Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

Discrete-time option pricing with stochastic liquidity

Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to significant bid-ask spreads. Within the framework of conic finance, we develop a stochastic liquidity model, extending the discrete-time constant liquidity model of Madan (2010). With this extension, we can replicate the term and skew structures of bid-ask spreads typically observed in option markets. We show how to implement such a stochastic liquidity model within our framework using multidimensional binomial trees and we calibrate it to call and put options on the S&P 500.     

Dynamic liquidation under market impact

The optimal liquidation problem with transaction costs, which includes a positive fixed cost, and market impact costs, is studied in this paper as a constrained stochastic optimal control problem. We assume that trading is instantaneous and the dynamics of the stock to be liquidated follows a geometric Brownian motion. The solution to the impulse control problem is computed at each time step by solving a linear partial differential equation and a maximization problem. In contrast to results obtained from the static formulation of Almgren and Chriss [J. Risk, 2000 Almgren, R and Chriss, N. 2000. Optimal execution of portfolio transactions. J. Risk, 3: 5–39. [Crossref] , [Google Scholar], 3, 5–39], when risk is not considered, the optimal liquidation strategy from our stochastic control formulation depends on temporary market impact cost and permanent market impact cost parameters. In addition, our computational results indicate the following properties of the optimal execution strategy from the stochastic control formulation. Due to the existence of a no-transaction region, it may not be optimal for some individuals to sell their assets on some trading dates. As the value of the permanent market impact parameter increases, the expected optimal amount liquidated at the terminal time increases. As the value of the quadratic temporary impact cost parameter increases, the expected optimal amount liquidated at trading times tends to be uniform, and the no-transaction region shrinks. In the presence of quadratic temporary market impact costs, in contrast to optimal strategies that result from fixed and/or proportional transaction costs alone, portfolios in the selling region are neither re-balanced into the no-transaction region nor into the sell and no-transaction interface.     

Partial liquidation under reference-dependent preferences

We propose a multiple optimal stopping model where an investor can sell a divisible asset position at times of her choosing. Investors have $S$-shaped reference-dependent preferences, whereby utility is defined over gains and losses relative to a reference level and is concave over gains and convex over losses. For a price process following a time-homogeneous diffusion, we employ the constructive potential-theoretic solution method developed by Dayanik and Karatzas (Stoch. Process. Appl. 107:173–212, 2003). As an example, we revisit the single optimal stopping model of Kyle et al. (J. Econ. Theory 129:273–288, 2006) to allow partial liquidation. In contrast to the extant literature, we find that the investor may partially liquidate the asset at distinct price thresholds above the reference level. Under other parameter combinations, the investor sells the asset in a block, either at or above the reference level.     

Managing liquidity: Optimal degree of centralization

Large banking groups face the question of how to optimally allocate and generate liquidity: in a central liquidity hub or in many decentralized branches. We translate this question into a facility location problem under uncertainty. We show that volatility is the key driver behind (de-)centralization. We provide an analytical solution for the 2-branch model and show that a liquidity center can be interpreted as an option on immediate liquidity. Therefore, its value can be interpreted as the price of information, i.e., the price of knowing the exact demand. Furthermore, we derive the threshold above which it is advantageous to open a liquidity center and show that it is a function of the volatility and the characteristic of the bank network. Finally, we discuss the n-branch model for real-world banking groups (10-60 branches) and show that it can be solved with high granularity (100 scenarios) within less than 30 s.     

Optimal portfolio liquidation in target zone models and catalytic superprocesses

We study optimal buying and selling strategies in target zone models. In these models, the price is modelled by a diffusion process which is reflected at one or more barriers. Such models arise, for example, when a currency exchange rate is kept above a certain threshold due to central bank interventions. We consider the optimal portfolio liquidation problem for an investor for whom prices are optimal at the barrier and who creates temporary price impact. This problem is formulated as the minimization of a cost–risk functional over strategies that only trade when the price process is located at the barrier. We solve the corresponding singular stochastic control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess. In this setting, the catalyst is given by the barriers of the price process. For the cases in which the unaffected price process is a reflected arithmetic or geometric Brownian motion with drift, we moreover give a detailed financial justification of our cost functional by means of an approximation with discrete-time models.     

