Contingent Claims Analysis Research Articles

Project Finance with Limited Recourse

Project finance has become an important method for financing large-scale, capital-intensive projects, such as power plants, oil pipelines, roads, tunnels, etc. We analyze debt capacity and risk choice in a project finance arrangement where the project9s lenders have limited recourse to the sponsoring company9s assets. We draw a parallel between vulnerable financial guarantee loans and project finance loans with limited recourse. Using contingent claims analysis, we illustrate the trade-offs between risk and debt capacity in those cases where the project9s lenders have recourse to the sponsor9s assets and in those where they do not. <b>TOPICS:</b>Credit risk management, project finance, volatility measures

Value creation with Dye’s disclosure option: optimal risk-shielding with an upper tailed disclosure strategy

Dye [J Account Res 23 (1985) 123] showed that the optimal disclosure policy, when a manager is randomly endowed with perfect private information, is upper tailed, i.e., the manager only discloses firm value above an appropriate cutoff level. We interpret this strategically as an optimal exercise by management of the embedded formal option to report value. Given any disclosure cutoff level, we value the corresponding option using contingent claims analysis. It is shown that the Dye disclosure cutoff value maximizes the formal option value. We find it to be the minimum possible conditional valuation (conditioned by non-disclosure) which is thus consistent with the intuition that investors should value conservatively. We show how the Dye cutoff can be interpreted as a strike price in a ‘protective put’ which offers a shield against risk of disclosure of low value. The strategic analysis is further extended by allowing the probability level that the manager is informed to be a choice variable. We show that the manager will never choose to be perfectly endowed with information, and is likely to be more endowed than unendowed. We also present a simple worked example which shows how the total value of the firm changes once the Dye option is formally incorporated.

A New Approach for Firm Value and Default Probability Estimation beyond Merton Models

In this paper we present a new model to assess the firm value and the default probability by using a bivariate contingent claim analysis and copula theory. First we discuss an unfeasible case, given the current derivative market on corporate bonds, which involves univariate digital options to compute the risk neutral probabilities. We then discuss a feasible model, which considers risky interest rates, instead. Moreover, we develop in this framework a new methodology to extract default probabilities from stock prices, only, going beyond the standard KMV-Merton model. Besides, the non-observability of the Merton model's state variable requires numerical methods, but the results can be unstable with noisy risky data. We show how the null price can be used as a useful barrier to separate an operative firm from a defaulted one, and to estimate its default probability. We then present an empirical application with both operative and defaulted firms to show the advantages of our approach.

Volatility of GDP, Macro Applications and Policy Implications of Real Options for Structure of Capital Markets

The traditional marshallian rule of investing (abandoning) when the value of an underlying asset is above (below) the cost of an alternative investment is modified in the presence of uncertainty and irreversibility giving rise to an option component into decisions. This component is affected by the degree of volatility of underlying assets, which in turn can derive their volatility from the economy as a whole, affecting the investment process and therefore the accumulation of capital and future growth. In the same tense, the evidence of volatility in the returns of the underlying assets of the economy affects the market value of debt contracts, conveying recommendations regarding the financial architecture of the economy and the type of financial instruments better suited. The paper explores the application of contingent claims analysis both to the potential effect of macro volatility on aggregate investment, and to the effect on the presence of high levels of indebtedness of the economy, with a special application to the Argentinean economy where we obtain that economies with high level of volatility would require a significant level of internal saving and capital markets driven mainly by equity instruments of financing, which helps to better accommodate uncertainty by means of the price of assets.

Valuation of Intergenerational Transfers in Funded Collective Pension Schemes

This paper applies contingent claim analysis to value pension contracts for real-life collective pension plans with intergenerational risk sharing and offering DB-like benefits. We rewrite the balance sheet of such a pension und as an aggregate of embedded generational options. This implies that a pension fund is a zero-sum game in value terms, so any policy change inevitably leads to value transfers between generations. We explore intergenerational value transfers that may arise from a plan redesign or from changes in funding policy and risk sharing rules. We develop a stochastic framework which accounts for time-varying investment opportunities and computes the embedded generational options. Changes in the values of the generational options enable us to evaluate the impact of policy modifications in the pension contract with respect to intergenerational transfers and redistribution. We find that a switch to a less risky asset mix is beneficial to elderly members at the expense of younger members who lose value. A reallocation of risk bearing from a plan with flexible contributions and fixed benefits to a plan with fixed contributions and flexible benefits leads to value redistribution from older plan members to younger ones.

