Incomplete Markets Research Articles

Market-oriented reforms and wealth inequality in China

Over the last few decades, China’s growing wealth inequality has mirrored the contemporary global trend. We investigate the effects of China’s market-oriented reforms on wealth inequality using a dynamic general equilibrium model with an incomplete market and idiosyncratic risks. Focusing on the relaxation of private entry and the easing of financial constraints as two pivotal reforms, we show that our model-generated results closely match the actual wealth distribution from 1995 to 2018, with the reform of private enterprise entry accounting for most of the widening wealth disparity. We elucidate the underlying mechanisms of these two reforms using counterfactual simulations and discover that through the savings rate mechanism, the two reforms will collectively form an inverted U-shaped Kuznets curve in wealth inequality as reforms deepen in the future. By calculating the transition dynamics from 1995 to 2035, we confirm that the Kuznets turning point in China lies between 2020 and 2025.

To Bequeath, or Not to Bequeath? On Labour Income Risk and Top Wealth Concentration

Abstract Recent theoretical advances suggest that capital income risk, rather than earnings uncertainty, is the key determinant of fat-tailed behavior of stationary wealth distributions. I provide novel insights into this issue by studying an incomplete market model with general time and state separable preferences, where parental altruism and unobservable idiosyncratic shocks engender non-linear bequest rules. I analytically pin down conditions on the preference structure and other model’s primitives under which optimal bequest behavior hinders intergenerational wealth transmission for any degree of capital income risk, causing the dynamics of wealth to converge to a unique (stationary) distribution with thin tails. These results imply, in particular, that (i) the stochastic properties of labour income risk (as shaped by, e.g. fiscal policies) may play a role in defining the structure of the upper tail of the limiting distribution of wealth, and that (ii) matching empirically documented fat tails with choice theoretic frameworks of wealth dynamics requires joint restrictions on preferences and calibrated earnings processes to be met.

EU's “three-in-seven” road haulage cabotage rule – Impact imbalances across member states and the geography

Road cabotage within the EU, as a share of domestic transport of goods, varies greatly across member states. This can partly be attributed to EU's regime for consecutive cabotage. In addition to economic factors that reflect incomplete market integration, spatial factors appear to affect the impact of the current regime. The impact seems stronger for geographically large and centrally located countries with interregional homogeneity in trade. This may reflect that foreign hauliers under such conditions can utilize the characteristics of their standardized long-range trucks better, or because the likelihood of successfully fixing three favourable long-distance cabotage assignments within the seven days limit increases. Potential amendments to regulations in order to equalize the impact of EU's consecutive cabotage regime across member states' spatial characteristics include removing the limits to the number of trips within the seven days' time frame or shortening the time frame for carrying out the current maximum of three trips.

Why has China invested heavily in countries with weak market environments? A new explanation and implications for China-Africa economic cooperation

This paper investigates why China has invested heavily in countries with weak market environments. We provide a theoretical hypothesis that experiences and abilities acquired by Chinese enterprises in dealing with incomplete market environments at home help them conduct investment abroad. We match many databases and use government work experience of executives to capture the enterprise's experiences and abilities. The results show that the government work experience of executives helps enterprises overcome the constraints of unfavorable market environments in the destination country, and this effect is strongly reflected in host countries where resources are scarce, wages are low, and patent stocks are limited. These research findings have important implications for economic cooperation between China and Africa. Chinese enterprises have grown in an incomplete market environment. The experience they have accumulated is helpful for expanding investment opportunities in the African market, which has a positive impact on bilateral economic cooperation.

Pricing and Hedging Contingent Claims by Entropy Segmentation and Fenchel Duality

We present a new approach to the problem of characterizing and choosing equivalent martingale pricing measures for a contingent claim, in a finite-state incomplete market. This is the entropy segmentation method achieved by means of convex programming, thanks to which we divide the claim no-arbitrage prices interval into two halves, the buyer’s and the seller’s prices at successive entropy levels. Classical buyer’s and seller’s prices arise when the entropy level approaches 0. Next, we apply Fenchel duality to these primal programs to characterize the hedging positions, unifying in the same expression the cases of super (resp. sub) replication (arising when the entropy approaches 0) and partial replication (when entropy tends to its maximal value). We finally apply linear programming to our hedging problem to find in a price slice of the dual feasible set an optimal partial replicating portfolio with minimal CVaR. We apply our methodology to a cliquet style guarantee, using Heston’s dynamic with parameters calibrated on EUROSTOXX50 index quoted prices of European calls. This way prices and hedging positions take into account the volatility risk.

Bridging the Gap: Factors Influencing Farmers' Willingness and Behaviour in Biopesticide Application

Replacing chemical pesticides with biopesticides is crucial for ensuring high-quality agricultural products and advancing environmental sustainability. This study examines farmers’ willingness and behaviors regarding the use of biopesticides. A survey of 127 farmers in Junagadh district, Gujarat, was conducted, and a logistic model was employed to analyze factors influencing deviations between farmers’ willingness and their actual behaviors. The findings revealed that 37% of farmers showed a discrepancy between their willingness to use biopesticides and their actual application. Factors significantly impacting this deviation included price affordability, peer influence, education level, land size, emergency conditions, awareness of biopesticides, knowledge of the harmful effects of chemical pesticides, and awareness of agricultural product safety and quality. The primary reason for the gap between willingness and behavior is the farmers’ insufficient knowledge about biopesticides and the incomplete market structure for these products. To address this issue, it is recommended to improve farmers’ professional skills, raise awareness about green production methods, and accelerate the development of the biopesticides market to boost their adoption.

