Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T08:31:59.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Fair-value analytical valuation of reset executive stock options consistent with IFRS9 requirements

Published online by Cambridge University Press:  23 January 2020

Otto Konstandatos
Otto Konstandatos*
Affiliation:
Finance Department, University of Technology Sydney, NSW 2007, Australia
*
*Corresponding author. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Executive stock options (ESOs) are widely used to reward employees and represent major items of corporate liability. The International Accounting Standards Board IFRS9 financial reporting standard which came into full effect on 1-Jan 2018, along with its Australian implementation AASB9, requires public corporations to report their fair-value cost in financial statements. Reset ESOs are typically issued to re-incentivise employees by allowing the option to be cancelled and re-issued with a lower exercise price or later maturity. We produce a novel analytical Reset ESO valuation consistent with the IFRS9 financial reporting standard incorporating the simultaneous resetting of vesting period, exercise window, reset level and maturity. We allow for voluntary and involuntary exercise. Our analytical result is expressed solely in terms of standardised European binary power option instruments. Using the multi-state mortality model of Hariyanto (2014, Mortality and disability modelling with an application to pricing a reverse mortgage contract, PhD thesis, University of Melbourne), we estimate longitudinal disability and death transition probabilities from cross-sectional data. We determine survival functions for pre-vesting forfeiture or post-vesting involuntary exercise for use with weighted portfolios of our formulae to illustrate the effect of survival on the fair value. We examine the IFRS9 method of valuation using expected time to option exercise and demonstrate a consistent overestimation of fair value of up to 27% for senior executives.

Keywords

Executive compensationExotic optionsResettingNon-life insurance liabilitiesIFRSM40G30G32J33
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 1 , March 2020 , pp. 188 - 218
Copyright
© Institute and Faculty of Actuaries 2020 

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.)

