Collusion Proof Transfer Payment Schemes with Multiple Agents

Most of the current studies on transfer pricing under asymmetric information focus on a single principal and a single agent. Under a separating management and ownership assumption, transfer pricing is at minimum a three-person problem involving one principal and two agents. This paper considers a transfer pricing problem with two agents who possess private information and seek to maximize their net cash flows, instead of divisional accounting profits. The objectives of this paper are: (1) to derive a direct-revelation mechanism that induces truth telling and efficient allocation; (2) to study the agents' collusion behaviors under the direct-revelation mechanism. The findings indicate that when agents have the option to quit after contracting, it is optimal for the center to produce less than the first-best output level unless the costs for both divisions are at their lowest levels. The optimal amount of underproduction varies according to the demand condition. In addition, two sets of transfer functions, named as identical and nonidentical functions, are derived to induce truth-telling and yield optimal equilibrium output. The two sets of transfer functions are subject to collusion. However, the functions induce different collusion behaviors among agents, that is, the collusion sets for both functions are not common sets. This property enables us to eliminate any collusion between agents, particularly prior to their observation of private information.     

Consistent pricing and hedging for a modified constant elasticity of variance model

Abstract

This paper considers a modification of the well known constant elasticity of variance model where it is used to model the growth optimal portfolio (GOP). It is shown that, for this application, there is no equivalent risk neutral pricing measure and therefore the classical risk neutral pricing methodology fails. However, a consistent pricing and hedging framework can be established by application of the benchmark approach.

Perfect hedging strategies can be constructed for European style contingent claims, where the underlying risky asset is the GOP. In this framework, fair prices for contingent claims are the minimal prices that permit perfect replication of the claims. Numerical examples show that these prices may differ significantly from the corresponding ‘risk neutral’ prices.     

Imperfectly Credible Disinflation under Endogenous Time‐Dependent Pricing

The real effects of an imperfectly credible disinflation depend critically on the extent of price rigidity. We examine this interaction in a model with endogenous time‐dependent pricing. Both the endogenous initial degree of price rigidity and changes in the duration of price spells during disinflation are important in explaining the effects of imperfect credibility. We initially consider a setup where the degree of credibility is fixed and then allow agents to update beliefs about the “type” of monetary authority that they face. In both cases, the interaction between endogeneity of pricing behavior and imperfect credibility increases the output costs of disinflation.     

Path-dependent game options: a lookback case

The game option, which is also known as Israel option, is an American option with callable features. The option holder can exercise the option at any time up to maturity. This article studies the pricing behaviors of the path-dependent game option where the payoff of the option depends on the maximum or minimum asset price over the life of the option (i.e., the game option with the lookback feature). We obtain the explicit pricing formula for the perpetual case and provide the integral expression of pricing formula under the finite horizon case. In addition, we derive optimal exercise strategies and continuation regions of options in both floating and fixed strike cases.     

A financial CCAPM and economic inequalities

This paper considers a wealth heterogeneous multi-agent (MA) financial pricing CCAPM model. It is based on the following observations: (a) A distinction between what agents are willing to pay for consumption and what they actually pay. The former is a function of a number of factors including the agent’s wealth and risk preferences and the latter is a function of all other agents’ aggregate consumption or equivalently, their wealth committed to consumption. (b) Unlike traditional pricing models that define a representative agent underlying the pricing model, this paper assumes that each agent is in fact ‘Cournot-gaming’ a market defined by all other agents. This results in a decomposition of an n-agents game into n games of two agents, one a specific agent and the other a synthetic agent (a proxy for all other agents), on the basis of which an equilibrium consumption price solution is defined. The paper’s essential results are twofold. First, a Martingale pricing model is defined for each individual agent expressing the consumer willingness to pay (his utility price) and the market price—the price that all agents pay for consumption. In this sense, price is unique defined by each agent’s ‘Cournot game’ Agents’ consumption are then adjusted accordingly to meet the market price. Second, the pricing model defined is shown to account for agents wealth distribution pointing out that all agents valuations are a function of their and others’ wealth, the information they have about each other and other factors which are discussed in the text. When an agent has no wealth or cannot affect the market price of consumption, then this pricing model is reduced to the standard CCAPM model while any agent with an appreciable wealth compared to other agents, is shown to value returns (and thus future consumption) less than wealth-poor agents. As a result, this paper will argue that even in a financial market with an infinite number of agents, if there are some agents that are large enough to affect the market price by their decisions, such agents have an arbitrage advantage over the poorer agents. The financial CCAPM MA pricing model has a number of implications, some of which are considered in this paper. Finally, some simple examples are considered to highlight the applicability of this paper to specific financial issues.     