Option Pricing in an Incomplete Market

The purpose of this paper is to illustrate the pricing of options in an incomplete market using the new consistent uplifted martingale measure methodology introduced by Grigorian and Jarrow [2024, Filtration Reduction and Incomplete Markets, Frontiers of Mathematical Finance, 3(1), 78–105; 2023, Filtration Reduction and Completeness in Brownian Motion Models. Working Paper, Cornell University; 2024, Filtration Reduction and Completeness in Jump-Diffusion Models. Working Paper, Cornell University]. We apply it to an incomplete market where a stock has stochastic volatility. Two valuation formulas are generated, depending upon whether the trader is more concerned about volatility or price risk in the construction of a partial replicating portfolio for the option’s payoff.

Do taxspots matter?: A study of optimal tax uncertainty

Should the government run an uncertain fiscal policy to finance its liabilities? We call the resulting uncertainty taxspots, and study conditions that make taxspots optimal and recurrent in standard Ramsey problems. We show that prudence and market incompleteness play a role in sustaining taxspots, and that equal-treatment randomizations can be decentralized via taxspots even in the absence of financial markets.

American option in a market generated by interactive agents

This study introduces a new financial market model inspired by Remita and Eisele's methodology, incorporating a substantial number of interacting agents denoted by “n”. Focusing on the valuation of European and American options within this vast network of agents, and more specifically on behavior when “n” tends to infinity, the research illustrates the convergence of an initially incomplete market towards completeness. In addition, the study scrutinizes the price stability of options on the underlying risky asset, St, in the context of an increasing number of agents. Taking into account a comprehensive set of internal and external factors influencing market dynamics, this study offers a holistic analysis of option price dynamics and market completeness. By examining the complex interactions between a large number of agents and option pricing, the research provides valuable insights into the complexity of financial markets. The results not only elucidate convergence phenomena within an expanding network of agents, they also shed light on the stability of option prices under ever-changing market conditions. This comprehensive analysis underlines the multifaceted nature of financial markets, highlighting the intrinsic relationship between option price dynamics and various market influences. Overall, this study makes a significant contribution to the understanding of financial market dynamics, particularly in the context of option pricing.

Deep learning for quadratic hedging in incomplete jump market

We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based on a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal option price, and the corresponding equivalent martingale measure through the means of the Stackelberg game approach. A deep learning algorithm based on the combination of the feed-forward and LSTM neural networks is tested on three different market models, two of which are incomplete. In contrast, the complete market Black–Scholes model serves as a benchmark for the algorithm’s performance. The results that indicate the algorithm’s good performance are presented and discussed. In particular, we apply our results to the special incomplete market model studied by Merton and give a detailed comparison between our results based on the minimal variance principle and the results obtained by Merton based on a different pricing principle. Using deep learning, we find that the minimal variance principle leads to typically higher option prices than those deduced from the Merton principle. On the other hand, the minimal variance principle leads to lower losses than the Merton principle.

Risk management under weighted limited expected loss

We present and solve an optimal asset allocation problem under a weighted limited expected loss (WLEL) constraint. This formulation encompasses the risk management problem with a limited expected loss (LEL) constraint as a specialized instance and offers a pertinent internal risk management instrument for firms. We observe that a WLEL constraint makes the optimizing investor pursue less volatile payoffs than the unconstrained Merton solution. Compared to the LEL-constrained problem with the same weighted default threshold, the WLEL optimal terminal wealth displays a less dispersed distribution with a smaller variance, suggesting a more secure risk management framework. Conducting a comprehensive equilibrium analysis in the presence of a WLEL risk manager, we validate the relatively conservative investment approach undertaken by the WLEL manager. Subsequently, we expand our findings to encompass broader incomplete market settings, wherein the uniqueness of the equivalent local martingale measure is not assured.

Stability of the Epstein–Zin problem

AbstractWe investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish.

Pricing derivatives on foreign assets using Markov-modulated cojump-diffusion dynamics

In this study, cross-currency derivatives pricing under stochastic interest rates is analyzed when Markov-modulated cojump-diffusion dynamics with both idiosyncratic and simultaneous jumps drive the underlying foreign equity price and foreign exchange rate processes. More specifically, the noise dynamics of these two assets are captured by the correlated Wiener processes, and the two types of jump events are described as two independent compound Poisson processes with log-normal jump amplitudes. Cojumping addresses the correlation between these two asset price jumps. In an incomplete market setting, the dynamic Esscher transform approach is applied to determine a pricing kernel. According to the resulting dynamics, explicit analytical formulas for evaluating values of European foreign equity call options are provided. Numerical experiments are also described.

