Incomplete Financial Market Research Articles

Financial Hedging of Operational Risk Constraints: A General Framework

We consider the operation of a non-financial corporation and present a novel risk-management framework that supports the joint optimization of the firm’s operational and financial decisions. Specifically, we study the problem of maximizing the firm’s operating profits when these profits depend on movements in the financial markets, and where the decision maker—the firm’s manager—is risk averse. Critically, our framework (i) imposes risk aversion through a generic class of risk constraints, and (ii) considers explicitly the differences that can exist between the shareholders’ and manager’s beliefs about future market risks. Together, these aspects allow us to remove speculation so that financial instruments can only be used for hedging purposes. We analyze our problem in an incomplete financial market setting and consider different informational assumptions. Within this framework, we characterize the optimal financial hedging strategy so that the problem reduces to a constrained maximization over operational policies. Our results show how financial hedging can be effectively used to expand the set of admissible operating policies, and identify conditions under which the risk constraint can be completely ignored when solving for an optimal operating policy. We illustrate our methodology in the context of an exporter firm which faces exchange rate risk in trading.

Robust asset-liability management games for n players under multivariate stochastic covariance models

This paper investigates a non-zero-sum stochastic differential game among n competitive CARA asset-liability managers, who are concerned about the potential model ambiguity and aim to seek the robust investment strategies. The ambiguity-averse managers are subject to uncontrollable and idiosyncratic random liabilities driven by generalized drifted Brownian motions and have access to an incomplete financial market consisting of a risk-free asset, a market index and a stock under a multivariate stochastic covariance model. The market dynamics permit not only stochastic correlation between the risky assets but also path-dependent and time-varying risk premium and volatility, depending on two affine-diffusion factor processes. The objective of each manager is to maximize the expected exponential utility of his terminal surplus relative to the average among his competitors under the worst-case scenario of the alternative measures. We manage to solve this robust non-Markovian stochastic differential game by using a backward stochastic differential equation approach. Explicit expressions for the robust Nash equilibrium investment policies, the density generator processes under the well-defined worst-case probability measures and the corresponding value functions are derived. Conditions for the admissibility of the robust equilibrium strategies are provided. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium investment strategies and draw some economic interpretations from these results.

American option evaluations using higher moments

PurposeBy using higher moments, this paper extends the quadratic local risk-minimizing approach in a general discrete incomplete financial market. The local optimization subproblems are convex or nonconvex, depending on the moment variants used in the modeling. Inspired by Lai et al. (2006), the authors propose a new multiobjective approach for the combination of moments that is transformed into a multigoal programming problem.Design/methodology/approachThe authors evaluate financial derivatives with American features using local risk-minimizing strategies. The financial structure is in line with Schweizer (1988): the market is discrete, self-financing is not guaranteed, but deviations are controlled and reduced by minimizing the second moment. As for the quadratic approach, the algorithm proceeds backwardly.FindingsIn the context of evaluating American option, a transposition of this multigoal programming leads not only to nonconvex optimization subproblems but also to the undesirable fact that local zero deviations from self-financing are penalized. The analysis shows that issuers should consider some higher moments when evaluating contingent claims because they help reshape the distribution of global cumulative deviations from self-financing.Practical implicationsA detailed numerical analysis that compares all the moments or some combinations of them is performed.Originality/valueThe quadratic approach is extended by exploring other higher moments, positive combinations of moments and variants to enforce asymmetry. This study also investigates the impact of two types of exercise decisions and multiple assets.

Robust optimal asset-liability management with mispricing and stochastic factor market dynamics

This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.

Debt structure, economic stimulus and firm investment efficiency

AbstractWe demonstrate that, in China, firm investment efficiency gains are associated with the use of short‐term debt, especially its trade credit component. During the 2009–2010 economic stimulus plan, such effects were heightened and generally remained persistent in the 2011–2013 poststimulus period. Our findings support the view that the rollover pressure of short‐maturity debt and the information advantage of supply chain financing are both effective mechanisms for enhancing firm governance in an environment more susceptible to financial market incompleteness. Consequently, the enormous credit boost during the stimulus plan was more efficiently invested when channelled through firms' supply chains.

On the neutrality of socially responsible investing: The general equilibrium perspective

This paper investigates the conditions under which socially responsible investment (SRI) is neutral from the viewpoint of general equilibrium theory. Three conditions are jointly sufficient for neutrality of SRI. First, the financial market is complete and SRI does not compromise the spanning opportunities it provides. Second, consumers' rankings of consumption bundles are unaffected by their asset holdings. Third, firms maximize shareholder value. Under an additional assumption that is satisfied, e.g., if SRI takes the form of negative screening, the taxes and transfers needed to implement a Pareto‐optimal allocation are the same as in the absence of SRI. SRI is neutral despite financial market incompleteness if there are perfect substitutes for targeted stocks.

