Does modeling framework matter? A comparative study of structural and reduced-form models

This study provides a rigorous empirical comparison of structural and reduced-form credit risk frameworks. The literature differentiates between structural models that are based on modeling of the evolution of the balance sheet of the issuer, and reduced-form models that specify credit risk exogenously by a hazard rate process. Until now, there has been no common agreement in academia and practice on which model framework better captures credit risk. As major difference we focus on the discriminative modeling of the default time. In contrast to the previous literature, we calibrate both approaches to the same data set, apply comparable estimation techniques, and assess the out-of-sample prediction quality on the same time series of credit default swap prices. As our empirical implementations of both approaches rely on the same market information we are able to judge whether empirically the model structure itself makes an important difference. Interestingly, our study shows that the models’ prediction power are quite close on average indicating that for pricing purposes the modeling type does not greatly matter compared to the input data used. Still, the reduced-form approach outperforms the structural for investment-grade names and longer maturities. In contrast the structural approach performs better for shorter maturities and sub-investment grade names.     

Pricing defaultable bonds: a middle-way approach between structural and reduced-form models

In this paper we present a valuation model that combines features of both the structural and reduced-form approaches for modelling default risk. We maintain the cause and effect or ‘structural’ definition of default and assume that default is triggered when a state variable reaches a default boundary. However, in our model, the state variable is not interpreted as the assets of the firm, but as a latent variable signalling the credit quality of the firm. Default in our model can also occur according to a doubly stochastic hazard rate. The hazard rate is a linear function of the state variable and the interest rate. We use the Cox et al. (A theory of the term structure of interest rates. Econometrica, 1985, 53(2), 385–407) term structure model to preclude the possibility of negative probabilities of default. We also horse race the proposed valuation model against structural and reduced-form default risky bond pricing models and find that term structures of credit spreads generated using the middle-way approach are more in line with empirical observations.     

Optimal Constrained Interest-Rate Rules

We show that if policymakers compute the optimal unconstrained interest-rate rule within a Taylor-type class, they may be led to rules that generate indeterminacy and/or instability under learning. This problem is compounded by uncertainty about structural parameters since an optimal rule that is determinate and stable under learning for one calibration may be indeterminate or unstable under learning under a different calibration. We advocate a procedure in which policymakers restrict attention to rules constrained to lie in the determinate learnable region for all plausible calibrations, and that minimize the expected loss, computed using structural parameter priors, subject to this constraint.     

Default and bankruptcy in an entrepreneurial economy with incomplete markets

We build a general equilibrium model with incomplete markets, production, default, and bankruptcy. The existence of equilibrium is proved. Theoretically, under appropriate conditions, we show that the reduced-form entrepreneurial equilibrium and profit-maximization entrepreneurial equilibrium, as defined by Magill and Quinzii (1996), are equivalent. In addition, we find an inverse relationship between the economy real interest rate and the probability of default. This result is empirically tested by applying the Cox proportional hazards model with time-dependent covariates for a sample of sole proprietorships’ unsecured credit operations in the Brazilian economy. The estimates confirm the findings from the theoretical model.     

The Equilibrium Exchange Rate of Mauritius: Evidence from Two Structural Models

In this paper we assess the equilibrium value of the Mauritian rupee in 2006-7 and over the medium run using two structural models. First, we derive a current account-based measure of the exchange rate equilibrium using the macroeconomic balance approach. Second, we estimate a reduced-form fundamental equilibrium exchange rate measure. Our results, which are robust to an alternative non-econometric approach, suggest that the Mauritian rupee was aligned with its equilibrium value in 2006-7 and little adjustment appeared necessary over the medium run.     

Generative Bayesian neural network model for risk-neutral pricing of American index options

Financial models with stochastic volatility or jumps play a critical role as alternative option pricing models for the classical Black–Scholes model, which have the ability to fit different market volatility structures. Recently, machine learning models have elicited considerable attention from researchers because of their improved prediction accuracy in pricing financial derivatives. We propose a generative Bayesian learning model that incorporates a prior reflecting a risk-neutral pricing structure to provide fair prices for the deep ITM and the deep OTM options that are rarely traded. We conduct a comprehensive empirical study to compare classical financial option models with machine learning models in terms of model estimation and prediction using S&P 100 American put options from 2003 to 2012. Results indicate that machine learning models demonstrate better prediction performance than the classical financial option models. Especially, we observe that the generative Bayesian neural network model demonstrates the best overall prediction performance.     

