OPTION PRICING AND HEDGING WITH EXECUTION COSTS AND MARKET IMPACT

This paper considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price‐taking agent in a frictionless market, traders cannot be perfectly hedged because of execution costs and market impact. They indeed face a trade‐off between hedging errors and costs that can be solved by using stochastic optimal control. Our modeling framework, which is inspired by the recent literature on optimal execution, makes it possible to account for both execution costs and the lasting market impact of trades. Prices are obtained through the indifference pricing approach. Numerical examples are provided, along with comparisons to standard methods.     

THE GENERAL STRUCTURE OF OPTIMAL INVESTMENT AND CONSUMPTION WITH SMALL TRANSACTION COSTS

We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time‐varying but small transaction costs, we derive simple formal asymptotics for the optimal policy and welfare. These reveal the roles of the investors' preferences as well as the market and cost dynamics, and also lead to a fully dynamic model for the implied trading volume. In frictionless models that can be solved in closed form, explicit formulas for the leading‐order corrections due to small transaction costs are obtained.     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.     

Optimal dynamic regulation of carbon emissions market

In this article, we deal with optimal dynamic carbon emission regulation of a set of firms. On the one hand, the regulator dynamically allocates emission allowances to each firm. On the other hand, firms face idiosyncratic, as well as common, economic shocks on emissions, and they have linear quadratic abatement costs. Firms can trade allowances so as to minimize total expected costs, which arise from abatement, trading, and terminal penalty. Using variational methods, we first exhibit in closed form the market equilibrium in function of the regulator's dynamic allocation. We then solve the Stackelberg game between the regulator and the firms. The result is a closed-form expression of the optimal dynamic allocation policies that allow a desired expected emission reduction. The optimal policy is unique in the presence of market impact. In absence of market impact, the optimal policy is nonunique, but all the optimal policies share common properties. The optimal policies are fully responsive, and therefore induce a constant abatement effort and a constant price of allowances. Our results are robust to some extensions, like different penalty functions.     

Optimal make–take fees for market making regulation

We address the mechanism design problem of an exchange setting suitable make– take fees to attract liquidity on its platform. Using a principal–agent approach, we provide the optimal compensation scheme of a market maker in quasi‐explicit form. This contract depends essentially on the market maker inventory trajectory and on the volatility of the asset. We also provide the optimal quotes that should be displayed by the market maker. The simplicity of our formulas allows us to analyze in details the effects of optimal contracting with an exchange, compared to a situation without contract. We show in particular that it improves liquidity and reduces trading costs for investors. We extend our study to an oligopoly of symmetric exchanges and we study the impact of such common agency policy on the system.     

Nonlinear price impact and portfolio choice

In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long‐term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the price impact function. Trading rates are finite as with linear impact, but are lower near the target portfolio, and higher away from the target. The model nests the square‐root impact law and, as extreme cases, linear impact and proportional transaction costs.     

TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS

We consider the linear‐impact case in the continuous‐time market impact model with transient price impact proposed by Gatheral. In this model, the absence of price manipulation in the sense of Huberman and Stanzl can easily be characterized by means of Bochner’s theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure‐valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko on the nonexistence of transaction‐triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.     

PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME

We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T] and can trade continuously at a traditional exchange (the “primary venue”) and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multidimensional Poisson process. We characterize the costs of trading by a linear‐quadratic functional which incorporates both the price impact costs of trading at the primary exchange and the market risk of the position. The solution of the cost minimization problem is characterized by a matrix differential equation with singular boundary condition; by means of stochastic control theory, we provide a verification argument. If a single‐asset position is to be liquidated, the investor slowly trades out of her position at the primary venue, with the remainder being placed in the dark pool at any point in time. For multi‐asset liquidations this is generally not the case; for example, it can be optimal to oversize orders in the dark pool in order to turn a poorly balanced portfolio into a portfolio bearing less risk.     

MODELING LIQUIDITY EFFECTS IN DISCRETE TIME

We study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox–Ross–Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options.     

SHADOW PRICES FOR CONTINUOUS PROCESSES

In a financial market with a continuous price process and proportional transaction costs, we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e., a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredients are the continuity of the price process and the hypothesis of “no unbounded profit with bounded risk.” A counterexample reveals that these hypotheses cannot be relaxed.     

