Arbitrage and deflators in illiquid markets

This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with transaction costs or bid–ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. In the presence of nonlinearities, the classical notion of arbitrage turns out to have two equally meaningful generalizations, a marginal and a scalable one. We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints.     

Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model

The paper develops a general discrete-time framework for asset pricing and hedging in financial markets with proportional transaction costs and trading constraints. The framework is suggested by analogies between dynamic models of financial markets and (stochastic versions of) the von Neumann–Gale model of economic growth. The main results are hedging criteria stated in terms of “dual variables” – consistent prices and consistent discount factors. It is shown how these results can be applied to specialized models involving transaction costs and portfolio restrictions.     

A simulation analysis of the microstructure of an order driven financial market with multiple securities and portfolio choices

In this paper we propose an artificial market where multiple risky assets are exchanged. Agents are constrained by the availability of resources and trade to adjust their portfolio according to an exogenously given target portfolio. We model the trading mechanism as a continuous auction order-driven market. Agents are heterogeneous in terms of desired target portfolio allocations, but they are homogeneous in terms of trading strategies. We investigate the role played by the trading mechanism in affecting the dynamics of prices, trading volume and volatility. We show that the institutional setting of a double auction market is sufficient to generate a non-normal distribution of price changes and temporal patterns that resemble those observed in real markets. Moreover, we highlight the role played by the interaction between individual wealth constraints and the market frictions associated with a double auction system to determine the negative asymmetry of the stock returns distribution.     

市场摩擦对特质风险溢价的影响效应——基于A股主板市场的实证分析

与国外发达市场相比,我国A股主板市场的市场摩擦因素对市场微观结构和资产定价的影响更大。在防范和化解系统性风险的过程中,进一步分析市场摩擦如何作用于特质风险定价效应的问题具有重要的理论和现实意义。本文通过采用多维市场摩擦指标来代理信息不对称、交易成本、买卖限制、卖空限制、风险对冲和外部冲击,检验中国股市特质风险和预期收益率的关系,并判断出市场摩擦因素间的差异性影响机制。回归发现,市场摩擦和特质风险因子(特质波动率和特质偏度)都具有定价效应。各维度市场摩擦因素降低了股票流动性,进而增强了特质波动率的负向定价效应,部分解释了“特质波动率之谜”,但市场摩擦对特质偏度因子溢价的影响较为微弱。同时,基于特质波动率和特质偏度因子的投资策略能够产生超越CAPM、三因子和五因子模型的绝对收益,并印证了市场摩擦对特质风险因子绝对收益的影响作用。     

Are Momentum Profits Robust to Trading Costs?

We test whether momentum strategies remain profitable after considering market frictions induced by trading. Intraday data are used to estimate alternative measures of proportional and non-proportional (price impact) trading costs. The price impact models imply that abnormal returns to portfolio strategies decline with portfolio size. We calculate break-even fund sizes that lead to zero abnormal returns. In addition to equal- and value-weighted momentum strategies, we derive a liquidity-weighted strategy designed to reduce the cost of trades. Equal-weighted strategies perform the best before trading costs and the worst after trading costs. Liquidity-weighted and hybrid liquidity/value-weighted strategies have the largest break-even fund sizes: $5 billion or more (relative to December 1999 market capitalization) may be invested in these momentum strategies before the apparent profit opportunities vanish.     

Hedging Strategies of Financial Intermediaries: Pricing Options with a Bid-Ask Spread

This paper uses a model similar to the Boyle-Vorst and Ritchken-Kuo arbitrage-free models for the valuation of options with transactions costs to determine the maximum price to be charged by the financial intermediary writing an option in a non-auction market. Earlier models are extended by recognizing that, in the presence of transactions costs, the price-taking intermediary devising a hedging portfolio faces a tradeoff: to choose a short trading interval with small hedging errors and high transactions costs, or a long trading interval with large hedging errors and low transactions costs. The model presented here also recognizes that when transactions costs induce less frequent portfolio adjustments, investors are faced with a multinomial distribution of asset returns rather than a binomial one. The price upper bound is determined by selecting the trading frequency that will equalize the marginal gain from decreasing hedging errors and the marginal cost of transactions.     

