Barrier Option Framework Research Articles

Political connections, government capital injection, and deposit insurance premium

PurposeThe purpose of this paper is to develop a capped barrier option framework to consider the politically preferential treatment for bank loans incentivized by government capital injections and calculate loan-risk sensitive insurance premiums.Design/methodology/approachThis paper takes a capped barrier option approach to the market valuation of the equity of the bank and the liability of the deposit insurer. The cap demonstrates the dynamics of a politically connected borrowing firm’s asset and highlights the truncated nature of loan payoffs. The barrier addresses that default can occur at any time before the maturity date. The bank participating in a government capital injection program is required to fund the politically connected firm that has preferential access to financing.FindingsPolitical connection as such makes the bank more prone to risk taking at a reduced interest margin, produces greater safety for the bank owing to government capital injections, and leads to increasing the fair deposit insurance premium. The positive effect of political connection on the deposit insurance premium, which ignores the cap and the barrier yields significant over-estimation.Originality/valueThe study on the politically connected borrowing firm shows that political connection is likely to affect the distressed bank’s performance, yielding the political-connection cost of a reduced bank interest margin and the political-connection benefit of a reduced bank equity risk, contributing the literature on political connection and bank bailout.

A barrier option framework for rescue package designs and bank default risks

Rescue packages adopted to stabilize the banking system are generally divided into three categories: government purchases of distressed assets, government guaranteed debt issuance programs, and direct equity capital injections. Countries afflicted by the recent financial crisis launched general programs in one or two, and even in three different categories. In this paper, we examine that the design of a government rescue package for a distressed bank depends on the expected reduction of the default risk in the bank's equity returns. We find that the bank's default risk is negatively related to distressed loan purchases, and to capital injections, but positively related to guaranteed debt issuance. We also find that the rescue package including all three categories is not guaranteed to increase stability for the rescued bank. Specifically, the combination of distressed loan purchases and capital injections is superior to the package of the three categories in addition to the solo instrument. This suggests that an effective design of a government rescue package for the financial services industry largely depends on its targets.

A barrier option framework for bank interest margin management under anticipatory regret aversion

This paper proposes a framework for bank equity valuation based on a path-dependent, barrier option model. A direct implication of this framework is that bank equity will be priced as a down-and-out call option. Using this approach, we examine how bank interest margin, i.e., the spread between the loan rate and the deposit rate, is determined when a bank is regret-averse. Regret-averse preferences are characterized by a down-and-in call, which is specified as the difference between a standard call and a down-and-out call. The model demonstrates how anticipatory regret aversion and the default barrier jointly determine an optimal bank interest margin decision. We find that a bank interest margin with a low level of default barrier is negatively related to anticipatory regret aversion and to the default barrier. Regret aversion and default barriers make a bank less prudent and more prone to risk-taking, thereby adversely affecting the stability of the banking system.

On the Determinants of the Implied Default Barrier

We use the maximum likelihood (ML) estimation approach to estimate the default barriers from market values of equities for a sample of 762 public industrial Canadian firms. The ML approach allows estimating simultaneously the asset's instantaneous drift, volatility and the barrier level, when the firm's equity is priced as a Down-and-Out European call (DOC) option. We find that the estimated barrier is positive and significant in our sample. Moreover, we compare the default prediction accuracy of the DOC framework with the KMV-Merton approach. Using probit estimation, we find that the default probability from the two structural models provides similar in-sample fits, but the barrier option framework achieves better out-of-sample forecasts. Regression analysis shows that leverage is not the only determinant of the default barrier. The implied default threshold is also positively related with financing costs, and negatively to liquidity, asset's volatility and firm's size. We also find that liquidation costs, renegotiation frictions and equity holders bargaining power increase the implied default barrier level.