Small‐cost asymptotics for long‐term growth rates in incomplete markets

This paper provides a rigorous asymptotic analysis of long‐term growth rates under both proportional and Morton–Pliska transaction costs. We consider a general incomplete financial market with an unspanned Markov factor process that includes the Heston stochastic volatility model and the Kim–Omberg stochastic excess return model as special cases. Using a dynamic programming approach, we determine the leading‐order expansions of long‐term growth rates and explicitly construct strategies that are optimal at the leading order. We further analyze the asymptotic performance of Morton–Pliska strategies in settings with proportional transaction costs. We find that the performance of the optimal Morton–Pliska strategy is the same as that of the optimal one with costs increased by a factor of . Finally, we demonstrate that our strategies are in fact pathwise optimal, in the sense that they maximize the long‐run growth rate path by path.     

Who Benefits from Workers with General Skills? Countervailing Incentives in Labour Contracts

In a principal–agent model with adverse selection and moral hazard the impact of the agent's transferable human capital on incentives is analysed. It is shown that under asymmetric information the employer (principal) prefers a worker (agent) with general skills to a similarly productive worker with firm‐specific skills although the reservation utility of a worker with general (i.e. marketable) skills is higher. The principal's information costs are lower when workers have general skills than in the case where workers possess only firm‐specific human capital because of countervailing incentives. The optimal contract for workers with general skills differs from the standard screening contract in that it involves pooling.     

The Merits of Dual Pricing of Russian Natural Gas

Our analysis reveals that, from Russia's perspective, there is no economic rationale to unify the price of natural gas it sells domestically and in Europe. We argue that pipelines allow Gazprom to segment the Russian market from the European (including Turkey) market and that Russia has market power in the European market. If Russia were to fail to exploit this market power in its European market, by selling its natural gas to Europe at only full long‐run marginal cost plus transportation costs, Russia would lose between $5 billion and $7.5 billion per year (almost two per cent of its GDP). If, instead, Russia were to raise its domestic prices to the prices it charges in Europe, Russian industry would incur very large investment adjustment and unemployment costs in the short run – adjustment costs that cannot be justified on the basis of comparative advantage. We estimate that the efficient world price would be achieved if Gazprom were to employ its optimal ‘two‐part tariff’. The optimal two‐part tariff would double Gazprom's annual profits in Europe, but it involves significant long‐term risks for Gazprom of lost market share.     

Can Industry Consolidation Lead to Greater Efficiencies? Evidence from the U.S. Defense Industry

The question of whether mergers in various industries lead to greater market power or improved efficiencies has been the subject of numerous public policy debates. This analysis focuses on the impact of consolidation in the U.S. defense industry over the past 20 years and examines the reasons behind the wave of defense consolidation, the results in terms of the reduction in contractors, the antitrust response to mergers, and evidence on the impact of the mergers on weapons systems’ total and per-unit costs. The analysis finds that merger activity was driven less by declines in spending following the Cold War than by a stronger economy and a vibrant financial market. The cost data show that 39 to 44 percent of systems experienced statistically significant change in either total costs or per-unit costs following a merger. Somewhat more systems were likely to exhibit lower postmerger per-unit costs than higher per-unit costs, suggesting improved efficiency. The analysis also examines the impact on weapon systems cost by type of weapons system, manufacturer, and service (Army, Navy, Air Force). The evidence suggested greater efficiencies following consolidation for many sectors. Army and Navy systems overall showed lower per-unit costs, but the Air Force weapons systems showed mixed results.     