Equilibrium in risk-sharing games

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. In this paper, we propose a game where agents’ strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow–Debreu sharing rules. First, it is shown that agents’ best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation, and it is proved to exist for an arbitrary number of agents and to be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different from their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk-tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium than compared to the Arrow–Debreu one.     

Continuous Maturity Diversification of Default-Free Bond Portfolios and a Generalization of Efficient Diversification

This paper presents a method for solving the mean-variance portfolio selection problem that is applicable to the case where the number of securities is nondenumerably infinite. Necessary conditions for the existence of an optimal portfolio density are obtained and an expression for the efficient frontier is derived. The conditions for the existence of an optimal portfolio of continuously maturing bonds when their covariance matrix is singular are used to derive an arbitrage-free bond pricing equation. A method for estimating the covariance matrix and the associated efficient frontier is presented.     

Capital market equilibrium without riskless assets: heterogeneous expectations

The existence theorem of Allingham (Econometrica 59:1169–1174, 1991) for the capital asset pricing model (CAPM) is generalized to the case where agents have heterogeneous expectations on the return distribution and the mean-variance utility functions are quasiconcave. This result is built upon new conditions which are distinct from and weaker than the conditions imposed on the CAPM in the literature.      

Pricing financial services innovations

The number of innovative financial solutions introduced to markets has grown considerably in the past decade owing to emerging digital technologies, deregulation and market fragmentation. Examples are abundant in the worldwide markets for insurance, credit products and transaction processing services. A question of growing interest is how firms should price these innovations. The optimal introductory pricing of financial innovations may vary as a function of factors such as price sensitivity of the market and competitors’ ability to introduce competing financial solutions. In this article, we examine the role of these factors in the optimal pricing of a financial innovation. Using an agent-based simulation framework, introductory pricing strategies that maximize profitability under various market conditions are identified. Results indicate that lower levels of market price sensitivity and longer time horizons for competitive entry create pricing opportunities for financial innovators. However, the relationship becomes more complex as market price sensitivity increases or competitive market entry becomes more immediate. Detailed recommendations for optimal pricing of financial innovations under various market conditions are provided, and the article concludes with strategic recommendations for pricing innovative financial services.     

The impact of keeping up with the Joneses behavior on asset prices and portfolio choice

This paper studies the asset pricing and portfolio choice implications of keeping up with the Joneses preferences. In terms of portfolio choice, we provide sufficient conditions on the utility function under which no portfolio bias can arise across agents in equilibrium. Regarding asset prices, we find that under Joneses behavior asset prices are a function of the economy's aggregate consumption, the agents preference parameters, the wealth endowment distribution and the weighting across agents in the Joneses definition. We present necessary and sufficient conditions such that equilibrium prices are only a function of aggregate wealth. Non-financial, non-diversifiable income is introduced in the model. In the presence of Joneses behavior, an under-diversified equilibrium emerges where investors will bias their portfolios towards the financial assets that better hedge their exposure to the non-financial income risk.     

Irreversible investment and discounting: an arbitrage pricing approach

This paper presents a unified approach to valuing investment projects under uncertainty, based on stochastic discount factors, by linking optimal stopping theory to the no-arbitrage principle in asset pricing. An investment threshold for the case where the discount factor and the project’s cash-flow both follow a geometric Brownian motion is derived. Comparative statics of the investment trigger are obtained adding to and clarifying on the uncertainty–investment debate. Finally, two different ways to obtain discount factors are illustrated: spanning assets and representative agent analysis. The link between the characteristics of these different approaches and the optimal investment policy is clarified.     

Uninsurable risk and financial market puzzles

We compare the empirical performances of three risk-sharing arrangements involving idiosyncratic skill shocks: (a) where individuals are unable to directly insure their consumption against individual-specific shocks, (b) where agents strike long-term insurance contract with financial intermediaries involving a truth revelation constraint as in Kocherlakota and Pistaferri (2009), (c) full risk sharing. Based on the widely accepted assumption of cross-sectional log-normality of individual consumption levels, we work out closed form expressions of the pricing kernels for (a) and (b). We put these three models to test four financial market anomalies, namely the equity premium, currency premium, risk-free rate, and consumption-real exchange rate puzzles simultaneously in an integrated framework. We find that the pricing kernel associated with (a) outperforms the other two models in terms of the produced estimates of the agent’s preference parameters and the model ability to predict the equity and currency premia, the risk-free rate, and the log growth in the exchange rate. However, the predictive ability is still far from satisfactory for all three models under scrutiny.     

