Abstract
Financial options, i.e., calls and puts, enable financial engineering and valuation at greater levels of complexity. This chapter explains the hedge-based valuation of calls by the Black–Scholes-Merton formula and some applications of options in finance policy.
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Notes
- 1.
Some options do not allow their holder to exercise them early. Those are called European options. The text describes the options that allow early exercise and are called American options.
- 2.
For example, a hedger may need to trade if price changes by 1%. However, price can change by, say, 3% overnight while the markets are closed. Then, the hedger wakes up to a portfolio that is carrying some risk.
- 3.
In the Cox, Ross & Rubenstein binomial option pricing model the variability of the outcomes changes as well. See John C. Cox Stephen A. Ross, & Mark Rubinstein, Option Pricing: A Simplified Approach, 7 J. Fin. Econ. 229 (1979).
- 4.
Some scholars have proposed altering the regime of limited liability for corporations; see, e.g., Henry Hansmann & Reinier Kraakman, Toward Unlimited Shareholder Liability for Corporate Torts, 100 Yale L.J. 1879 (1991); but see Nicholas L. Georgakopoulos, Avoid Automatic Piercing: A Comment on Blumberg and Strasser, 1 Acct. Econ. and L. (2011). https://doi.org/10.2202/2152-2820.1002. If limited liability were to be relaxed, the valuation of calls would need radical revision.
- 5.
See Gurdip Bakshi, Charles Gao, & Zhiwu Chen, Empirical Performance of Alternative Option Pricing Models, 52 J. Fin. 2003 (1997).
- 6.
See, e.g., Geyer v. Irgensoll Publ’ns Co., 621 A.2d 784, 791 (Del. Ch. 1992) (“[T]he fact of insolvency … causes fiduciary duties to creditors to arise.”); In re NCS Healthcare, Inc., S’holders Litig., 825 A.2d 240, 256 (Del. Ch. 2002) (“[A]s directors of a corporation in the ‘zone of insolvency,’ the NCS board members also owe fiduciary duties to the Company’s creditors.”); Credit Lyonnais Bank Nederland, N.V. v. Pathe Commc’ns Corp., Civ. A. No. 12150, 1991 WL 277613, at *34 (Del. Ch. Dec. 30, 1991) (“At least where a corporation is operating in the vicinity of insolvency, a board of directors is not merely the agent of the residue risk bearers, but owes its duty to the corporate enterprise.”); cf N.A. Catholic Educational Programming Found., Inc., v. Gheewalla, 930 A.2d 92 (Del. 2007) (creditors of corporation in zone of insolvency who are adequately protected by contract clauses do not have standing for direct action about breach of fiduciary duties against its directors).
- 7.
In the vast literature on executive compensation, evidence that managers take more risk in firms that offer executive compensation with more options appears; see, e.g., Matthew L. O’Connor & Matthew Rafferty, Incentive Effects of Executive Compensation and the Valuation of Firm Assets, 16 J. Corp. Fin. 431 (Sep. 2010); see also, e.g., Neil Brisley, Executive Stock Options: Early Exercise Provisions and Risk-Taking Incentives, 61 J. Fin. 2487 (2006).
- 8.
Lucian A. Bebchuk, A New Approach to Corporate Reorganizations, 101 Harv. L. Rev. 775 (1988).
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Georgakopoulos, N.L. (2018). Options. In: Illustrating Finance Policy with Mathematica. Quantitative Perspectives on Behavioral Economics and Finance. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-95372-4_6
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DOI: https://doi.org/10.1007/978-3-319-95372-4_6
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