Decimalization,ETFs and futures pricing efficiency

This study investigates the impact of decimalization (penny pricing) on the arbitrage relationship between index exchange‐traded funds and E‐mini index futures. The empirical results reveal that subsequent to penny pricing, there is a significant fall in the mean ex ante arbitrage profit, especially in the cases with higher transaction costs. Using the ordinary least squares and quantile regressions to control for the influences of changes in other market characteristics, it is found that the overall pricing efficiency has deteriorated in the post‐decimalization period. These results are consistent with the hypothesis that, due to the lowered market depth and increased execution risks, the introduction of decimalization has in general resulted in weakening the ability and the willingness of arbitrageurs to initiate arbitrage trades, which subsequently leads to a reduction in the general efficiency of the cash/futures pricing system. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 29:157–178, 2009     

GENERAL INTENSITY SHAPES IN OPTIMAL LIQUIDATION

The classical literature on optimal liquidation, rooted in Almgren–Chriss models, tackles the optimal liquidation problem using a trade‐off between market impact and price risk. It answers the general question of optimal scheduling but the very question of the actual way to proceed with liquidation is rarely dealt with. Our model, which incorporates both price risk and nonexecution risk, is an attempt to tackle this question using limit orders. The very general framework we propose to model liquidation with limit orders generalizes existing ones in two ways. We consider a risk‐averse agent, whereas the model of Bayraktar and Ludkovski only tackles the case of a risk‐neutral one. We consider very general functional forms for the execution process intensity, whereas Guéant, Lehalle and Fernandez‐Tapia are restricted to exponential intensity. Eventually, we link the execution cost function of Almgren–Chriss models to the intensity function in our model, providing then a way to see Almgren–Chriss models as a limit of ours.     

A NOTE ON THE EFFECTS OF TAXES ON OPTIMAL INVESTMENT

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.     

RISK METRICS AND FINE TUNING OF HIGH‐FREQUENCY TRADING STRATEGIES

We propose risk metrics to assess the performance of high‐frequency (HF) trading strategies that seek to maximize profits from making the realized spread where the holding period is extremely short (fractions of a second, seconds, or at most minutes). The HF trader maximizes expected terminal wealth and is constrained by both capital and the amount of inventory that she can hold at any time. The risk metrics enable the HF trader to fine tune her strategies by trading off different metrics of inventory risk, which also proxy for capital risk, against expected profits. The dynamics of the midprice of the asset are driven by information flows which are impounded in the midprice by market participants who update their quotes in the limit order book. Furthermore, the midprice also exhibits stochastic jumps as a consequence of the arrival of market orders that have an impact on prices which can give rise to market momentum (expected prices to trend up or down). The HF trader's optimal strategy incorporates a buffer to cover adverse selection costs and manages inventories to maximize the expected gains from market momentum.     

UNIVERSAL INVESTMENT IN MARKETS WITH TRANSACTION COSTS

In this paper we investigate growth optimal investment in two-asset discrete-time markets with proportional transaction costs and no distributional assumptions on the market return sequences. We construct a policy with growth rate at least as large as any interval policy. Since interval policies are ε-optimal for independent and identically distributed (i.i.d.) markets ( Iyengar 2002 ), it follows that our policy when employed in an i.i.d. market is able to "learn" the optimal interval policy and achieve growth optimality; in other words, it is a universal growth optimal policy for i.i.d. markets.     

Enhancing marketing with engineering: Optimal product line design for heterogeneous markets

Successful product line design and development often require a balance of technical and market tradeoffs. Quantitative methods for optimizing product attribute levels using preference elicitation (e.g., conjoint) data are useful for many product types. However, products with substantial engineering content involve critical tradeoffs in the ability to achieve those desired attribute levels. Technical tradeoffs in product design must be made with an eye toward market consequences, particularly when heterogeneous market preferences make differentiation and strategic positioning critical to capturing a range of market segments and avoiding cannibalization.We present a unified methodology for product line optimization that coordinates positioning and design models to achieve realizable firm-level optima. The approach overcomes several shortcomings of prior product line optimization models by incorporating a general Bayesian account of consumer preference heterogeneity, managing attributes over a continuous domain to alleviate issues of combinatorial complexity, and avoiding solutions that are impossible to realize. The method is demonstrated for a line of dial-readout scales, using physical models and conjoint-based consumer choice data. The results show that the optimal number of products in the line is not necessarily equal to the number of market segments, that an optimal single product for a heterogeneous market differs from that for a homogeneous one, and that the representational form for consumer heterogeneity has a substantial impact on the design and profitability of the resulting optimal product line — even for the design of a single product. The method is managerially valuable because it yields product line solutions efficiently, accounting for marketing-based preference heterogeneity as well as engineering-based constraints with which product attributes can be realized.