Payments and liquidity under adverse selection

Informational asymmetries regarding the future value of assets affect their role in exchange. I construct a random-matching economy composed of two assets: a risk-free bond and a Lucas tree whose terminal value is privately known to its holder. No restrictions are imposed on payment arrangements. The main finding supports a pecking-order theory of payments: Agents use their risk-free bonds first in order to finance their spending shocks, and they use their information-sensitive assets only if their holdings of bonds are depleted. The theory has implications for the optimal provision of risk-free bonds, the structure of asset returns, and liquidity.     

Currency hedging for multinationals under liquidity constraints

This paper examines the impact of liquidity risk on the behavior of a risk-averse multinational firm (MNF) under exchange rate uncertainty in a two-period dynamic setting. The MNF has operations domiciled in the home country and in a foreign country, each of which produces a single homogeneous good to be sold in the home and foreign markets. To hedge the exchange rate risk, the MNF has access to one-period currency futures and option contracts in each period. The MNF is liquidity constrained in that it is obliged to terminate its risk management program in the second period whenever the net loss due to its first-period hedge position exceeds a predetermined threshold level. We show that the MNF optimally sells less (more) and produces more (less) in the foreign (home) country in response to the imposition of the liquidity constraint. We show further that the liquidity constrained MNF optimally uses the currency option contracts in the first period for hedging purposes in general, and opts for a long option position if its utility function is quadratic in particular.     

Corporate liquidity and dividend policy under uncertainty

We examine optimal liquidity (retained earnings) and dividend choice incorporating debt financing with risk of default and bankruptcy costs as well as growth options under revenue uncertainty. We revisit the conditions for dividend policy irrelevancy and the broader role of retained earnings and dividends. Retained earnings have a net positive impact on firm value in the presence of growth options, high external financing costs and low default risk. High levels of retained earnings enhance debt capacity but have a negative effect on equity value due to the likelihood of losing accumulated cash balances in case of default, unless offset by high external financing costs. Opposite directional effects of retained earnings on equity and debt create a U-shaped relation with firm value. The framework is extended to analyze management-shareholder conflicts, demonstrating that managers accumulate higher than optimal cash.     

Optimal execution with stochastic delay

Finance and Stochastics - We show how traders use marketable limit orders (MLOs) to liquidate a position over a trading window when there is latency in the marketplace. MLOs are liquidity-taking...     

Adaptive basket liquidation

We consider the infinite-horizon optimal basket portfolio liquidation problem for a von Neumann–Morgenstern investor in a multi-asset extension of the liquidity model of Almgren (Appl. Math. Finance 10:1–18, 2003) with cross-asset impact. Using a stochastic control approach, we establish a “separation theorem”: the sequence of portfolios held during an optimal liquidation depends only on the (co-)variance and (cross-asset) market impact of the assets, while the speed with which these portfolios are reached depends only on the utility function of the trader. We derive partial differential equations for both the sequence of portfolios reached during the execution and the trading speed.     

Investment timing and optimal capital structure under liquidity risk

Deterioration in debt market liquidity reduces debt values and affects firms' decisions. Considering such risk, we develop an investment timing model and obtain analytic solutions. We carry out a comprehensive analysis in optimal financing, default, and investment strategies, and stockholder–bondholder conflicts. Our model explains stylized facts and replicates empirical findings in credit spreads. We obtain six new insights for decision makers. We propose a ‘new trade-off theory’ for optimal capital structure, a new tax effect, and new explanations of ‘debt conservatism puzzle’ and ‘zero-leverage puzzle’. Failure in recognizing liquidity risk results in substantially over-leveraging, early bankruptcy or investment, overpriced options, and undervalued coupons and credit spreads. In addition, agency costs are surprisingly small for a high liquidity risk or a low project risk. Interestingly, the risk shifting incentive and debt overhang problem decrease with liquidity risk under moderate tax rates while they increase under high tax rates.     

