Literature Review of Bankruptcy Problem

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high cost. Effective market mechanisms generally deliver better outcomes than regulation. However, when regulators enact a recovery plan for a distressed insurance company, it is important to construct an appropriate benchmark related to the guarantee benefit that can supplement the supervision mechanism. The implementation standards of governance forbearance are directly correlated to financial leverage and the insurer’s obligation of guaranteed payment.

Regulatory forbearance should focus regulation wherever it is needed most.

Regulatory forbearance involves a gradual removal of preemptive regulations and an accompanying increase in the use of general post competition regulation. There are two aspects to regulatory forbearance: (1) a regulator may refrain from applying certain regulatory actions, or from intervening in certain business activities on regulated institutions; (2) a regulator may reduce the enforcement of a certain regulation, or withdraw entirely from regulating specified market conducts, since substantial costs are potentially involved. Financial restructuring should be carefully designed to ease moral hazards.

4.1.3. Literature Review of Bankruptcy Problem

The first use of a contingent claim model to investigate the corporate bankruptcy problem appeared in Merton’s (1974) study. Merton suggested that risky debt should be modeled as risk free debt and a put option and equity as a call option on firm assets.

Earlier, Merton (1973) adopted closed-form solutions. Merton (1977, 1978, and 1989) extended his previous work to discuss default issues such as deposit insurance and other financial intermediaries. Black and Cox (1976) extended Merton’s approach to a general case in which ruin may strike at any instant. Following Merton (1974), Briys and de Varenne (1994) modeled the risk of insurer default at maturity through an option triggered by shareholders with limited liability in insurance contracts. Grosen

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and Jorgensen (2002) adopted a European type option. If the insurer is not capable of fulfill his obligation to the insured at maturity, the shareholder is not required to contribute additional collateral for insolvent debt. Since equity holders do not carry out entire default obligations, they might have certain advantages in the event of default. This is because the asymmetric return can increase the value of the bankruptcy put option, motivating the insurer to take more risk.

Briys and de Varenne (1997) extended their model by allowing a Vasicek type stochastic interest rate framework. Grosen and Jogensen (2002) extended the Black and Cox framework to model the default risk of insurance companies at any time.

Bernard et al. (2005a, 2006) built on Grosen and Jogensen's work to evaluate the solvency problem of the insurer in stochastic interest rate environments. Based on the framework of Briys and de Varenne (1994, 1997) and Grosen and Jorgensen (2002), the policyholder is the major liability holder of the insurance company. The rights of the policy holder can be decomposed into three type options at maturity. The bonus option, which provides the insured with a share of the company’s investment profit, the minimal guaranteed benefit at maturity, and a short put option, in which the insurer owns the option and can swap the asset with the liability in his balance sheet to government when the insurer defaults.

When life insurers are facing financial distress, the intervention benchmark of government authorities may require them to pay a rebate to policyholders in the event of premature closure of the firm. The total payoff to the equity holder at maturity is given through two call options, i.e., a long call option on the assets with strike equal to the promised payment at maturity, called a residual call, and a short call option offsetting the exact bonus call option of the policyholder. The firm offers a rebate to equity holders in the event of premature liquidation. This rebate also depends on the residual value of the firm after debt repayment. To evaluate the insolvency of the

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insurance company, Grosen and Jorgensen (2002) introduced the barrier option component involve in different position of the insurance policy. The barrier feature is based on the intervention rule of the regulatory authority.

The event is defined so that the value of the total assets of the life insurance company is always sufficient to cover the life insurance policyholder's initial premium compounded with the guaranteed rate of return. A bankruptcy problem exists when the insurer does not have enough assets to cover his liabilities. Under the Grosen and Jorgensen framework, firm liquidation is immediate. This is the feature of the U.S.

bankruptcy code Chapter 7; the firm will announce bankruptcy and be liquidated simultaneously.

In related bankruptcy studies, Mello and Parsons (1992), Leland (1994), Goldstein et al. (2001), and Morellec (2001) discussed Chapter 7 conditions, in which default and liquidation coincide. In practice, a company can deal with its insolvency problem not only through Chapter 7 of the U.S. Bankruptcy Code, but by attempting to renegotiate the terms of notable outstanding debts. Anderson and Sundaresan (1996), Mella-Barral and Perraudin (1997), and Fan and Sundaresan (2000) considered out-of-court renegotiation regarding the terms of outstanding debt. These papers assume that renegotiation involves no cost, relieving the firm’s debt problem.