Optimal investment strategies for asset-liability management with affine diffusion factor processes and HARA preferences

<p style='text-indent:20px;'>This paper investigates an optimal asset-liability management problem within the expected utility maximization framework. The general hyperbolic absolute risk aversion (HARA) utility is adopted to describe the risk preference of the asset-liability manager. The financial market comprises a risk-free asset and a risky asset. The market price of risk depends on an affine diffusion factor process, which includes, but is not limited to, the constant elasticity of variance (CEV), Stein-Stein, Schöbel and Zhu, Heston, 3/2, 4/2 models, and some non-Markovian models, as exceptional examples. The accumulative liability process is featured by a generalized drifted Brownian motion with possibly unbounded and non-Markovian drift and diffusion coefficients. Due to the sophisticated structure of HARA utility and the non-Markovian framework of the incomplete financial market, a backward stochastic differential equation (BSDE) approach is adopted. By solving a recursively coupled BSDE system, closed-form expressions for both the optimal investment strategy and optimal value function are derived. Moreover, explicit solutions to some particular cases of our model are provided. Finally, numerical examples are presented to illustrate the effect of model parameters on the optimal investment strategies in several particular cases.</p>

The Metric Generalized Inverse and Its Single-Value Selection in the Pricing of Contingent Claims in an Incomplete Financial Market

The Metric Generalized Inverse and Its Single-Value Selection in the Pricing of Contingent Claims in an Incomplete Financial Market

DYNAMIC UTILITY AND RELATED NONLINEAR SPDES DRIVEN BY LÉVY NOISE

In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied by the optimal processes. Based on this connection, stochastic flow technics for SDEs and characteristic method, the SPIDE is completely solved and monotony and concavity properties of the solution are proved.

Financial market incompleteness and international cooperation on capital controls

AbstractWe examine how the degree of financial market incompleteness affects welfare gains from international cooperation on capital controls. When financial markets are incomplete, international risk sharing is disturbed. However, the optimal global policy significantly reverses the welfare deterioration due to inefficient risk sharing. We show that when financial markets are more incomplete, the welfare gap between the optimal global policy and the Nash equilibrium increases, and the welfare gains from international cooperation on capital controls then become larger.

LOCALLY RISK-MINIMIZING HEDGING FOR EUROPEAN CONTINGENT CLAIMS WRITTEN ON NON-TRADABLE ASSETS WITH COMMON JUMP RISK

This article investigates the optimal hedging problem of the European contingent claims written on non-tradable assets. We assume that the risky assets satisfy jump diffusion models with a common jump process which reflects the correlated jump risk. The non-tradable asset and jump risk lead to an incomplete financial market. Hence, the cross-hedging method will be used to reduce the potential risk of the contingent claims seller. First, we obtain an explicit closed-form solution for the locally risk-minimizing hedging strategies of the European contingent claims by using the Föllmer–Schweizer decomposition. Then, we consider the hedging for a European call option as a special case. The value of the European call option under the minimal martingale measure is derived by the Fourier transform method. Next, some semi-closed solution formulae of the locally risk-minimizing hedging strategies for the European call option are obtained. Finally, some numerical examples are provided to illustrate the sensitivities of the optimal hedging strategies. By comparing the optimal hedging strategies when the underlying asset is a non-tradable asset or a tradable asset, we find that the liquidity risk has a significant impact on the optimal hedging strategies.

Optimal strategies for a defined contribution pension plan with SAHARA utility under DEV model

This paper investigates the optimal investment problems for a defined contribution pension plan in an incomplete financial market that consists of a risk-free asset anda risky asset whose price process obeys the dynamic elasticity of variance model and a correlated inflation risk model. The pension plan participant aims to maximize the expected utility of the terminal wealth under the symmetric asymptotic hyperbolic absolute risk aversion utility. This paper derives the Hamilton-Jacobi-Bellman equations and the verification results, develops lower and upper bounds for the value function, and computes optimal strategies by applying the dual control Monte Carlo algorithm. Numerical examples are presented to verify the accuracy of the approach.

An existence theorem for generalized quasi-variational inequalities involving the Grassmannian manifold with an application

We present an existence theorem for a class of generalized quasi-variational problem involving Grassmannian manifolds. This class is directly inspired by a general equilibrium problem with time, uncertainty and incomplete financial market with real assets. The problem of the existence of this equilibrium cannot be analyzed using standard techniques employed in similar models. Then, we show how the concept of equilibrium is strictly related to the concept of Grassmannian manifolds. Finally, we present a variational inequality problem, whose solutions are equilibria of the proposed model.

Incomplete Financial Markets and the Booming Housing Sector in China

Housing is by far the most important asset in Chinese households’ balance sheets. However, despite forceful and frequent government interventions, the rise in Chinese housing prices has not been contained as much as intended, a trend that has not been reversed by the COVID-19 shock. In this paper, we first provide some stylized facts and then a DSGE model (encompassing both demand and supply channels) to highlight the impact of a “slow-moving” structural vulnerability—financial market incompleteness—on China’s housing prices. The model implies that to eradicate the root causes of the rising housing price, policymakers need to go beyond the housing market itself; instead, it would be desirable to deepen financial markets because these markets would help channel financial resources to productive sectors rather than to housing speculation. This is particularly important in the COVID era because without addressing this structural vulnerability, the higher household savings and the government stimulus may fuel the housing bubble and sow seeds for a future crisis. The paper can also shed light on the housing markets in other economies that face similar vulnerabilities.