A Comparison of Measures of Earnings Per Share

This paper explores alternative methods for computing earnings per share (EPS) for a company whose capital structure consists of ordinary shares and warrants. The methods for computing EPS identified by the FASB (1996) are critically evaluated and an alternative measure, the holding period approach,is developed within the framework of contingent claims analysis. Two types of errors are shown to characterize the accounting measures of EPS. One arises from failure of accounting measures to fully recognize the contingent nature of the warrant. The other arises from the practice of not recognizing instances of anti-dilution. A further factor is the treatment of any difference between the proceeds from the issue of the warrants and their fair value at that time. This is ignored in existing measures and yet may have a significant effect on the value of the claims of ordinary shareholders on the company’s earnings. Using a simulation method it is shown that the imputed earnings method of computing EPS is a very close approximation to the holding period method and is considerably more accurate than treasury stock measures favoured by accounting standards bodies.

On Debt Service and Renegotiation when Debt-Holders are More Strategic

The contingent claims analysis of the firm financing often presents a debt renegotiation game with a passive bank which does not use strategically its capability to force liquidation, contrary to what is observed in practice. The first purpose of this paper is to introduce more strategic bank behaviour into the continuous-time model developed by Mella-Barral and Perraudin (1997) and Hackbarth, Hennessy, and Leland (2007). Its second purpose is to account for variations in the information obtained by the parties during the contract period. We show that with public information and private debt only, the optimal probability of debt renegotiation is high when the firm's anticipated liquidation value is high. When we add public debt and asymmetric information, the good-type firm may be tempted to mimic the bad-type to reduce its debt service. We show that to deter such mimicking, banks may sometimes refuse to renegotiate with strong firms having a low liquidation value. We consider private and public debt. At the date of debt emission (when the bank and the firm agree on the private debt level), the bank and the firm do not know the LGD value, so both use the ex ante expected value that set the anticipated ex post renegotiation possibility. After the signature of the debt contract, the firm learns its private LGD while the bank does not observe it, so there is asymmetric information on this parameter at the renegotiation stage. Two scenarios are considered. When we consider an economy where the tax rate is high and a corresponding high debt capacity, the bank has no incentive to fix a renegotiation probability lower than one on any firm type because this would reduce debt value, and thus the firm's debt capacity. However, when the tax rate is sufficiently low, the bank may find it beneficial to use a self-selection mechanism to separate the firm types and increase its debt capacity. We show that a renegotiation probability strictly between zero and one for the bad-type (lower liquidation value) allows the bank to deter the good-type from mimicking the bad-type in order to obtain better renegotiation conditions (sooner and with a lower debt service). Our results are in line with the empirical observation that recovery rate at emergence of bankruptcy is function of the share of private debt in all the firm's debt and is relatively low (Carey and Gordy, 2007).

Extending the Merton Model: A hybrid approach to assessing credit quality

In this paper we have combined fundamental analysis and contingent claim analysis into a hybrid model of credit risk measurement. We have extended the standard Merton approach to estimate a new risk neutral distance to default metric, assuming a more complex capital structure, adjusting for dividend payments, introducing randomness to the default point and allowing a fractional recovery when default occurs. Then, using financial ratios, other accounting based measures and the risk neutral distance to default metric from our structural model as explanatory variables we estimate the hybrid model with an ordered probit regression method. Using the same econometric method, we estimate a model using financial ratios and accounting variables as explanatory variables and a model using our risk neutral distance to default metric as unique explanatory variable. We have found that by enriching the risk neutral distance to default metric with financial ratios and accounting variables into the hybrid model, we can improve both in-sample fit of credit ratings and out-of-sample predictability of defaults. Our main conclusion is that financial ratios and accounting variables contain significant and incremental information; thus the risk neutral distance to default metric does not reflect all available information regarding the credit quality of a firm.