Since liquidation incurs some costs, liability holders will inevitably suffer some loss immediately. This gives the board the option for a strategic default, meaning that the debtor only needs to pay a partial value of the whole liability.

However, few studies use the contingent claim model to analyze court supervised debt renegotiation. Indeed, Chapter 11 bankruptcy renegotiations differ from out-of-court renegotiations in many aspects that affect the renegotiation process and the firm value.

Franks and Torous (1989) and Longstaff (1990) both modeled debt value under Chapter 11 with the right to extend the maturity date of the debt. The longer this

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extension, the less valuable it is to bondholders, and hence the credit spread becomes larger on corporate debt. Francois and Morellec (2004) analyzed the optimal leverage problem under Chapter 11. Chen and Suchanecki (2007) generalized Grosen and Jogensen’s model (2002) to allow for Chapter 11 bankruptcy. Their approach adds a Parisian barrier option feature instead of the standard knock-out barrier option feature.

In guaranty fund research, Cummins (1988) provided a risk-based guaranty fund premium to reflect the risk of the insurer. This fund premium also considers stochastic liabilities and jumps in liabilities (catastrophes) and policy cohort, where liabilities are gradually reduced as claims are paid. Cummins extended Merton’s (1976) jump diffusion model and Kummer’s function to find a closed form solution in three different scenarios. Duan and Yu (2005) extended Cummins’ (1988) work, using a Monte Carlo method to incorporate interest rate uncertainty and RBC regulation in pricing guaranty fund premium. Basically, Cummins (1988) and Duan and Yu (2005) assume a US bankruptcy code Chapter 7 framework. Lee et al. (1997) considered other factors affecting the guaranty fund. They developed three different hypotheses (risk-subsidy, monitoring, and ownership-structure) to determine which guaranty fund affects risk-taking for a property-liability insurance company. Their empirical evidence supports the risk-subsidy and ownership-structure hypothesis, which means that guaranty founds increase the insurers’ risk-taking in investment activities and stock company more significant than mutual company. The monitoring hypothesis, in which the monitor between insurance competitors cannot offset the incentive for insurance company to increase their investment risk, was not supported. Downs and Sommer (1999) extended the findings of Lee et al. (1997) by addressing insider ownership. Brewer et al. (1997) found similar evidence in the life insurance industry.

They concluded that a guaranty fund system increased the risk-taking of the insurer.

The effect of regulatory forbearance on the insurance guaranty fund is the primary

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focus of this study. Following the works of Briys and de Varenne (1994, 1997), Grosen and Jogensen (2002), and Chen and Suchanecki (2007), this study extends the market framework by measuring the bankruptcy costs and compensation of the insurance guaranty fund given regulatory forbearance. This study is the first to incorporate the US Chapter 11 bankruptcy code in to the guaranty fund system. This study shows that financial leverage, performance stability, and government intervention are crucial factors influencing the cost of the guaranty fund. Section 4.2 introduces the market and cost of the guaranty fund. Section 4.3 presents the numerical results. Finally, Section 4.4 draws conclusions.

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This section reviews the insurance market framework presented in the seminal work of Briys and de Varenne (1994, 1997) and the different bankruptcy procedures presented by Grosen and Joensen (2002) and Chen and Suchanecki (2007). Extending the work in Chen and Suchanecki (2007), this study incorporates the regulatory forbearance and US bankruptcy code Chapter 11 into guaranty fund system. The Parisian barrier option features captures the effect of regulatory forbearance. Finally, embedded options are computed according to the compensation mechanism of the guaranty fund.

4.2.1. Market Framework

The basic market framework in this study was developed by Briys and de Varenne (1994), based on Merton’s (1977, 1978, 1989) approach to financial intermediaries.

The market is assumed to be a continuous-time frictionless economy with a perfect financial market. Any imperfections in the market are ignored. The initial capital structure of the insurance company at time t=0 in Briys and de Varenne (1994, 1997), Grosen and Joensen (2002) and Chen and Suchanecki (2007) is assumed in the following table:

Table 4.1 Balance Sheet of Insurance Company Asset Liability and

Owner’s equity