Optimal monetary policy with endogenous entry and product variety

Deviations from long-run price stability are optimal in the presence of endogenous entry and product variety in a sticky-price model in which price stability would be optimal otherwise Long-run inflation (deflation) is optimal when the benefit of variety to consumers falls short of (exceeds) the market incentive for creating that variety—the desired markup; Price indexation exacerbates this mechanism. Plausible preference specifications and parameter values justify positive long-run inflation rates. However, short-run price stability (around this non-zero trend) is close to optimal, even in the presence of endogenously time-varying desired markups that distort the intertemporal allocation of resources.     

Optimal consumption policies in illiquid markets

We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613–627, 2008). Our main result is to derive smoothness C ¹ results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.     

Optimal portfolios in commodity futures markets

We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization.     

Common ownership and competition in product markets

We investigate the relation between common institutional ownership of the firms in an industry and product market competition. We find that common ownership is neither robustly positively related with industry profitability or output prices nor is it robustly negatively related with measures of nonprice competition, as would be expected if common ownership reduces competition. This conclusion holds regardless of industry classification choice, common ownership measure, profitability measure, nonprice competition proxy, or model specification. Our point estimates are close to zero with tight bounds, rejecting even modestly sized economic effects. We conclude that antitrust restrictions seeking to limit intra-industry common ownership are not currently warranted.     

Optimal liberalization of financial markets

As financial markets become completely liberalized, countries gain from improved risk sharing, but less wealthy countries can no longer profit from borrowing abroad at the lower rate and reinvesting at home at the higher rate. With decreasing rather than constant returns to capital, the gain from risk sharing is more likely to dominate the loss of the difference between the borrowing rate abroad and the decreasing reinvestment rate at home. Complete liberalization is likely to be optimal for less wealthy countries unless their labor endowment is large, their productivity is large, or holdings by foreigners are small, as in China.     

Optimal dynamic hedging in incomplete futures markets

This article derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding, and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those that obtain under complete markets, incompleteness leads in fact to second-best optima.     

Optimal order placement in limit order markets

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by characteristics of the order flows and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows the study of how the optimal order placement decision depends on the interplay between the state of order books, the fee structure, order flow properties and the aversion to execution risk. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general case of order placement across multiple exchanges, we propose a stochastic algorithm that computes the optimal routing policy and study the sensitivity of the solution to various parameters. Our algorithm does not require an explicit statistical model of order flow but exploits data on recent order fills across exchanges in the numerical implementation of the algorithm to acquire this information through a supervised learning procedure.     

Intermediaries and product quality in used car markets

We present empirical evidence supporting that used cars sold by dealers have higher quality: (i) dealer transaction prices are higher than unmediated market prices, and this dealer premium increases in the age of the car as a ratio and is hump-shaped in dollar value, and (ii) used cars purchased from dealers are less likely to be resold. In a model, we show that these empirical facts can be rationalized either when dealers alleviate information asymmetry, or when dealers facilitate assortative matching. The model predictions allow us to distinguish these two theories in the data, and we find evidence for both.     

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.     

Optimal investment and contingent claim valuation in illiquid markets

This paper extends basic results on arbitrage bounds and attainable claims to illiquid markets and general swap contracts where both claims and premiums may have multiple payout dates. Explicit consideration of swap contracts is essential in illiquid markets where the valuation of swaps cannot be reduced to the valuation of cumulative claims at maturity. We establish the existence of optimal trading strategies and the lower semicontinuity of the optimal value of optimal investment under conditions that extend the no-arbitrage condition in the classical linear market model. All results are derived with the “direct method” without resorting to duality arguments.     

Optimal auction design in two‐sided markets

A key feature of online markets for advertising (e.g., sponsored links) is that clicking rates depend on the searchers' expectations that the platform selects relevant advertisers. This article studies auction design by a platform that maximizes profits in the long run, where clicking rates are mechanism dependent. In line with the practice of the major search engines, the revenue‐maximizing mechanism is a scoring auction that combines the willingness to pay and the relevance to searchers of advertisers. By trading off rent extraction and clicking volume, this mechanism works as a cross‐subsidization device between searchers and advertisers.     

Optimal international hedging in commodity and currency forward markets

This paper derives optimal hedging and production rules for an exporting firm which faces both commodity-price and foreign- exchange-rate uncertainty. The size of the commodity hedge is independent of the properties of the foreign-exchange market. However, the optimal foreign-exchange hedge depends on the commodity hedge and the properties of the commodity forward market. The firm's production decision is independent of its objective function if both forward markets exist, but depends on the consumption beta of the unhedgeable risks in the absence of one or both of the markets.     

