Fixed‐ and Variable‐Rate Mortgages,Business Cycles,and Monetary Policy

This paper studies how the proportion of fixed‐ and variable‐rate mortgages affects business cycles and welfare. I develop and solve a New Keynesian dynamic stochastic general equilibrium model with a housing market and a group of constrained individuals who need housing collateral to obtain loans. The model predicts that with mostly variable‐rate mortgages, an exogenous interest rate shock has larger effects on borrowers than in a fixed‐rate economy. For plausible parameterizations, aggregate differences are muted by wealth effects on labor supply and by the presence of savers. For given monetary policy, a high proportion of fixed‐rate mortgages is welfare enhancing.     

Pricing of guaranteed minimum withdrawal benefits in variable annuities under stochastic volatility,stochastic interest rates and stochastic mortality via the componentwise splitting method

This paper values guaranteed minimum withdrawal benefit (GMWB) riders embedded in variable annuities assuming that the underlying fund dynamics evolve under the influence of stochastic interest rates, stochastic volatility, stochastic mortality and equity risk. The valuation problem is formulated as a partial differential equation (PDE) which is solved numerically by employing the operator splitting method. Sensitivity analysis of the fair guarantee fee is performed with respect to various model parameters. We find that (i) the fair insurance fee charged by the product provider is an increasing function of the withdrawal rate; (ii) the GMWB price is higher when stochastic interest rates and volatility are incorporated in the model, compared to the case of static interest rates and volatility; (iii) the GMWB price behaves non-monotonically with changing volatility of variance parameter; (iv) the fair fee increases with increasing volatility of interest rates parameter, and increasing correlation between the underlying fund and the interest rates; (v) the fair fee increases when the speed of mean-reversion of stochastic volatility or the average long-term volatility increases; (vi) the GMWB fee decreases when the speed of mean-reversion of stochastic interest rates or the average long-term interest rates increase. We investigate both static and dynamic (optimal) policyholder's withdrawal behaviours; we present the optimal withdrawal schedule as a function of the withdrawal account and the investment account for varying volatility and interest rates. When incorporating stochastic mortality, we find that its impact on the fair guarantee fee is rather small. Our results demonstrate the importance of correct quantification of risks embedded in GMWBs and provide guidance to product providers on optimal hedging of various risks associated with the contract.     

Fiscal policy with banks and financial frictions

We assess the role of banks to the transmission of optimal and exogenous changes in fiscal policy to the economy. We built-up a dynamic stochastic general equilibrium model with patient and impatient agents, banks and a government to find that banks and their associated capital-adequacy constraint mitigate the negative spill-over effects to the economy from higher taxes. Specifically, we confirm that labour income tax is the most distortionary fiscal instrument. The optimal choice of a housing tax is the most favorable funding source to a temporary increase in public spending. The combination of housing and labour taxes is the most preferred tax bundle to be optimally chosen under negative output shocks. Moreover, a permanent increase in housing tax is beneficial if it is welfare enhancing and the existence of banks benefits mainly impatient households under permanently higher consumption taxes. Finally, these results remain robust to various robustness checks.     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

Optimal incentive contract in continuous time with different behavior relationships between agents

Dynamic contracts with multiple agents is a classical decentralized decision-making problem with asymmetric information, it is usually discussed according to moral hazard and the behavioral relationship between agents. To do so, in this paper, according to behavior relationships between agents, we analyze continuous time optimal contracting in principal multi-agent moral hazard settings. According to stochastic optimal control theory, the optimal contract of the generalized principal-agent dynamic problem is given, the optimal behavior selection and incentive mechanism of agents are analyzed. The result shows that, in the two-agent model, the incentive effect of cooperative relationship is greater than that of competitive relationship; when they are in a cooperative relationship, with the more influential agent receiving higher pay; under multi-agent model, an increase in the number of agents reduces effort and rewards, this indicates that the team size has strict boundaries. The research conclusions can be applied to solve two kinds of principal-agent problems that the principal needs to motivate the agent to compete or cooperate in the actual social production and life.     

Labor Selection,Turnover Costs,and Optimal Monetary Policy

We study optimal monetary policy and welfare properties of a dynamic stochastic general equilibrium (DSGE) model with a labor selection process, labor turnover costs, and Nash bargained wages. We show that our model implies inefficiencies that cannot be offset in a standard wage bargaining regime. We also show that the inefficiencies rise with the magnitude of firing costs. As a result, in the optimal Ramsey plan, the optimal inflation volatility deviates from zero and is an increasing function of firing costs.     

Pollution Externalities in a Model of Endogenous Fertility and Growth

An endogenous growth model with human capital formation, pollution caused by production of consumption goods, and endogenous fertility decisions made by altruistic agents with infinite horizons is presented. Consequences for optimal policy of modelling fertility as an explicit decision variable are examined. Because ordinary lump-sum transfers to individuals are no longer neutral, either revenue from a pollution tax must be redistributed to dynasties (working as an implicit tax on child births), or lump-sum transfers must be supplemented with an explicit fertility tax. Alternatively, the government can avoid distortions of the fertility decisions by maintaining an appropriate public debt. When abatement is highly productive, it can be optimal to subsidize fertility in order to increase total production.     