流动性过剩与农信社流动性不足

2007年以来,为缓解流动性过剩,控制货币信贷过快增长,央行频繁运用公开市场操作和上调存款准备金率等手段,加大货币回收力度.这虽然抑制了银行体系的流动性过剩,但对于作为弱势金融群体的农村信用社来说,紧缩货币政策实施所产生的累积效应对一些经济欠发达山区农信社的流动性管理带来了不利的影响,隐含的支付性风险不容忽视.     

Global liquidity trap

How should monetary policy respond to a “global liquidity trap,” where the two countries may fall into a liquidity trap simultaneously? Using a two-country New Open Economy Macroeconomics model, we first characterize optimal monetary policy, and show that the optimal rate of inflation in one country is affected by whether or not the other country is in a liquidity trap. We next examine how well the optimal monetary policy is approximated by relatively simple monetary policy rules. The interest-rate rule targeting the producer price index performs well in this respect.     

A model of optimal portfolio selection under liquidity risk and price impact

We study a financial model with one risk-free and one risky asset subject to liquidity risk and price impact. In this market, an investor may transfer funds between the two assets at any discrete time. Each purchase or sale policy decision affects the rice of the risky asset and incurs some fixed transaction cost. The objective is to maximize the expected utility from terminal liquidation value over a finite horizon and subject to a solvency constraint. This is formulated as an impulse control problem under state constraints and we characterize the value function as the unique constrained viscosity solution to the associated quasi-variational Hamilton–Jacobi–Bellman inequality. We would like to thank Mihail Zervos for useful discussions.     

Hedging and liquidity

This article develops a model for evaluating alternative hedgingstrategies for financially constrained firms. A key advantageof the model is the ability to capture the intertemporal effectsof hedging on the firm's financial situation. We characterizethe optimal hedge. A wide range of alternative hedging strategiescan be specified and the model allows us to determine in eachcase if the hedging strategy raises or lowers firms value andby how much. We show that hedging firm value, hedging cash flowfrom operations and hedging sales revenue are not optimal. Thearticle highlights the fact that every hedging strategy comespackaged with a borrowing strategy which requires careful consideration.     

Aggregate liquidity shortages, idiosyncratic liquidity smoothing and banking regulation

This paper develops a model of banking fragility driven by aggregate liquidity shortages. Inefficiencies arise from a failure of the interbank market to smooth the available liquidity in such a shortage. We find that a standard lender of last resort policy is ineffective in restoring efficiency as it leads to offsetting changes in the banks’ supply of liquidity. In contrast, subsidizing the purchase of assets from troubled banks increases welfare by improving the banks’ liquidity holdings. The first best, however, is achieved by redistributing existing liquidity from healthy to troubled banks in a crisis.     

Capital reallocation and liquidity

This paper shows that the amount of capital reallocation between firms is procyclical. In contrast, the benefits to capital reallocation appear countercyclical. We measure the amount of reallocation using data on flows of capital across firms and the benefits to capital reallocation using several measures of the cross-sectional dispersion of the productivity of capital. We then study a calibrated model economy where capital reallocation is costly and impute the cost of reallocation. We find that the cost of reallocation needs to be substantially countercyclical to be consistent with the observed joint cyclical properties of reallocation and productivity dispersion.     

CEO incentive plans and corporate liquidation policy

To investigate CEOs' incentives to liquidate their firms, we examine the effects of insider ownership and compensation in stock options on 30 voluntary liquidation decisions by industrial firms in the period 1975–1986. We find that liquidation decisions are influenced by CEO incentive plans and increase shareholder value. Firms with more outside board members, smaller market-to-book ratios, and attempts by outsiders to gain control are more likely to be liquidated. Although few top executives of liquidating firms subsequently take comparable jobs, at least 41% of CEOs who downsize are made better off by liquidation.