Avoiding market dominance: product compatibility in markets with network effects

As is well recognized, market dominance is a typical outcome in markets with network effects. A firm with a larger installed base offers a more attractive product which induces more consumers to buy its product which produces a yet bigger installed base advantage. Such a setting is investigated here but with the main difference that firms have the option of making their products compatible. When firms have similar installed bases, they make their products compatible in order to expand the market. Nevertheless, random forces could result in one firm having a bigger installed base, in which case the larger firm may make its product incompatible. We find that strategic pricing tends to prevent the installed base differential from expanding to the point that incompatibility occurs. This pricing dynamic is able to neutralize increasing returns and avoid the emergence of market dominance.     

Optimal portfolio choice for a behavioural investor in continuous-time markets

The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time financial market framework and assuming that asset prices are modelled by semimartingales, we derive sufficient and necessary conditions for the well-posedness of the optimisation problem in the case of piecewise-power probability distortion and utility functions. Finally, under straightforwardly verifiable conditions, we further demonstrate the existence of an optimal strategy.     

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.     

Retailers' choice of product variety and exclusive dealing under asymmetric information

This article considers vertical relations between an upstream manufacturer and a downstream retailer that can independently obtain a low‐quality, discount substitute. The analysis reveals that under full information, the retailer offers both varieties if and only if it is optimal to do so under vertical integration. However, when the retailer is privately informed about demand, it offers both varieties even if under vertical integration it is profitable to offer only the manufacturer's product. If the manufacturer can impose exclusive dealing, then under asymmetric information it will do so and foreclose the low‐quality substitute even if under vertical integration it is profitable to offer both varieties.     

Endogenous product differentiation in credit markets: What do borrowers pay for?

This paper studies strategies pursued by banks in order to differentiate their services and soften competition. More specifically we analyze whether bank's ability to avoid losses, its capital ratio, or bank size can be used as strategic variables to make banks different and increase the interest rates banks can charge their borrowers in equilibrium. Using a panel of data covering Norwegian banks between 1993 and 1998 we find empirical support that the ability to avoid losses, measured by the ratio of loss provisions, may act as such a strategic variable. A likely interpretation is that borrowers use high-quality low-loss banks to signal their creditworthiness to other stakeholders. This supports the hypothesis that high-quality banks serve as certifiers for their borrowers. Furthermore, this suggests that not only lenders and supervisors but also borrowers may discipline banks to avoid losses.     

Optimal monetary policy in an economy with incomplete markets and idiosyncratic risk

This study investigates an incomplete markets economy in which the saving behavior of a continuum of infinitely lived agents is influenced by precautionary saving motives and borrowing constraints. Agents can use two types of assets (interest bearing IOUS and money) to smooth consumption. Money is valued because of a timing friction in the bond market. In particular, the bond market closes before agents observe their idiosyncratic productivity shock. I find that the Friedman rule is not optimal for this economy. The results indicate that the optimal allocation has a rate of inflation of 10%, and a positive amount of private credit held by the government. A positive inflation rate transfers resources from agents with big endowments to those holding bonds which improves risk sharing, and therefore, welfare. However, for higher rates of inflation, agents economize on money holdings, offsetting the insurance effects, and causing a reduction in welfare. Furthermore, higher rates of inflation discourage agents from borrowing, and the endogenous lower bound on bond holdings is higher than the exogenous borrowing limit. High rates of inflation, therefore, exacerbate frictions in the bond market.     

Vertical divestitures through equity carve-outs and spin-offs: A product markets perspective

Using a product markets perspective to investigate the decision to vertically disintegrate, we find that vertical divestitures are more likely in response to positive industry demand shocks, favorable industry financing conditions, and lower parent firm relative productivity and are less likely when the potential for contracting problems is high. Conditional on vertical divestitures, equity carve-outs are more likely in environments in which relationship-specific investments are more prevalent and when the need for external funds is high, while spin-offs are more likely in larger industries and in industries that experience positive demand shocks. Our examinations of announcement-period wealth effects and changes in operating performance indicate that vertical divestitures are motivated by efficiency considerations.     

Debt financing: Does it boost or hurt firm performance in product markets?

Previous research seeks to establish whether debt boosts or hurts a firm's product market performance. This paper proposes that both of these outcomes can be observed: debt can boost and hurt performance. I first model a nonmonotonic relation between debt-like finance and competitive conduct. I then empirically examine the within-industry relation between leverage and sales performance using data from 115 industries over 30 years. My tests deal with the endogeneity of debt in a novel fashion: I use creditors’ valuation of assets in liquidation to identify financial leverage. I find that moderate debt taking is associated with relative-to-rival sales gains; high indebtedness, however, leads to product market underperformance.