References

AAA (2006). American academy of actuaries practice note: Valuation of employee stock options. Available online at the address https://www.actuary.org/files/publications/Draft_practice_note_Valuation_of_Employee_Stock_Options_oct2006.pdfGoogle Scholar
AASB9 (2014). Australian accounting standards board standard: Financial instruments. Available online at the address https://www.aasb.gov.au/admin/file/content105/c9/AASB9_12-14.pdf Google Scholar
ABS (2004). Disability, ageing and carers: Summary of findings, Australia. ABS Cat. No. 4430.0, Canberra.Google Scholar
Acharya, V. V., John, K. & Sundaram, R.K. (2000). On the optimality of resetting executive stock options. Journal of Financial Economics 57, 65–101.CrossRefGoogle Scholar
AIA (2014). Australian institute of actuaries information note: Valuation of share-based payments. Available online at the address http://www.actuaries.asn.au/Library/Standards/FinanceInvestment/2014/ValuationofShareBasedPaymentsJune2014.pdf Google Scholar
Bermin, H., Buchen, P., & Konstandatos, O. (2008). Two exotic lookback options. Applied Mathematical Finance, 15(4), 387–402.10.1080/13504860802012824CrossRefGoogle Scholar
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.10.1086/260062CrossRefGoogle Scholar
Brenner, M., Sundaram, R., & Yermack, D. (2000). Altering the terms of executive stock options. Journal of Financial Economics, 57, 103–128.CrossRefGoogle Scholar
Buchen, P. (2001). Image options and the road to barriers. Risk Magazine, 14(9), 127–130.Google Scholar
Buchen, P. (2004). The pricing of dual-expiry exotics. Quantitative Finance, 4(1), 101–108.CrossRefGoogle Scholar
Buchen, P. (2012). An Introduction to Exotic Option Pricing. CRC Press, Taylor & Francis Group, USA.CrossRefGoogle Scholar
Buchen, P. & Konstandatos, O. (2005). A new method of pricing lookback options. Mathematical Finance 15(2), 245–259.CrossRefGoogle Scholar
Buchen, P. & Konstandatos, O. (2009). A new approach to pricing double barrier options with arbitrary payoffs and curved boundaries. Applied Mathematical Finance, 16(6), 497–515.CrossRefGoogle Scholar
Carpenter, J. (1998). The exercise and valuation of executive stock options. Journal of Financial Economics, 48(2), 127–158.CrossRefGoogle Scholar
Carpenter, J., Stanton, R. & Wallace, N. (2010). Optimal exercise of executive stock options and implications for firm cost. Journal of Financial Economics, 98, 315–337.CrossRefGoogle Scholar
Carr, P. & Linetsky, V. (2000). The valuation of executive stock options in an intensity-based framework. European Finance Review 4, 211–230.10.1023/A:1011441824560CrossRefGoogle Scholar
Carter, M.E. & Lynch, L. J. (2001). An examination of executive stock option repricing. Journal of Financial Economics, 61, 207–255.10.1016/S0304-405X(01)00060-5CrossRefGoogle Scholar
Carter, M.E. & Lynch, L. J. (2004). The effect of stock option repricing on employee turnover. Journal of Accounting and Economics, 37(1), 91–112.CrossRefGoogle Scholar
Chance, D., Kumar, R., & Todd, R. (2000). The “repricing” of executive stock options. Journal of Financial Economics, 57, 129–154.CrossRefGoogle Scholar
Corrado, C., Jordan, B., Jr, T. M., & Stansfield, J. (2001). Repricing and employee stock option valuation. Journal of Banking and Finance, 25(6), 1059–1082.CrossRefGoogle Scholar
Dai, M. & Kwok, Y.K. (2005). Options with combined reset rights on strike and maturity. Journal of Economic Dynamics and Control, 29(9), 1495–1515. Available online at the address https://doi.org/10.1016%2Fj.jedc.2004.09.001 CrossRefGoogle Scholar
Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1(2), 141–149.Google Scholar
Goergen, M. & Renneboog, L. (2011). Managerial compensation. Journal of Corporate Finance, 17, 1068–1077.10.1016/j.jcorpfin.2011.06.002CrossRefGoogle Scholar
Hall, B. & Murphy, K. (2002). Stock options for undiversified employees. Journal of Accounting and Economics 33, 3–42.10.1016/S0165-4101(01)00050-7CrossRefGoogle Scholar
Hariyanto, E.A. (2014). Mortality and disability modelling with an application to pricing a reverse mortgage contract. Ph.D. thesis, University of Melbourne.Google Scholar
Hu, Y., Jin, H., & Zhou, X. (2017). Time-inconsistent stochastic linear quadratic control: Characterisation and uniqueness of equilibrium. Siam Journal on Control and Optimization, 5(3), 475–488.Google Scholar
Hull, J., & White, A. (2004). How to value employee stock options. Financial Analysts Journal 60(1), 114–119.CrossRefGoogle Scholar
Johnson, J., & Tian, Y. (2000). The value and incentive effects of nontraditional executive stock option plans. Journal of Financial Economics, 57(1), 3–34.10.1016/S0304-405X(00)00049-0CrossRefGoogle Scholar
Konstandatos, O. (2003). A new framework for pricing barrier and lookback options. Ph.D. thesis, University of Sydney.Google Scholar
Konstandatos, O. (2008). Pricing Path Dependent Options: A Comprehensive Mathematical Framework. VDM Verlag, Saarbruecken, Germany.Google Scholar
Kyng, T., Konstandatos, O. & Bienek, T. (2016). Valuation of employee stock options using the exercise multiple approach and life tables. Insurance: Mathematics and Economics, 68(5), 17–26.Google Scholar
Lambert, R., Larcker, D. & Verrechia, R. (1991). Portfolio considerations in valuing executive compensation. Journal of Accounting Research, 29, 129–149.CrossRefGoogle Scholar
Leung, E. (2004). Projecting the needs and costs of long term care in Australia. Australian Actuarial Journal, 10(2), 343–385.Google Scholar
Leung, E. (2006). A multiple state model for pricing and reserving private long term care insurance contracts in Australia. Australian Actuarial Journal, 12(2), 187–247.Google Scholar
Leung, K.S. & Kwok, Y.K. (2008). Employee stock option valuation with repricing features. Quantitative Finance, 8(6), 561–569.CrossRefGoogle Scholar
Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4(1), 141–183.10.2307/3003143CrossRefGoogle Scholar
Oberman, A. & Zariphopoulou, T. (2003). Pricing early exercise contracts in incomplete markets. Computational Management Science, 1(1), 75–107.CrossRefGoogle Scholar
Rickayzen, B. & Walsh, D. (2002). Multi-state model of disability for the United Kingdom: Implications for future need for long-term care for the elderly. British Actuarial Journal, 8(2), 341–393.CrossRefGoogle Scholar
Rubinstein, M. & Reiner, E. (1991). Breaking down the barriers. Risk Magazine, 4(8), 28–35.Google Scholar
Sircar, R. & Xiong, W. (2007). A general framework for evaluating executive stock options. Journal of Economic Dynamics and Control, 31, 2317–2349.CrossRefGoogle Scholar
Wilmoth, J., Andreev, K., Jdanov, D. & Glei, D. (2007). Protocol for the Human Mortality Database. http://www.mortality.org/Public/Docs/MethodsProtocol.pdf Google Scholar
Wu, Y.W. (2009). The incentive effect of repricing in employee stock options. Review of Accounting and Finance, 8(1), 38–53.Google Scholar