Listing Specialization and Pricing Precision

This paper investigates the relationship between property pricing precision (deviation from an expected property value) and specialization in the listing process by agents. It is hypothesized that financially constrained, risk-averse sellers prefer finer gradations of pricing precision, i.e., less deviation from expected property value, and that a set of agents will rise to meet this preference. The findings in this work indicate that agents specializing in listing properties increase pricing precision. The contributions of this work are twofold: (a) it provides a unique and heretofore uninvestigated metric as its dependent variable, thus allowing for further investigation into the brokerage intermediation process beyond the scope of price and marketing time, and (b) it provides an identifiable agent trait that can allow for a better matching of sellers’ preferences with agents’ abilities.     

Optimal design of derivatives in illiquid markets*

Abstract

The aim of this paper is to determine the optimal structure of derivatives written on an illiquid asset, such as a catastrophic or a weather event. This transaction involves two agents: a bank which wants to hedge its initial exposure towards this illiquid asset and an investor which may buy the contract. Both agents also have the opportunity to invest their residual wealth on a financial market.

Based on a utility maximization point of view, we determine an optimal profile (and its value) such that it maximizes the bank's utility given that the investor decides to make the deal only if it increases its utility. In the case of exponential utility, we show that the pricing rule is a non-linear function of the structure and that the bank always transfers the same proportion of its initial exposure. In the general case, an additional term appears, depending only on the relative log-likelihood of the two agents' views of the distribution of the illiquid asset.     

Stochastic orders in dynamic reinsurance markets

We consider a dynamic reinsurance market, where the traded risk process is driven by a compound Poisson process and where claim amounts are unbounded. These markets are known to be incomplete, and there are typically infinitely many martingale measures. In this case, no-arbitrage pricing theory can typically only provide wide bounds on prices of reinsurance claims. Optimal martingale measures such as the minimal martingale measure and the minimal entropy martingale measure are determined, and some comparison results for prices under different martingale measures are provided. This leads to a simple stochastic ordering result for the optimal martingale measures. Moreover, these optimal martingale measures are compared with other martingale measures that have been suggested in the literature on dynamic reinsurance markets.Received: March 2004, Mathematics Subject Classification (2000): 62P05, 60J75, 60G44JEL Classification: G10     

Reinsuring Climatic Risk Using Optimally Designed Weather Bonds

The aim of this paper is to determine the optimal structure of a weather bond, i.e. a bond whose coupons depend on the occurence of a weather event. The stress is put more on the structuration than on the simple pricing of the bond. Therefore, instead of looking only at the bond issue, we consider it as a part of a more general transaction, involving three agents: a firm, which wants to be hedged against its weather risk, an investor, which buys the bond and a bank, which has an intermediary key role. Then, we derive the optimal characteristics of the whole transaction. But the bond structure which is obtained, corresponds to a minimal structure: indeed, only the bond optimal price function and its optimal reimbursement level (amount which is paid back when an event occurs) can be determined while there is a degree of freedom in the choice of the optimal coupon. Therefore, this indeterminacy may be interpreted as a marketing tool and it could play an important role in the negotiation process between the issuer and the investor.     

A Fair Pricing Approach to Weather Derivatives

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No measure transformation is needed for the proposed fair pricing. For weather derivative payoffs that are independent of the value of the growth optimal portfolio, it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics. The fair prices of some particular weather derivatives are derived using historical and Gaussian residuals. The question of weather risk as diversifiable risk is also discussed. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: C16, G10, G13     

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

In a market with stochastic investment opportunities, we study an optimal consumption–investment problem for an agent with recursive utility of Epstein–Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The superdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein–Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein–Zin aggregator is neither Lipschitz nor jointly concave in all its variables.     

Optimal exchange rate flexibility with large labor unions

We study the optimal volatility of the exchange rate in a two-country model with sectoral non-atomistic wage setters, non-traded goods, nominal rigidities and alternative pricing assumptions – producer or local currency pricing. Labor unions internalize the sectoral impact of their wage settlements through firms' labor demand. With local currency pricing, exchange rate depreciation raises sales revenue, which in turn boosts domestic consumption and labor demand. Unions anticipate this effect and set higher wages accordingly. With small unions and low wage markup, optimal monetary policy enhances exchange rate movements to improve its terms of trade. With large unions and high wage markup, optimal monetary policy curbs exchange rate movements to restrain inflationary wage demands and to stabilize employment.     

The Quality and Price of Investment Banks’ Service: Evidence from the PIPE Market

We investigate the market structure and the pricing by placement agents of private investments in public equities (PIPEs). Our findings indicate that more reputable agents are associated with larger offers and with firms possessing lower risk. Agent reputation is positively associated with lower discounts and an enhanced post-PIPE trading environment. Issuers pay a higher dollar fee for these benefits, although more reputable agents charge a lower percentage fee. The evidence suggests that it is the quality of the issuing firm, and the pricing and reputational concern of the placement agent, that drives the equilibrium in the PIPE market.