Using Survey Data of Inflation Expectations in the Estimation of Learning and Rational Expectations Models

Does survey data contain useful information for estimating macroeconomic models? We address this question by using survey data of inflation expectations to estimate the New Keynesian model by Smets and Wouters ( 2007 ) and compare its performance under rational expectations and adaptive learning. The survey information serves as an additional moment restriction and helps us to determine the learning agents' forecasting model for inflation. Adaptive learning fares similarly to rational expectations in fitting macro data, but clearly outperforms rational expectations in fitting macro and survey data simultaneously. In other words, survey data contain additional information that is not present in the macro data alone.     

Credit valuation adjustment of cap and floor with counterparty risk: a structural pricing model for vulnerable European options

This study develops a structural pricing model based on the Black 76 formula for the evaluation of the credit value adjustment (CVA) of OTC traded caps and floors, which is mandated as an integral part of Basel III. The proposed structural pricing model improves the existing structural pricing models for vulnerable European options by allowing payments to be made after the exercise of the options. Five crucial determinants of caps’ and floors’ CVAs are identified by the proposed structural model, they are: the cap’s/floor’s tenor, the writer’s total asset value, the correlation between the cap’s/floor’s underlying and the writer’s total asset value, the volatility of the writer’s total asset value, and the writer’s aggregate liabilities. Numerical examples are given to demonstrate the effects of the crucial parameters. Compared to the market practice of CVA calculation based on reduced-form models, the five crucial parameters are the unique features of the proposed structural model.     

Product market competition and credit risk

This study theoretically and empirically investigates effects of product market competition on credit risk. We first develop a real-options-based structural model in a homogeneous oligopoly and show that credit spreads are positively related to the number of firms in an industry. The disparity of firm size in an industry is relevant to both product market competition and credit risk, and we therefore extend the model to an asymmetric duopoly case. In particular, we demonstrate that credit spreads of relatively small (large) firms within an industry are positively (negatively) related to Herfindahl-Hirschman index, and the relative firm size in an industry is an important determinant of credit risk. The models’ implications are empirically scrutinized by a reduced-form hazard model and generally supported. By performing out-of-sample analyses, the results demonstrate that firm size together with the interaction terms between intra-industry firm size dummies and competition intensity can effectively predict default.     

Learnability and monetary policy: A global perspective

The recent literature on monetary policy design has emphasized the importance of equilibrium determinacy and learnability in the choice of policy rules. This paper contains an analysis of the learnability of the equilibrium in a class of simple, micro-founded models in which the policy authority uses a Taylor-type monetary policy rule. Unlike previous analyses, the model economy is not linearized about a steady state—instead, a global perspective is adopted. Globally, the nonlinear model economy can possess rational expectations equilibria other than the steady state consistent with the inflation target of the monetary authorities. These include a second, low inflation ‘liquidity trap’ steady state, periodic equilibria, and sunspot equilibria. The main results in the paper characterize the conditions under which these alternative equilibria maybe stable under adaptive learning, even when the policy rule obeys the Taylor principle. The stability of multiple equilibria is associated with policy rules which are forecast-based. An important finding is that backward-looking Taylor-type policy rules can guarantee that the unique learnable equilibrium is the steady state associated with the inflation target of the monetary authority.     

Does Ricardian Equivalence Hold When Expectations Are Not Rational?

This paper considers the Ricardian Equivalence proposition when expectations are not rational and are instead formed using adaptive learning rules. We show that Ricardian Equivalence continues to hold provided suitable additional conditions on learning dynamics are satisfied. However, new cases of failure can also emerge under learning. In particular, for Ricardian Equivalence to obtain, agents’ expectations must not depend on government’s financial variables under deficit financing.     