Quadratic minimization with portfolio and intertemporal wealth constraints

We address a problem of stochastic optimal control motivated by portfolio optimization in mathematical finance, the goal of which is to minimize the expected value of a general quadratic loss function of the wealth at close of trade when there is a specified convex constraint on the portfolio, together with a specified almost-sure lower-bound on intertemporal wealth over the full trading interval. A precursor to the present work, by Heunis (Ann Financ 11:243–282, 2015), addressed the simpler problem of minimizing a general quadratic loss function with a convex portfolio constraint and a stipulated almost-sure lower-bound on the wealth only at close of trade. In the parlance of optimal control the problem that we shall address here exhibits the combination of a control constraint (i.e. the portfolio constraint) together with an almost-sure intertemporal state constraint (on the wealth over the full trading interval). Optimal control problems with this combination of constraints are well known to be quite challenging even in the deterministic case, and of course become still more so when one deals with these same constraints in a stochastic setting. We nevertheless find that an ingenious variational approach of Rockafellar (Conjugate duality and optimization, CBMS-NSF series no. 16, SIAM, 1974), which played a key role in the precursor work noted above, is fully equal to the challenges posed by this problem, and leads naturally to an appropriate vector space of dual variables, together with a dual functional on the space of dual variables, such that the dual problem of maximizing the dual functional is guaranteed to have a solution (or Lagrange multiplier) when the problem constraints satisfy a simple and natural Slater condition. We then establish necessary and sufficient conditions for the optimality of a candidate wealth process in terms of the Lagrange multiplier, and use these conditions to construct an optimal portfolio.     

Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints

We consider the dynamic portfolio choice problem in a jump-diffusion model, where an investor may face constraints on her portfolio weights: for instance, no-short-selling constraints. It is a daunting task to use standard numerical methods to solve a constrained portfolio choice problem, especially when there is a large number of state variables. By suitably embedding the constrained problem in an appropriate family of unconstrained ones, we provide some equivalent optimality conditions for the indirect value function and optimal portfolio weights. These results simplify and help to solve the constrained optimal portfolio choice problem in jump-diffusion models. Finally, we apply our theoretical results to several examples, to examine the impact of no-short-selling and/or no-borrowing constraints on the performance of optimal portfolio strategies.     

Trading costs and price discovery

The price discovery roles of a set of related markets or securities have been investigated in many different settings where trading costs effect is often commingled with other trading arrangement factors. In Hong Kong, regular futures and mini futures contracts as well as their underlying spot asset are all traded on a same electronic trading platform. The trading arrangements thus provide us with a unique setting where we can isolate the impacts of transaction costs on price discovery. Using Hasbrouck’s (J Finance 50:1175–1199, 1995) information share approach, it is found that in Hong Kong, the regular futures contracts market plays a dominant role in price discovery while the mini futures and cash index markets play minor roles. The results in this paper provide an unequivocal support to the trading costs hypothesis.     

The Effect of Sequential Information Arrival on Asset Prices: An Experimental Study

A complete understanding of security markets requires a simultaneous explanation of price behavior, trading volume, portfolio composition (ie., asset allocation), and bid-ask spreads. In this paper, these variables are observed in a controlled setting—a computerized double auction market, similar to NASDAQ. Our laboratory allows experimental control of information arrival—whether simultaneously or sequentially received, and whether homogeneous or heterogeneous. We compare the price, volume, and share allocations of three market equilibrium models: telepathic rational expectations, which assumes that traders can read each others minds (strong-form market efficiency); ordinary rational expectations, which assumes traders can use (some) market price information, (a type of semi-strong form efficiency); and private information, where traders use no market information. We conclude 1) that stronger-form market models predict equilibrium prices better than weaker-form models, 2) that there were fewer misallocation forecasts in simultaneous information arrival (SIM) environments, 3) that trading volume was significantly higher in SIM environments, 4) and that bid-ask spreads widen significantly when traders are exposed to price uncertainty resulting from information heterogeneity.     

Efficient trading strategies in the presence of market frictions

We provide a price characterization of efficient contingentclaims - that is, chosen by at least a rational agent - in multiperiodeconomies with market frictions. Frictions include market incompleteness,transaction costs, short-selling, and borrowing costs. We characterizethe inefficiency cost of a trading strategy - its required investmentminus the largest amount necessary to obtain the same utilitylevel - and we propose a measure of portfolio performance. