Hostname: page-component-cb9f654ff-hqlzj Total loading time: 0 Render date: 2025-08-26T17:07:18.215Z Has data issue: false hasContentIssue false
  • English
  • Français

THE VALUATION OF EXECUTIVE STOCK OPTIONS UNDER GARCH MODELS

Published online by Cambridge University Press:  11 August 2017

Xingchun Wang ,
Zhiwei Su  and
Guangli Xu
Xingchun Wang
Affiliation:
School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China E-mail: xchwangnk@aliyun.com
Zhiwei Su
Affiliation:
PBC School of Finance, Tsinghua University, Beijing 100083, China E-mail: zhiweisu@foxmail.com
Guangli Xu
Affiliation:
School of Statistics, University of International Business and Economics, Beijing 100029, China E-mail: xuguangli@uibe.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

departure riskendogenous departureexecutive stock optionsGARCH models

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 3 , July 2018 , pp. 409 - 433
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Albrecher, H., Mayer, P., Schoutens, W., & Tistaert, J. (2007). The little Heston trap. Wilmott Magazine, pp. 83–92.Google Scholar
2.Carmona, J., León, A., & Vaello-Sebastià, A. (2011). Pricing executive stock options under employment shocks. Journal of Economic Dynamics and Control 35: 97–114.Google Scholar
3.Carpenter, J. (1998). The exercise and valuation of executive stock options. Journal of Financial Economics 48: 127–158.Google Scholar
4.Carr, P. & Linetsky, V. (2000). The valuation of executive stock options in an intensity-based framework. European Finance Review 4: 211–230.Google Scholar
5.Chong, T., Ding, Y., & Li, Y. (2015). Executive stock option pricing in China under stochastic volatility. Journal of Futures Markets 35: 953–960.Google Scholar
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: 447–472.Google Scholar
7.Cuny, C. & Jorion, P. (1995). Valuing executive stock options with endogenous departure. Journal of Accounting and Economics 20: 193–205.Google Scholar
8.Duan, J. & Wei, J. (2005). Executive stock options and incentive effects due to systematic risk. Journal of Banking and Finance 29: 1185–1211.Google Scholar
9.Engle, R. & Ng, V. (1993). Measuring and testing the impact of news on volatility. Journal of Finance 43: 1749–1778.Google Scholar
10.Heston, S. & Nandi, S. (2000). A closed-form GARCH option valuation model. Review of Financial Studies 13: 585–625.Google Scholar
11.Hull, J. (2015). Options, futures, and other derivatives. New Jersey: Prentice-Hall.Google Scholar
12.Johnson, S. & Tian, Y. (2000). Indexed executive stock options. Journal of Financial Economics 57: 35–64.Google Scholar
13.Kendall, M. & Stuart, A. (1977). The advanced theory of statistics, vol. 1. New York: Macmillan.Google Scholar
14.Laux, V. (2012). Stock option vesting conditions, CEO turnover, and myopic investment. Journal of Financial Economics 106: 513–526.Google Scholar
15.Shephard, N. (1991). From characteristic function to a distribution function: a simple framework for theory. Econometric Theory 7: 519–529.Google Scholar
16.Sircar, R. & Xiong, W. (2007). A general framework for evaluating executive stock options. Journal of Economic Dynamics and Control 31: 2317–2349.Google Scholar
17.Tzang, S., Wang, C., & Yu, M. (2016). Systematic risk and volatility skew. International Review of Economics and Finance 43: 72–87.Google Scholar
18.Wang, X. (2017a). Pricing vulnerable European options with stochastic correlation. Probability in the Engineering and Informational Sciences, forthcoming.Google Scholar
19.Wang, X. (2017b). Differences in the prices of vulnerable options with different counterparties. Journal of Futures Markets 37: 148–163.Google Scholar
20.Warner, J., Watts, R., & Wrack, K. (1988). Stock prices and top management changes. Journal of Financial Economics 20: 461–492.Google Scholar