Optimal investment-reinsurance with dynamic risk constraint and regime switching

We study an optimal investment–reinsurance problem for an insurer who faces dynamic risk constraint in a Markovian regime-switching environment. The goal of the insurer is to maximize the expected utility of terminal wealth. Here the dynamic risk constraint is described by the maximal conditional Value at Risk over different economic states. The rationale is to provide a prudent investment–reinsurance strategy by taking into account the worst case scenario over different economic states. Using the dynamic programming approach, we obtain an analytical solution of the problem when the insurance business is modeled by either the classical Cramer–Lundberg model or its diffusion approximation. We document some important qualitative behaviors of the optimal investment–reinsurance strategies and investigate the impacts of switching regimes and risk constraint on the optimal strategies.     

The Response of Hours to a Technology Shock: A Two-Step Structural VAR Approach

The response of hours to a technology shock is a controversial issue in macroeconomics. Part of the difficulty lies in that the estimated response is sensitive to the specification of hours in structural vector autoregressions (SVARs). This paper uses a simple two-step approach to consistently estimate the response of hours. The first step considers a SVAR model with a relevant stationary variable, but excluding hours. Given a consistent estimate of technology shocks in the first step, the response of hours to this shock is estimated in a second step. Simulation experiments from an estimated dynamic stochastic general equilibrium (DSGE) model show that this approach outperforms standard SVARs. When applied to U.S. data, the two-step approach predicts a short-run decrease followed by a hump-shaped positive response. This result is robust to other specifications and data.     

Real options with unknown-date events

The real options literature has provided new insights on how to manage irreversible capital investments whose payoffs are uncertain. Two of the most important predictions from such theory are: (i) greater risk delays a firm’s investment timing, and (ii) greater risk increases the option value of waiting. This paper challenges such conclusions in a setting in which the relevant random variable is the arrival time of an unfavorable event. In particular, we model situations in which a firm must choose the time at which to invest in a project whose profit grows at a known rate until a random date is reached and decays thereafter, which may be representative of stochastic product or industry life cycles. This is a novel framework in which a firm can update its beliefs about the profitability of an investment opportunity by simply waiting to invest. Thus, a wait-and-see approach allows the firm to capitalize on favorable market evolutions and avoid adverse ones to some extent. Our framework is simple and does not require using stochastic calculus, which allows for an economic interpretation of optimal investment policies for the cases of one-time and sequential investments.     

Competition leverage: how the demand side affects optimal risk adjustment

We study optimal risk adjustment in imperfectly competitive health insurance markets when high‐risk consumers are less likely to switch insurer than low‐risk consumers. Insurers then have an incentive to select even if risk adjustment perfectly corrects for cost differences. To achieve first best, risk adjustment should overcompensate insurers for serving high‐risk agents. Second, we identify a trade‐off between efficiency and consumer welfare. Reducing the difference in risk adjustment subsidies increases consumer welfare by leveraging competition from the elastic low‐risk market to the less elastic high‐risk market. Third, mandatory pooling can increase consumer surplus further, at the cost of efficiency.     

Macroprudential regulation and macroeconomic activity

I develop a dynamic stochastic general equilibrium model to examine the impact of macroprudential regulation on banks’ financial decisions and the implications for the real sector. I model an occasionally binding capital requirement constraint and analyze its costs and benefits. This friction means that the banks refrain from valuable lending. At the same time, capital requirements provide structural stability to the financial system. I show that higher capital requirements can dampen the business cycle fluctuations and raise welfare. I also show that switching to a countercyclical capital requirement regime can help reduce volatility and raise welfare. Finally, by means of the welfare analysis, I also obtain the optimal level of capital requirement.     

Optimal consumption and investment for markets with random coefficients

We consider an optimal investment and consumption problem for a Black–Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamic programming approach leads to an investigation of the Hamilton–Jacobi–Bellman (HJB) equation which is a highly nonlinear partial differential equation (PDE) of the second order. By using the Feynman–Kac representation, we prove uniqueness and smoothness of the solution. Moreover, we study the optimal convergence rate of iterative numerical schemes for both the value function and the optimal portfolio. We show that in this case, the optimal convergence rate is super-geometric, i.e., more rapid than any geometric one. We apply our results to a stochastic volatility financial market.     

Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps

This paper considers a robust optimal excess-of-loss reinsurance-investment problem in a model with jumps for an ambiguity-averse insurer (AAI), who worries about ambiguity and aims to develop a robust optimal reinsurance-investment strategy. The AAI’s surplus process is assumed to follow a diffusion model, which is an approximation of the classical risk model. The AAI is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset whose price is described by a jump-diffusion model. Under the criterion for maximizing the expected exponential utility of terminal wealth, optimal strategy and optimal value function are derived by applying the stochastic dynamic programming approach. Our model and results extend some of the existing results in the literature, and the economic implications of our findings are illustrated. Numerical examples show that considering ambiguity and reinsurance brings utility enhancements.     