Model Implied Credit Spreads

I propose a new procedure for extracting probabilities of default from structural credit risk models based on model implied credit spreads (MICS) and implement this approach assuming a barrier option framework nesting the Merton (1974) model of capital structure. MICS are the increase in the payout to debt-holders necessary to oset the impact of an increase in asset variance on the option value of debt and equity. In contrast to real-world credit spreads, MICS do not contain risk premia for default timing and recovery uncertainty, thus yielding a purer estimate of physical default probabilities. Relative to a standard distance to default (DD) measure, my measure (i) predicts higher credit risk for safe rms and lower credit risk for rms with high volatility and leverage (ii) requires fewer parameter assumptions (iii) clearly outperforms the DD measure when used to predict corporate default.

Risk-Shifting Behavior at Commercial Banks Under Different Deposit Insurance Systems: Further Evidence from U.S. Markets

This paper provides further evidence regarding the effect of deposit insurance on the risk-shifting behavior at commercial banks in the United States. In particular, we compare the risk-shifting behavior of commercial banks before and after adopting the risk-based capital requirements in the U.S. market. To test the risk-shifting behaviors, we propose a new pricing model for the valuation of deposit insurance premium using a barrier option framework. We also estimate the unknown parameters using a maximum likelihood estimation method rather than Ronn and Verma’s (1986) two-equation approach. We find that the risk-shifting behaviors at commercial banks have reduced significantly but have not disappeared after the adoption of a risk-based deposit insurance system. The risk-shifting behavior at commercial banks still exists, especially for those banks with high risks or high financial distress probabilities. We find that the deposit insurance reform prevents large banks from shifting their risk to the deposit insurers as well.

Model Implied Credit Spreads

I propose a new measure of credit risk, model implied credit spreads (MICS), which can be extracted from any structural credit risk model in which debt values are a function of asset risk and the payout ratio. I implement MICS assuming a barrier option framework nesting the Merton (1974) model of capital structure. MICS are the increase in the payout to creditors necessary to offset the impact of an increase in asset variance on the option value of debt. Endogenizing asset payouts, my measure (i) predicts higher credit risk for safe firms and lower credit risk for firms with high volatility and leverage than a standard distance to default (DD) measure and (ii) clearly outperforms the DD measure when used to predict corporate default or to explain variations in credit spreads.

EMPIRICAL STUDIES OF STRUCTURAL CREDIT RISK MODELS AND THE APPLICATION IN DEFAULT PREDICTION: REVIEW AND NEW EVIDENCE

This paper first reviews empirical evidence and estimation methods of structural credit risk models. Next, an empirical investigation of the performance of default prediction under the down-and-out barrier option framework is provided. In the literature review, a brief overview of the structural credit risk models is provided. Empirical investigations in extant literature papers are described in some detail, and their results are summarized in terms of subject and estimation method adopted in each paper. Current estimation methods and their drawbacks are discussed in detail. In our empirical investigation, we adopt the Maximum Likelihood Estimation method proposed by Duan [Mathematical Finance10 (1994) 461–462]. This method has been shown by Ericsson and Reneby [Journal of Business78 (2005) 707–735] through simulation experiments to be superior to the volatility restriction approach commonly adopted in the literature. Our empirical results surprisingly show that the simple Merton model outperforms the Brockman and Turtle [Journal of Financial Economics67 (2003) 511–529] model in default prediction. The inferior performance of the Brockman and Turtle model may be the result of its unreasonable assumption of the flat barrier.

PRICING DEFAULT RISK WITH PARISIAN OPTIONS: EMPIRICAL EVIDENCE FROM HIGH GROWTH COMPANIES

In the stock market crash of 2000 many internet firms that were ostensibly bankrupt were able to stave off bankruptcy by seeking protection under Chapter 11 or avoid it completely through refinancing or merging with another company. The implication is that these firms had a de facto option to choose when to default and that this option had substantial value. This paper builds on this insight and investigates how the value of a company is affected by the default option and the choice of the relevant bankruptcy procedures. We use a Parisian barrier option framework and extend Schwartz and Moon's (2000) contingent claim model, which implies only a Chapter 7 bankruptcy procedure, to allow for the more general bankruptcy procedure of Chapter 11. We consider bankruptcy procedures that are explicitly based on the time spent in financial distress and include a "grace" period in the model to more realistically capture the effects of default risk on firm value. Finally, we develop an efficient Monte Carlo method to price approximations for the Parisian options. Some numerical results and comparative statics are also performed to demonstrate the characteristics of cumulative and consecutive Parisian options and investigate their effects on the value of high growth firms.