Incomplete Financial Markets and the Over-Development of the Chinese Housing Sector

Housing is by far the most important asset in households’ balance sheets across many countries including China, and the policy relevance of the housing sector has been increasingly recognized (as evident by the inclusion of the housing cost into ECB’s inflation measure proposed in its new monetary policy strategy published in July 2021). However, despite forceful and frequent government interventions, the rise in Chinese housing prices has not been contained as much as intended, a trend that has not been reversed by the COVID-19 shock. In this paper, we first provide some stylized facts and then a DSGE model (encompassing both demand and supply channels) to highlight the impact of financial market incompleteness (e.g., inadequate investment channels) on China’s housing prices. The model implies that to eradicate the root causes of the rising housing price, policymakers need to go beyond the housing market itself; instead, it would be desirable to deepen financial markets because these markets would help channel financial resources to productive sectors rather than to housing speculation. This is particularly important in the COVID era because without addressing this structural vulnerability, the higher household savings and the government stimulus may fuel the housing bubble and sow seeds for a future crisis. The paper can also shed light on the housing markets in other economies that face similar vulnerabilities.

Incomplete Financial Markets and the Booming Housing Sector in China

Housing is by far the most important asset in Chinese households’ balance sheets. However, despite forceful and frequent government interventions, the rise in Chinese housing prices has not been contained as much as intended, a trend that has not been reversed by the COVID-19 shock. In this paper, we first provide some stylized facts and then a DSGE model (encompassing both demand and supply channels) to highlight the impact of a “slow-moving” structural vulnerability—financial market incompleteness—on China’s housing prices. The model implies that to eradicate the root causes of the rising housing price, policymakers need to go beyond the housing market itself; instead, it would be desirable to deepen financial markets because these markets would help channel financial resources to productive sectors rather than to housing speculation. This is particularly important in the COVID era because without addressing this structural vulnerability, the higher household savings and the government stimulus may fuel the housing bubble and sow seeds for a future crisis. The paper can also shed light on the housing markets in other economies that face similar vulnerabilities.

Mean-variance asset–liability management with partial information and uncertain time horizon

ABSTRACT This paper studies a mean-variance asset–liability management (ALM) problem with uncertain time horizon and partial information. The ALM can invest in an incomplete financial market consisting of one riskless asset and n risky stocks. The stocks price process is described by a multidimensional diffusion process with random coefficients. The uncontrollable liability process is modelled by a general diffusion process with hedgeable risks and unhedgeable risks. The uncertainty of the time horizon is assumed to come from randomness of financial assets and the liability and some other stochastic factors. The ALM may get only partial information about the liability. We derive efficient strategies and efficient frontiers in terms of the solutions of two BSDEs under complete and partial information. The closed-form expressions of efficient strategies and efficient frontiers are obtained under some special cases.

The implied Sharpe ratio

In an incomplete market, including liquidly traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept—the implied Sharpe ratio—which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor's portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's risk-aversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.

Incomplete Financial Markets and the Booming Housing Sector in China

Housing is by far the most important asset in Chinese households' balance sheets. However, despite forceful and frequent government interventions, the rise in Chinese housing prices has not been contained as much as intended, a trend that has not been reversed by the COVID-19 shock. In this paper, we first provide some stylized facts and then a DSGE model (encompassing both demand and supply channels) to highlight the impact of a 'slow-moving' structural vulnerability-financial market incompleteness-on China's housing prices. The model implies that to eradicate the root causes of the rising housing price, policymakers need to go beyond the housing market itself; instead, it would be desirable to deepen financial markets because these markets would help channel financial resources to productive sectors rather than to housing speculation. This is particularly important in the COVID era because without addressing this structural vulnerability, the higher household savings and the government stimulus may fuel the housing bubble and sow seeds for a future crisis. The paper can also shed light on the housing markets in other economies that face similar vulnerabilities.

The Role of Household Income on Child Labor: A Lesson From the Indonesian Crisis

Child labor is often considered a logical consequence in a household trying to meet the economic needs of poverty-stricken families. Reallocating a child's time as a buffer stock in household life is one of the last strategies or mechanisms carried out in developing countries when faced with various shocks. The purpose of this study is to determine the role of household income on child labor in Indonesia. The model used in this study was conducted in two stages through the fixed effects and conditional fixed-effects model. The results showed that permanent income affects child labor in Indonesia. This shows that child labor cannot be separated due to many factors, which include differences in economic conditions that underlie household choices and income among economic actors, incomplete financial market conditions, and constraints from resource and credit that may limit the investment decision that an individual makes. Therefore, the household would conduct consumption smoothing through children involved in the workforce. One thing that should be noted is that in households, females are more prone and susceptible than males when faced with shock. Therefore, to reduce the effects of shock, females tend to become involved in the workforce, primarily in the fields of agriculture and domestic work.