Merton Structural Model Research Articles

The performance of debt and equity markets in Anglo American Plc and BHP Billiton Plc in the period 2006 to 2015 through the lens of Merton’s structural model

This article applies the Merton structural model in evaluating the performance of the debt and equity markets in Anglo American Plc and BHP Billiton Plc in the period 2006 to 2015. We consider statistical and economic measures of the efficacy of the Merton model in explaining observed market behaviour. We find strong but unstable statistical support for the Merton model as a descriptor of market behaviour. We generated superior risk adjusted returns when applying the results of our analysis to an investment strategy. Market prices deviate from model behaviour; however, the relationship appears to be mean reverting which supports the investment thesis.

Contingent Claims and Hedging of Credit Risk with Equity Options

We introduce a novel methodology to hedge changes in the market values of credit exposures using equity put options. Our new hedge ratios are derived from the application of contingent-claims valuation and are fundamentally different from existing hedging methods aimed at neutralizing the loss following the occurrence of a credit event. We provide evidence that the theoretical hedge ratios are in line with the empirical sensitivities of credit spread changes to put option returns and that, relative to the latter, reduce volatility by a further 15% in an out-of-sample setting including a portfolio of North American firms. Based on in-sample estimates, hedging with options reduces portfolio volatility by an additional 13% relative to hedging with equity. We show that option hedge ratios capture option-specific credit exposure related to the VIX index and the default spread, which is unaccounted for by Merton (1974)'s equity hedge ratios alone. These findings shed new light on the puzzling weak relation between equity and credit returns reported in previous studies and suggest that the predictions of Merton's structural model can be enhanced by combining equity-specific with option-specific information.

Research on CDS pricing model with endogenous recovery rate

Default probability and recovery rate are two important factors in credit risk management. These factors are negatively correlated with each other. In the previous literature, it is often assumed that these factors are independent or obey specified exogenous function. This simplified approach facilitates the calculation but may affect credit risk management. This paper deduces the functional relationship between the default probability and the expected recovery rate based on the Merton's structural model, calculates the expression of default probability using the Martingale method and the Laplace transform based on a reduced approach, and constructs a CDS pricing model with an endogenous recovery rate according to the non-arbitrage pricing principle.

Value of the Firm Using Merton's Structural Model and Numerical Integration

Value of the Firm Using Merton's Structural Model and Numerical Integration

Tempered stable structural model in pricing credit spread and credit default swap

In this paper, we explore the features of a structural credit risk model wherein the firm value is driven by normal tempered stable (NTS) process belonging to the larger class of Levy processes. For the purpose of comparability, the calibration to the term structure of a corporate bond credit spread is conducted under both NTS structural model and Merton structural model. We find that NTS structural model provides better fit for all credit ratings than Merton structural model. However, it is noticed that probabilities of default derived from the calibration of the term structure of a bond credit spread might be overestimated since the bond credit spread could contain non-default components such as illiquidity risk or asymmetric tax treatment. Hence, considering CDS spread as a reflection of the pure credit risk for the reference entity, we calibrate it in order to obtain more reasonable probability of default and obtain valid results in calibration of the market CDS spread with NTS structural model.

A capital adequacy buffer model

ABSTRACTWe develop a new capital adequacy buffer model (CABM) that is sensitive to dynamic economic circumstances. The model, which measures additional bank capital required to compensate for fluctuating credit risk, is a novel combination of the Merton structural model, which measures distance to default and the timeless capital asset pricing model (CAPM), which measures additional returns to compensate for additional share price risk. We apply the model to a portfolio of mid-cap loan assets over a 10-year period that includes pre-GFC (global financial crisis), GFC and post-GFC. An analysis of actual defaults over this period shows the model to be far more accurate in determining the capital adequacy levels needed to counter credit risk than an unresponsive ratings model such as the Basel standardized approach.

Performance and determinants of the Merton structural model: Evidence from hedging coefficients

Abstract We empirically test the effectiveness of the Merton (1974) model in measuring the sensitivity of corporate bond returns to changes in equity value. We study the main variables that affect the performance of the model and relax the assumption of normally distributed rates of return. Results show that less than 6% of the bonds have a hedge ratio within 10% from the model predicted value. Volatility, time to maturity, size, distress, liquidity and information quality are found to be significant determinants of the efficacy of the model.

A structural model for credit risk with switching processes and synchronous jumps

This paper studies a switching regime version of Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a switching Lévy process. The novelty of this approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, two models are presented. In the first one, the default happens at bond maturity, when the firm's value falls below a predetermined barrier. In the second version, the firm can enter bankruptcy at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. With synchronous jumps, the firm's asset and state processes are no longer uncorrelated. Finally, some econometric evidence that switching Lévy processes, with synchronous jumps, fit well historical time series is provided.