Are Supply Networks Efficiently Resilient?

We show that supply networks are inefficiently, and insufficiently, resilient. Upstream firms can expand their production capacity to hedge againstsupply and demand shocks. But the social benefits of such investments arenot internalized due to market power and market incompleteness. Upstreamfirms under-invest in capacity and resilience, passing-on the costs to downstreamfirms, and drive trade excessively towards the spot markets. There isa wedge between the market solution and a constrained optimal benchmark,which persists even without rare and large shocks. Policies designed to incentivizecapacity investment, reduce reliance on spot markets, and enhancecompetition ameliorate the externality.

A Discrete Risk-Theory Approach to Manage Equity-Linked Policies in an Incomplete Market

We construct a model where, at each time instance, risky securities can only take a limited number of values and the equity-linked policy sold by the insurer to policyholders pays benefits linked to these securities. Since the number of states in the model exceeds the number of securities in the (incomplete) market, the martingale measure is not unique, posing a problem in pricing insurance instruments. In this framework, we consider how a super-replicating strategy violates the assumption of absence of arbitrage, yet simultaneously allows the insurance company to fully hedge against financial risk. Since the super-replicating strategy, when considered alone, would be too costly for any rational insured person, through the definition of the safety loading, we demonstrate how the insurer can still hedge against financial risk, albeit at the expense of increasing its exposure to demographic risk. This approach does not aim to show how the pricing of the index-linked policy can actually be performed but rather highlights how risk theory-based approaches (via the definition of the profit and loss random variable) enable the management of the trade-off between financial risk and demographic risk.

Effects of partial demand uncertainty reduction on private equity financing in small and medium-sized enterprises: A supply chain perspective.

The effect of demand uncertainty reduction (DUR) on supply chain management has received tremendous attention. From a financial perspective, studying the impact of DUR is equally significant. This study explores the relationship between DUR and private equity (PE) financing in retail enterprises within a supply chain, which comprises a dominant supplier and a subordinate retailer. This article establishes decision models for a retailer backed by PE under three market demand conditions: range, mean, and range with mean. The study further investigates the impact of partial demand uncertainty reduction (PDUR) on the retailer and PE through comparative analysis of these scenarios. To address incomplete market demand information during the decision-making process, the study employs the minimax regret criterion to construct and solve the model. An intriguing finding of this study is that contrary to intuition, PDUR not only fails to promote PE but also reduces the retailer's willingness to finance and decreases the asset size for both the retailer and PE. In addition, the better the growth potential for the retail enterprise, the more severe the negative impact brought about by PDUR. Moreover, the impact of PDUR on supplier and supply chain performance is two-fold. PDUR based on range information has a negative impact on the expected profit of the supplier and the supply chain, while PDUR based on mean information has a positive impact on their expected profit.

Short-term impact of climate change on labor market in China: Quantitative spatial analysis based on an oligopsony model

Assessing the impact of climate change on the economy is an important issue for designing climate policy. By constructing an oligopsony model to depict the incompleteness of the labor market and using the quantitative spatial model analysis method, we quantitatively estimated the short-term impact of climate change on the labor market in China. Then, to control climate change, the optimal climate change governance intensities (CCGI) of multi-governments satisfying CD preferences and Stackelberg game are designed and solved. The results show that climate change leads to a decrease in wages and labor supply in labor market equilibrium and a loss of market aggregate income and labor scale. Climate change has led to a shift in labor from the agricultural and dirty sectors to the clean sector. The regional labor distribution is also being “disrupted” due to climate change. Moreover, declining migration costs and increased subsidies help to reduce the negative impacts of climate change. The optimal CCGI of the central government is higher than that of the provincial government. The optimal CCGI is higher in the eastern provinces than in the central and western regions. Implementing CCGI would mitigate the negative climate change shocks to the labor market in China and increase welfare. The conclusions of this paper provide strong support for preventing climate change risks and actively participating in global climate change governance.

SYSTEMIC PERSPECTIVE OF TERM RISK IN BANK FUNDING MARKETS

The transition from term-based reference rates to overnight reference rates has created a dislocation in the market-making processes between the interbank and non-interbank funding, and their respective derivatives markets. This dislocation can be attributed to differences in funding and corresponding interest rate swap transactions, a thesis we explain and characterize in detail. It is then shown how this dislocation may be resolved. Based on a systemic perspective of a stylized financial system, an aggregated banking system is constructed that is void of idiosyncratic credit risks but still vulnerable to liquidity risks. Within this setup, a mathematical modeling framework for term-cognizant interest rate systems is derived that enables the pricing and valuation of bank term funding and associated derivatives transactions with varying liquidity characteristics. Other outcomes include: (i) a detailed analysis of the incomplete market paradigm that encapsulates bank term funding rates and the risk management processes involved therein; and (ii) a recovery of consistency in the pricing and valuation between funding and related interest rate swap transactions, along with a mechanism to exchange term risk.

Aggregation, Liquidity, and Asset Prices with Incomplete Markets

Aggregation, Liquidity, and Asset Prices with Incomplete Markets

Option Pricing in an Incomplete Market

Option Pricing in an Incomplete Market