A re-examination of the impact of credit ratings and economic factors on state bond yields

In this article we re-examine the impact of credit ratings and economic factors on state bond yields using a two-step model. In the first step, we adopt an ordered probit technique to obtain consistent estimates of state bond default risk. In the second step, we estimate state bond risk premiums using a regression analysis with a categorized risk variable obtained from the first step. Similar to Terza (1987) and Hsiao (1983), the model involves a categorized ordinal explanatory (rating) variable. However, our two-step model deals with a case where category thresholds are unknown and dependent on economic factors. The model provides consistent estimates for the effects of ratings and economic factors on state bond yields. Contrary to previous findings, we find that state bond yields are mainly affected by fundamental economic variables.     

Precautionary Saving and Consumption Smoothing across Time and Possibilities

This paper examines how aversion to risk and aversion to intertemporal substitution determine the strength of the precautionary saving motive in a two-period model with Selden/Kreps–Porteus preferences. For small risks, we derive a measure of the strength of the precautionary saving motive that generalizes the concept of "prudence" introduced by Kimball (1990b) . For large risks, we show that decreasing absolute risk aversion guarantees that the precautionary saving motive is stronger than risk aversion, regardless of the elasticity of intertemporal substitution. Holding risk preferences fixed, the extent to which the precautionary saving motive is stronger than risk aversion increases with the elasticity of intertemporal substitution. We derive sufficient conditions for a change in risk preferences alone to increase the strength of the precautionary saving motive and for the strength of the precautionary saving motive to decline with wealth. Within the class of constant elasticity of intertemporal substitution, constant-relative risk aversion utility functions, these conditions are also necessary.     

Price‐Level Targeting and Stabilization Policy

We construct a dynamic stochastic general equilibrium model to study optimal monetary stabilization policy. Prices are fully flexible and money is essential for trade. Our main result is that if the central bank pursues a price‐level target, it can control inflation expectations and improve welfare by stabilizing short‐run shocks to the economy. The optimal policy involves smoothing nominal interest rates that effectively smooths consumption across states.     

Changes in Background Risk and the Demand for Insurance

The demand for insurance against loss from a particular risky asset is likely to depend on other risks the decision-maker faces. For independently distributed other risks, referred to as background risk, Eeckhoudt and Kimball [1992] determine the effect on insurance demand of introducing background risk. Recently, Eeckhoudt, Gollier, and Schlesinger [1996] determine conditions on preferences such that first- and second-degree stochastic deteriorations in background risk lead to a decrease in the decision-maker's willingness to accept other risks. These results, although formulated in a general decision model, also apply to insurance demand. This article continues analysis of this question by determining the effect on insurance demand of several other general changes in background risk.     

A stochastic differential game for optimal investment of an insurer with regime switching

We introduce a model to discuss an optimal investment problem of an insurance company using a game theoretic approach. The model is general enough to include economic risk, financial risk, insurance risk, and model risk. The insurance company invests its surplus in a bond and a stock index. The interest rate of the bond is stochastic and depends on the state of an economy described by a continuous-time, finite-state, Markov chain. The stock index dynamics are governed by a Markov, regime-switching, geometric Brownian motion modulated by the chain. The company receives premiums and pays aggregate claims. Here the aggregate insurance claims process is modeled by either a Markov, regime-switching, random measure or a Markov, regime-switching, diffusion process modulated by the chain. We adopt a robust approach to model risk, or uncertainty, and generate a family of probability measures using a general approach for a measure change to incorporate model risk. In particular, we adopt a Girsanov transform for the regime-switching Markov chain to incorporate model risk in modeling economic risk by the Markov chain. The goal of the insurance company is to select an optimal investment strategy so as to maximize either the expected exponential utility of terminal wealth or the survival probability of the company in the ‘worst-case’ scenario. We formulate the optimal investment problems as two-player, zero-sum, stochastic differential games between the insurance company and the market. Verification theorems for the HJB solutions to the optimal investment problems are provided and explicit solutions for optimal strategies are obtained in some particular cases.     

Quantifying and sustaining welfare gains from monetary commitment

Our objectives are: to quantify the stabilization welfare gains from commitment; to examine how commitment to an optimal rule can be sustained as an equilibrium; to find a simple interest rate rule that approximates the optimal commitment one. We utilize an empirical micro-founded euro-area DSGE model, a quadratic approximation of household utility as the welfare criterion, employing a nominal interest rate lower bound. In contrast to previous studies, we find significant commitment stabilization gains of around a 0.4-0.5% equivalent permanent consumption increase, and with higher price stickiness gains over 2%. We find that a simple optimized commitment rule responding to inflation and the real wage mimics the optimal one.