The Market Value of Life Insurance Liabilities Under a Regime Switching Process

This paper studies the values of the equity and liabilities of life insurance companies in the presence of regime switching in the economy. Following the contingent claim work of Grosen and Jorgensen (2002), where the equity and liability of a life insurance company are evaluated as a barrier option framework, this paper proposes a model where the dynamic evolution of the assets follows a geometric Brownian motion with parameters switching according to a continuous-time Markov chain process with discrete state values. After deriving valuation formulas, numerical implementation is illustrated using US life insurance data, providing strong evidence of switching behavior on the market affecting the contingent claim valuation.

On the Determinants of the Implied Default Barrier

We use the maximum likelihood (ML) estimation approach to estimate the default barriers from market values of equities for a sample of 762 public industrial Canadian firms. The ML approach allows us to estimate the asset instantaneous drift, volatility and barrier level simultaneously, when the firm's equity is priced as a Down-and-Out European call (DOC) option. We find that the estimated barrier is positive and significant in our sample. Moreover, we compare the default prediction accuracy of the DOC framework with the KMV-Merton approach. Using probit estimation, we find that the default probability from the two structural models provides similar in-sample fits, but the barrier option framework achieves better out-of-sample forecasts. Regression analysis shows that leverage is not the only determinant of the default barrier. The implied default threshold is also positively related to financing costs, and negatively to liquidity, asset volatility and firm size. We also find that liquidation costs, renegotiation frictions and equity holders' bargaining power increase the implied default barrier level.

Bank capital regulation in a barrier option framework

The barrier options theory of corporate security valuation is applied to the contingent claims of a regulated bank. The regulator/insurer of a bank owns a down-and-in call option on the bank assets which can be balanced against the expected coverage cost. Raising the regulatory barrier (critical asset level triggering bank closure) leads to a transfer of wealth from stockholders to the insurer and reduces stockholder incentives to increase asset risk. Empirical tests on a sample of 152 one-bank holding companies show that regulatory barriers are priced in the stock market and are inversely related to Tier 1 leverage ratios.

Performance of default risk model with barrier option framework and maximum likelihood estimation: Evidence from Taiwan

We investigate the performance of a default risk model based on the barrier option framework with maximum likelihood estimation. We provide empirical validation of the model by showing that implied default barriers are statistically significant for a sample of construction firms in Taiwan over the period 1994–2004. We find that our model dominates the commonly adopted models, Merton model, Z-score model and ZETA model. Moreover, we test the n-year-ahead prediction performance of the model and find evidence that the prediction accuracy of the model improves as the forecast horizon decreases. Finally, we assess the effect of estimated default risk on equity returns and find that default risk is able to explain equity returns and that default risk is a variable worth considering in asset-pricing tests, above and beyond size and book-to-market.

Estimating default barriers from market information

Brockman and Turtle [J. Finan. Econ., 2003, 67, 511–529] develop a barrier option framework to show that default barriers are significantly positive. Most implied barriers are typically larger than the book value of corporate liabilities. We show theoretically and empirically that this result is biased due to the approximation of the market value of corporate assets by the sum of the market value of equity and the book value of liabilities. This approximation leads to a significant overestimation of the default barrier. To eliminate this bias, we propose a maximum likelihood (ML) estimation approach to estimate the asset values, asset volatilities, and default barriers. The proposed framework is applied to empirically examine the default barriers of a large sample of industrial firms. This paper documents that default barriers are positive, but not very significant. In our sample, most of the estimated barriers are lower than the book values of corporate liabilities. In addition to the problem with the default barriers, we find significant biases on the estimation of the asset value and the asset volatility of Brockman and Turtle.