Analysing the determinants of insolvency risk for general insurance firms in the UK

This paper estimates a reduced-form model to assess the insolvency risk of General Insurance (GI) firms in the UK. In comparison to earlier studies, it uses a much larger sample including 30 years of data for 515 firms, and also considers a much wider set of possible determinants of insolvency risk. The empirical results suggest that macroeconomic and firm-specific factors both play important roles. Other key findings are the following: insolvency risk varies across firms depending on their business lines; there is default clustering in the GI industry; different reinsurance levels also affect the insolvency risk of insurance firms. The implications of these findings for regulators of GI firms under the newly launched Solvency II are discussed.     

Thinking and Learning in the Tax Evasion Game

Equilibrium behaviour is one of the fundamental concepts of economics: that each player's strategy is a best response to their beliefs about other players' strategies (and that these beliefs are realised). It is therefore striking that one of the most utilised economic models of tax compliance (Allingham and Sandmo, 1972) lacks this property as random audit selection is not a best response for the tax administration. The game theory literature of tax compliance has solved the equilibrium under assumptions of perfect information, full rationality and representative agents (Reinganum and Wilde, 1986; Erard and Feinstein, 1994). The recent application of behavioural economics to tax compliance (Hashimzade et al., 2014) allows richer assumptions such as heterogeneity and asymmetric information to be included in agent‐based models. This paper investigates the tax administration's best‐response audit strategy with heterogeneous taxpayers, imperfect information and evolutionary survival of taxpayers. It finds that, under these conditions, the tax administration's best‐response audit strategy is an adaptive learning approach and not a well‐defined audit function. This fits with actual practice of ‘predictive analytics’ by OECD tax administrations. Behavioural game theory also predicts that when actors are information rich, adaptive learning will dominate abstract thinking.     

Learning and the Yield Curve

Two central implications of Expectations Hypothesis under rational expectations are inconsistent with yield curve data: (i) future expected long yields fall, instead of rising, when yield spread rises; (ii) long yields are excessively volatile relative to short yields. I propose an optimization framework in which boundedly rational agents use adaptive learning to form expectations. The belief structure rationalizes pattern of yields observed in the data so that the first puzzle does not arise with subjective expectations: intertemporal income and substitution effects are amplified relative to rational expectations. The second puzzle is partly accounted for by extra volatility due to parameter uncertainty.     

Valuation of reverse mortgages under (limited) default risk

In this paper, we develop a consistent valuation framework for reverse mortgages based on reduced-form intensity models as used in credit risk modelling. Within our modelling framework, we explicitly calculate the probability that the total loan amount exceeds the house value at termination of the contract and derive the maximum payment(s) which can be made to the homeowner under certain constraints. We apply our results to data from the German market and discuss implications for the design of reverse mortgages from a lender's perspective.     

Inference in models with adaptive learning

Identification of structural parameters in models with adaptive learning can be weak, causing standard inference procedures to become unreliable. Learning also induces persistent dynamics, and this makes the distribution of estimators and test statistics non-standard. Valid inference can be conducted using the Anderson-Rubin statistic with appropriate choice of instruments. Application of this method to a typical new Keynesian sticky-price model with perpetual learning demonstrates its usefulness in practice.     

Market Pricing of Deposit Insurance

We provide an approach to the market valuation of deposit insurance that is based on reduced-form methods for the pricing of fixed-income securities under default risk. By reference to bank debt prices as well as qualitative-response models of the probability of bank failure, we suggest how a risk-neutral valuation model for deposit insurance can be applied both to the calculation of fair-market deposit insurance premia and to the valuation of long-term claims against the insurer.     

Anticipated fiscal policy and adaptive learning

The impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations is considered. Agents are assumed to combine limited structural knowledge with a standard adaptive learning rule. These issues are analyzed using two well-known set-ups, an endowment economy and the Ramsey model. In our scenario there are important deviations from both rational expectations and purely adaptive learning. The approach could be applied to other frameworks.     

Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling

We study, in the framework of Back [Rev. Financial Stud. 5(3), 387–409 (1992)], an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm. The market consists of a risk-neutral informed agent, noise traders, and a market maker who sets the price using the total order. When the insider does not trade, the default time possesses a default intensity in the market’s view as in reduced-form credit risk models. However, we show that, in equilibrium, the modelling becomes structural in the sense that the default time becomes the first time that some continuous observation process falls below a certain barrier. Interestingly, the firm value is still not observable. We also establish the no expected trade theorem that the insider’s trades are inconspicuous.