James HC Britten Robert W Vivian School of Economic and Business Sciences

1. A CRITIQUE OF THE INSOLVENCY PUT OPTION FRAMEWORK AND ITS ROLE WITHIN CAPITAL-BASED INSURANCE REGULATION James HC Britten Robert W Vivian School of Economic and Business Sciences University of the Witwatersrand SAFA 2012 Conference, January 19, Cape Town

2. Purpose of the Paper • To examine the influence of the insolvency put option framework on capital-based regulation within a short-term insurer • This paper argues that when a firm defaults on its debt, shareholders have allowed an embedded call option to expire unexercised • Importantly, viewing insolvency from the perspective of a call option results in very different incentives than that predicted by the insolvency put option framework

3. Babbel et al’s value of the firm • Babbel et al (1983; 1997; 1998; 1999; 2000; 2002; 2005) • Market value of a firm • Franchise value + • (Value of assets – Value of liabilities) + • Put option = F + (A-L) + OP

4. Market Value of an Insurer vs. Risk Source: Babbel and Merrill (2005)

5. Limited liability and option theory • “Put option value arises from the limited liability enjoyed by equity holders when their firm issues (sic) [incurs] debt” Babbel et al 2005 • Hence, when shareholders default on their obligations they are said to have exercised their insolvency put option • P = Max(L – A, 0)

6. Path of the Literature • Black and Scholes (1973) and Merton (1973b), opened the door to nearly limitless applications of option methodologies to value any financial claim on a firm • Yet it was Merton (1974, 1977)’s use of option pricing techniques to value risky debt that set the idea of the insolvency put option in motion • More recent applications of the insolvency put option framework have been put forward by Myers and Read (2001); Mildenhall (2004); Venter (2004); Sherris (2006); Sherris and van derHoek (2006)

7. Introduction of the corporate form • The 1855 Limited Liability Act • Separated legal personality of the shareholder from that of the firm • Shareholders were provided with a cap on their liability exposure to the amount of their invested share capital • The introduction of the limited liability company resulted in an asymmetrical payoff profile for shareholders • An equity investment in a limited liability company possessed an inherent call option quality

8. Two problems with Babbel (1998) & Babbel and Merrill (2005) • Equity holders do not place any value on a so-called insolvency put option • The market value of a firm will not increase as risk increases

9. The insolvency put model: only appropriate for analysing third party guarantees • The original association of default with the exercising of a put option was expressed by Merton (1977) to specifically describe deposit insurance

10. The insolvency put model: only appropriate for analysing third party guarantees • He made no suggestion that bankruptcy occurs when shareholders exercise a valuable put • Shareholders payoff remains a Max(0, A – X) regardless of any third-party guarantees

11. The Importance of the Call Option Perspective • The incentives behind put and a call options are starkly different • Call option holders will want to defer exercise (even if the option is in-the-money) until expiration; put option holders will want to exercise an in-the-money put immediately • By holding an implicit call option on an insurer’s assets, shareholders have an incentive to keep the company running: • Shareholders typically try and avoid bankruptcy proceedings whereas creditors try and force default in order to recover as much of their loans as possible

12. The Importance of the Call Option Perspective • A shareholder will default on their firm’s debt if their implicit call is out-of-the-money with no time value • Thus, an out-of-the-money call option is only a risk at expiration • If positive time to expiration exists, the call option will be kept in place • Consequently, time value can be viewed as a firm’s going concern • The insolvency put option model emphasizes the non expiration periods • Overstates the possibility of exercise and thus, overstates the risk of default

13. The Insolvency Put Option and Capital Adequacy • The interaction of the insolvency put and the regulatory emphasis on Basel style capital adequacy can lead to problems • Market procyclicality can cause capital to become scarce (Borio, 2009; Adrian & Shin, 2009) • When minimum capital standards are breached during a market crisis (such as the credit crisis of 2007/2008), the ensuing lack of liquidity will prevent the recapitalisation of an insurer: • Those that have ample capital will be reluctant to assist an insurer faced with regulatory intervention • Overall, the scarcity of capital will eliminate the time value of the implicit call option, forcing an otherwise healthy insurer into bankruptcy

14. Incorporating the Implicit Call Option • Any investment, be it for an individual or a company, begins with an initial level of wealth, Xt0. If an investor purchases ∆0 share of assets initially and later buys more of the asset, say ∆1 at time t, then the progressive change in wealth can be expressed as: …1 Where St denotes the price of the asset.

15. Incorporating the Implicit Call Option • If P0 = S0 and if ∆i shares are held over the period ti to ti+1,it follows then that the wealth expression becomes: …2

16. Incorporating the Implicit Call Option • Equation (2) can be generalised further: …3 Where, Ksis an adapted process

17. Incorporating the Implicit Call Option • Equation (3) demonstrates how regulatory intervention enforcing capital requirements during a financial crisis can lead to default; time value will be eliminated, leading to a zero value for Ps. • All that will remain is c, which in the context of insolvency can be regarded as salvage value

19. Conclusion • When creditors trade with a firm they implicitly, conceptually, grant a call option to the shareowners of the firm on the value of their assets in the firm (ie their claims against the firm) • As a result of holding an implicit call option, shareholders have an incentive to delay bankruptcy for as long as possible, making insolvency less likely than that predicted by the insolvency put option model • The combination of the insolvency put framework and capital-based regulation can have unintended consequences • Forcing an insurer to recapitalise at a time when capital dries up will eliminate the time value of the implicit call option • Focusing on premium income and not capital, will help mitigate the disruptions caused by the procyclicality of the capital markets