Default risk, bankruptcy procedures and the market value of life insurance liabilities

The topic of insolvency risk in connection with life insurance companies has recently attracted a great deal of attention. In this paper, the question is investigated of how the values of the equity and of the liability of a life insurance company are affected by the default risk and the choice of the relevant bankruptcy procedure. As an example, the US Bankruptcy Code with Chapter 7 and Chapter 11 bankruptcy procedures is used. Grosen and Jørgensen’s [Grosen, A., Jørgensen, P.L., 2002. Life insurance liabilities at market value: An analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework. J. Risk Insur. 69 (1), 63–91] contingent claim model, implying only a Chapter 7 bankruptcy procedure, is extended to allow for more general bankruptcy procedures such as Chapter 11. Thus, more realistically, default and liquidation are modelled as distinguishable events. This is realized by using so-called standard and cumulative Parisian barrier option frameworks. It is shown that these options have appealing interpretations in terms of the bankruptcy mechanism. Furthermore, a number of representative numerical analyses and comparative statics are performed in order to investigate the effects of different parameter changes on the values of the insurance company’s equity and liability, and hence on the value of the life insurance contract. To complete the analysis, the shortfall probabilities of the insurance company implied by the proposed models are computed and compared.

A barrier option framework for corporate security valuation

This paper proposes a framework for corporate security valuation based on path-dependent, barrier option models instead of the commonly used path-independent approach. We argue that path dependency is an intrinsic and fundamental characteristic of corporate securities because equity can be knocked out whenever a legally binding barrier is breached. A direct implication of this framework is that equity will be priced as a down-and-out call option. We provide empirical validation of the barrier model by showing that implied barriers are statistically and economically significant for a large cross-section of industrial firms. Additional robustness tests confirm that barriers remain significant over a wide range of input variable estimates. And finally, we apply the barrier option framework to bankruptcy prediction and find that implied failure probabilities dominate Z-scores in most cases.

Life Insurance Liabilities at Market Value: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework

AbstractThis article takes a contingent claim approach to the market valuation of equity and liabilities in life insurance companies. A model is presented that explicitly takes into account the following: (i) the holders of life insurance contracts (LICs) have the first claim on the company's assets, whereas equity holders have limited liability; (ii) interest rate guarantees are common elements of LICs; and (iii) LICs according to the so‐called contribution principle are entitled to receive a fair share of any investment surplus. Furthermore, a regulatory mechanism in the form of an intervention rule is built into the model. This mechanism is shown to significantly reduce the insolvency risk of the issued contracts, and it implies that the various claims on the company's assets become more exotic and obtain barrier option properties. Closed valuation formulas are nevertheless derived. Finally, some representative numerical examples illustrate how the model can be used to establish the set of initially fair contracts and to determine the market values of contracts after their inception.

Life Insurance Liabilities at Market Values: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework

This article takes a contingent claim approach to the market valuation of equity and liabilities in life insurance companies. A model is presented that explicitly takes into account the following: (i) the holders of life insurance contracts (LICs) have the first claim on the company's assets, whereas equity holders have limited liability; (ii) interest rate guarantees are common elements of LICs; and (iii) LICs according to the so-called contribution principle are entitled to receive a fair share of any investment surplus. Furthermore, a regulatory mechanism in the form of an intervention rule is built into the model. This mechanism is shown to significantly reduce the insolvency risk of the issued contracts, and it implies that the various claims on the company's assets become more exotic and obtain barrier option properties. Closed valuation formulas are nevertheless derived. Finally, some representative numerical examples illustrate how the model can be used to establish the set of initially fair contracts and to determine the market values of contracts after their inception.