Xtreme Credit Risk Models: Implications for Bank Capital Buffers

The Global Financial Crisis (GFC) highlighted the importance of measuring and understanding extreme credit risk. This paper applies Conditional Value at Risk (CVaR) techniques, traditionally used in the insurance industry to measure risk beyond a predetermined threshold, to four credit models. For each of the models we use both Historical and Monte Carlo Simulation methodology to create CVaR measurements. The four extreme models are derived from modifications to the Merton structural model (which we term Xtreme-S), the CreditMetrics Transition model (Xtreme-T), Quantile regression (Xtreme-Q), and the author’s own unique iTransition model (Xtreme-i) which incorporates industry factors into transition matrices. For all models, CVaR is found to be significantly higher than VaR, and there are also found to be significant differences between the models in terms of correlation with actual bank losses and CDS spreads. The paper also shows how extreme measures can be used by banks to determine capital buffer requirements.

A Structural Model for Credit Risk with Markov Modulated Lévy Processes and Synchronous Jumps

This paper presents a switching regime version of the Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a Markov modulated Levy process. The novelty of our approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, we present two models. In the first one, the default occurs at bond maturity if the firm's value falls below a predetermined barrier. In the second version, the company can bankrupt at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. Finally, with synchronous jumps, the firm's asset and state processes are no longer uncorrelated.

A Structural Approach to Estimate Market-Assessed Sovereign Credit Risk

This paper explores the economic determinants of market-assessed sovereign risk of members of the European monetary union. The empirical work is innovative in its specification of appropriate inputs. The Merton structural model provides a theoretical background for the empirical investigation of sovereign risks. We make use of publicly available government financial statistics as well as national stock market volatility estimated by EGARCH, implied from traded options and by fitting a generalized Pareto distribution. We show a high degree of association between our modelled spreads and credit default swap spreads using volatility estimates based on option implied and generalized Pareto distribution. Model performance holds in outof-sample prediction and the non-linear model derived from structural theory is shown to outperform a benchmark linear regression model. These results provide policy makers and regulators with a set of insights into the factors which influence credit market activity enabling them to take an informed approach to policy and regulatory settings which will be subject to market appraisal.

Corporate Governance and Corporate Creditworthiness

We examine the relation between corporate governance and bankruptcy risk as an underlying force affecting a bond’s yield. The level of corporate governance is captured by the G-index, along with the explicit groups of governance provisions. We estimate bankruptcy risk by Z-score, by cash-flow-score, by O-score, through Merton structural model default probabilities, and by S&P credit ratings. After addressing endogeneity and while controlling for firm-specific factors, based on the four objective methodologies we find that corporate governance is inversely related to bankruptcy risk. Yet, rating agencies take a mixed approach towards this association likely because of the conflicting impact of different governance provisions.

Explaining and Predicting Sovereign Credit Risk with Exchange Rate Volatility

Merton's structural model for sovereigns is proven to be useful to analyze the default risk of a country. We are the first to investigate how fast CDS spreads react to changes in model inputs and outputs. CDS spread changes strongly correlate with exchange rate returns, which are an input to the model. But CDS spread changes on average react with a delay to changes in model outputs such as the distance to default, the default probability and model spreads. Hence contingency claim analysis for sovereigns provides useful predictions for CDS spreads.

Merton structural model and IRB compliance

This paper discusses the 1974 Merton's model in light of the minimum regulatory requirements of the Internal Ratings-Based (IRB) Approach provided in the Directive 2006/48/EC of the European Parliament and of the Council for the calculation of capital requirement for credit risk. The basic purpose is to illustrate potential deficiencies of the model in assigning obligors ratings and/or estimating probability of default to which supervisors should be attentive when validating this model in bank's IRB approach. The procedures of three estimation methods of Merton's model are described (calibration, Moody's KMV, maximum likelihood estimation), based on which deficiencies of this model can be identified. The Merton's model per se does not ensure compliance with the minimum requirements of the IRB approach for the estimation of probability of default, as its theoretical assumptions often do not reflect reality. It is therefore necessary to calibrate the fundamental parameters estimated by the model using empirical data on defaults, which must be defined in accordance with the regulatory minimum requirements, and must be representative of the population for which the model is valid. Results on the simulated data also show that calibration method provides different estimates of probability of default for the same obligors compared to other two methods. Differences are mainly influenced by the volatility of equity and leverage in the time series, which calibration method does not sufficiently account for. Some regulatory minimum requirements can be relaxed when obligors are being assigned ratings on the basis of the Merton's model estimation methods. However, the results of the analysis on simulated and empirical data show that different estimation methods generate different obligor credit rating assignments.