A New Framework for Analyzing and Managing Macrofinancial Risks of an Economy

The high cost of international economic and financial crises highlights the need for a comprehensive framework to assess the robustness of national economic and financial systems. This paper proposes a new comprehensive approach to measure, analyze, and manage macroeconomic risk based on the theory and practice of modern contingent claims analysis (CCA). We illustrate how to use the CCA approach to model and measure sectoral and national risk exposures, and analyze policies to offset their potentially harmful effects. This new framework provides economic balance sheets for inter-linked sectors and a risk accounting framework for an economy. CCA provides a natural framework for analysis of mismatches between an entity's assets and liabilities, such as currency and maturity mismatches on balance sheets. Policies or actions that reduce these mismatches will help reduce risk and vulnerability. It also provides a new framework for sovereign capital structure analysis. It is useful for assessing vulnerability, policy analysis, risk management, investment analysis, and design of risk control strategies. Both public and private sector participants can benefit from pursuing ways to facilitate more efficient macro risk accounting, improve price and volatility discovery, and expand international risk intermediation activities.

The Value of Fighting Irreversible Demise by Softening the Irreversible Cost

We study a novel issue in the real-options-based technology innovation literature by means of double barrier contingent claims analysis. We show how much a firm with the monopoly over a project is willing to spend in investment technology innovation that softens the irreversible cost of accessing the project before its irreversible demise. The answer depends on the project's characteristics and on the effectiveness demanded from technology innovation.

Comparing petroleum fiscal regimes under oil price uncertainty

This study investigates and compares five upstream petroleum fiscal systems under crude oil price uncertainty. The fiscal systems analyzed are: the Alberta Canada tax and royalty system, the Papua New Guinea (PNG) (pre-2003) traditional Rate of Return (ROR) system, the Sao Tome and Principe/Nigerian Joint Development Zone (SNJDZ) Production Sharing Contract (PSC), the Tanzanian PSC/ROR hybrid system and the Trinidad and Tobago PSC. Contingent claims analysis is used to value the governments’ tax claims under uncertainty using a numerical approach, viz., Monte Carlo simulation. Each system is tested to obtain the after-tax value accruing to firms as well as the distortionary effects introduced by the fiscal systems. The results are then ranked. The Alberta Canada and PNG fiscal systems provide companies with the highest after-tax values while also being the least distortionary. The Tanzanian system is the lowest in both rankings, providing relatively low after-tax values and introducing strong distortionary effects. The SNJDZ PSC imposed a relatively high tax burden on companies with median distortionary effects. The Trinidadian PSC generated a median tax burden on companies but has strong distortionary effects.

THE VALUE OF FIGHTING IRREVERSIBLE DEMISE BY SOFTENING THE IRREVERSIBLE COST

We study a novel issue in the real-options-based technology innovation literature by means of double barrier contingent claims analysis. We show how much a firm with the monopoly over a project is willing to spend in investment technology innovation that softens the irreversible cost of accessing the project before its irreversible demise. The answer depends on the project's characteristics and on the effectiveness demanded from technology innovation.

Modelling suicide risk in later life

Affective disorder is generally regarded as the prominent risk factor for suicide in the old age population. Despite the large number of empirical studies available in the literature, there is no attempt in modelling the dynamics of an individual’s level of suicide risk theoretically yet. In particular, a dynamic model which can simulate the time evolution of an individual’s level of risk for suicide and provide quantitative estimates of the probability of suicide risk is still lacking. In the present study we apply the contingent claims analysis of credit risk modelling in the field of quantitative finance to derive a theoretical stochastic model for estimation of the probability of suicide risk in later life in terms of a signalling index of affective disorder. Our model is based upon the hypothesis that the current state of affective disorder of a patient can be represented by a signalling index and exhibits stochastic movement and that a threshold of affective disorder, which signifies the occurrence of suicide, exists. According to the numerical results, the implications of our model are consistent with the clinical findings. Hence, we believe that such a dynamic model will be essential to the design of effective suicide prevention strategies in the target population of older adults, especially in the primary care setting.

Merton Unraveled

Popular approaches to default probability estimation are often based on the approach initially described in Merton [1974]. By explicitly modeling a firm9s market value, market value volatility and liability structure over time using contingent claims analysis the Merton model defines a firm as defaulted when the firm9s value falls below its debt. This article demonstrates how a simplified “spread sheet” version of the Merton model produces distance to default measures similar to the original Merton model. Moreover, when applied to a sample of US firms, the simplified model gives a relative ranking of firms that is essentially unchanged compared to the Merton model.

