vulnerable European options with stochastic correlation. Probability in the Engineering and Informational Sciences, forthcoming.
19. Wang, X. (2017b). Differences in the prices of vulnerable options with different counterparties. Journal of Futures Markets 37: 148163.
20. Warner, J., Watts, R., & Wrack, K. (1988). Stock prices and top management changes. Journal of Financial Economics 20: 461492.
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Probability in the Engineering and Informational Sciences
  • ISSN: 0269-9648
  • EISSN: 1469-8951
  • URL: /core/journals/probability-in-the-engineering-and-informational-sciences
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