The Merton Structural Model and IRB Compliance

This paper discusses the 1974 Merton’s model in light of the minimum regulatory requirements of the Internal Ratings-Based (IRB) Approach provided in the Directive 2006/48/EC of the European Parliament and of the Council for the calculation of capital requirement for credit risk. The basic purpose is to illustrate potential deficiencies of the model in assigning obligors ratings and/or estimating probability of default to which supervisors should be attentive when validating this model in bank’s IRB approach. The procedures of three estimation methods of Merton’s model are described (calibration, Moody’s KMV, maximum likelihood estimation), based on which deficiencies of this model can be identified. The Merton’s model per se does not ensure compliance with the minimum requirements of the IRB approach for the estimation of probability of default, as its theoretical assumptions often do not reflect reality. It is therefore necessary to calibrate the fundamental parameters estimated by the model using empirical data on defaults, which must be defined in accordance with the regulatory minimum requirements, and must be representative of the population for which the model is valid. Results on the simulated data also show that calibration method provides different estimates of probability of default for the same obligors compared to other two methods. Differences are mainly influenced by the volatility of equity and leverage in the time series, which calibration method does not sufficiently account for. Some regulatory minimum requirements can be relaxed when obligors are being assigned ratings on the basis of the Merton’s model estimation methods. However, the results of the analysis on simulated and empirical data show that different estimation methods generate different obligor credit rating assignments.

Pricing a CDO on stochastically correlated underlyings

In this paper, we propose a method to price collateralized debt obligations (CDO) within Merton's structural model on underlyings with a stochastic mean-reverting covariance dependence. There are two key elements in our development, first we reduce dimensionality and complexity using principal component analysis on the assets' covariance matrix. Second, we approximate this continuous multidimensional structure using a tree method. Trinomial-tree models can be developed for both the principal components and the eigenvalues assuming the eigenvectors are constant over time and the eigenvalues are stochastic. Our method allows us to compute the joint default probabilities for k defaults of stochastically correlated underlyings and the value of CDOs in a fast manner, without having lost much accuracy. Furthermore we provide a method based on moments to estimate the parameters of the model.

Private equity and regulatory capital

Regulatory capital requirements for European banks have been put forward in the Basel II Capital Framework and subsequently in the capital requirements directive (CRD) of the EU. We provide a detailed discussion of the capital requirements for private equity investments under different approaches. For the internal model approach we present a structural model that we calibrate to a proprietary dataset. We modify the standard Merton structural model to make it applicable in practice and to capture stylized facts of private equity investments. We also implement the early default feature with a fast simulation algorithm. Our results support capital requirements lower than in Basel II, but not as low as in CRD, thereby giving adverse incentives to banks for using advanced risk models. A sensitivity analysis shows that this finding is robust to parameter uncertainty and stress scenarios.

Private Equity and Regulatory Capital

Regulatory Capital requirements for European banks have been put forward in the Basel II Capital Framework and subsequently in the Capital Requirements Directive (CRD) of the EU. We provide a detailed discussion of the capital requirements for private equity investments under the simple risk weight approach, the PD/LGD approach and the internal model approach. For the latter we present a structural model for which we calibrate the parameters from a proprietary dataset. We modify the standard Merton structural model to make it applicable in practice and to capture stylized facts of these investments. We also show how to implement the early default features of our model in a simulation algorithm with very low computational costs. Our results support capital requirements lower than in Basel II, but not as low as in CRD. A sensitivity analysis shows that this finding is robust to parameter uncertainty and stress scenarios. This is likely to give adverse incentives to banks for using advanced risk models.

Estimation of the Default Risk of Publicly Traded Canadian Companies

Two models of default risk are prominent in the financial literature: Merton's structural model and Altman's non-structural model.

Latent Variable Approach to Modelling Dependence of Credit Risks: Application to French Firms and Implications for Regulatory Capital

This paper extends the analysis in Migration Correlation: Estimation Method and Application to the French Companies Rated by the Banque de France and provides a methodology for valuing dependent defaults based on the latent variable approach. This methodology underlies all models derived from the Merton's structural model and includes in particular the Basel II proposition. The latent correlation is calibrated by developing factor models that relate changes in unobservable variable to changes in a small number of economic factors. Our model exploits the relationship between the default correlation and the latent correlation throughout the joint probability of default. Using a comprehensive rating database managed by the Banque de France, we employ this relationship to calibrate latent correlations and finally to compute credit risk charges at a portfolio level.