Using contingent-claims analysis to value opportunities lost due to moral hazard risk

Long-term contracts may contain valuable embedded options. I develop an alternative approach to traditional discounted cash flow (DCF) analysis for valuing the profits that are lost when a long-term contract is breached, resulting in the loss of potentially valuable options. One recent example concerns the much publicized supervisory goodwill contracts, some of which were scheduled to expire more than 30 years from the time the US government breached them. I illustrate the contingent-claims approach using this example. I develop a contingent-claims damages model and use it to measure the lost profits damages that two thrifts - California Federal Bank and Glendale Federal Bank - suffered when the US government extinguished supervisory goodwill and prematurely terminated their long-dated goodwill options. The same analytical approach can be adapted to value other opportunities lost due to moral hazard risk.

A Dynamic Model of Risk-Shifting Incentives with Convertible Debt

Green (1984) demonstrates in a one-period setting that convertible debt can eliminate the asset substitution problem. However, in a multi-period setting the terms of the convertible issue will in general be set before the specific asset substitution opportunity presents itself. This leaves room for a strategic non-cooperative game between shareholders and convertible debtholders. We show that two risk-shifting scenarios arise as attainable Nash equilibria. Pure asset substitution occurs when, despite convertible debtholders not exercising their conversion option, shareholders still find it profitable to shift risk. Strategic conversion occurs when, despite convertible debtholders giving up the conversion option value, they are better off receiving their share of the wealth expropriation from straight debtholders. We use contingent claims analysis and the Black and Scholes (1973) setup to characterize the equilibria. Even when initial convertible debt is endogenously designed so as to minimize the likelihood of risk-shifting equilibria, we show that asset substitution cannot be completely eliminated. Our overall conclusion is that -- in contrast to agency theory's claim -- convertible debt is an imperfect instrument for mitigating shareholders' incentive to increase risk.

Innovation diffusion uncertainty, advertising and pricing policies

We develop and analyze a normative and structurally stochastic model of innovation diffusion by depicting the market at an aggregate level. Model dynamics are defined through the flow pattern of individuals that move from the innovation unaware stage, to the innovation aware, and ultimately to the adopter stages. The stochastic evolution of this stage-wise transition unfolds according to tractable stochastic processes and is influenced by such factors as price, word of mouth, and advertisement efforts. In this environment, techniques of contingent claims analysis and stochastic control theory are employed to obtain optimal pricing or advertising policies that maximize the value of the innovation. To account for their optimal adjustment over time, these policies are modeled as positive real-valued adapted processes. Given this setting, policy adjustments over time (i.e. advertising or pricing) are viewed as a value additive sequence of nested real options. We present closed-form analytic results regarding the optimal policies. Simulations provide a numeric insight to the models' behavior.

Capital Budgeting with Taxes under Uncertainty and Irreversibility / Investitionsplanung mit Steuern bei Unsicherheit und Irreversibilität

Summary This article investigates the derivation of post-tax investment rules and neutral tax systems under risk neutrality and risk aversion for irreversible investment projects. Integrating taxes into real option theory, it can be shown that the possible approaches dynamic programming and contingent claims analysis yield identical investment rules under risk neutrality. Under risk aversion, contingent claims analysis requires a sophisticated capital market model which is still missing. In contrast, dynamic programming as an individual approach permits explicit investment rules at least in the pre-tax case. After taxes, both approaches fail to reach general solutions. Nevertheless, we succeed in proving neutral tax systems for the first time under risk aversion in the real option context using dynamic programming.

Takeover bids, unconditional offer price and investor protection

In this paper, we develop a contingent claim analysis on shareholders' right to sell unconditionally their shares at the acquisition bid price during a takeover bid procedure. Compared with a situation without any guarantee, this regulation brings about wealth transfer towards outside shareholders. Why, in an apparently irrational way, do outside shareholders, who may benefit from a price guarantee, not systematically sell their shares? That question emphasizes the outside shareholders' behavior. Using a real option valuation model to evaluate the price guarantee opportunity, we show that an equal treatment rule between controlling and outside shareholders may lead outside shareholders to sell their shares.

Slotting Allowances as Real Options: An Alternative Explanation

This article offers an alternative explanation for slotting allowances using contingent claims analysis, or real option pricing. Slotting allowances arise because retailers hold call options on their shelf space while suppliers must buy these options to introduce a new product. A simulated model of new‐product introduction shows that stocking a new product contains a significant, imbedded real option component. We also show that advertising and promotional support can reduce the real option value.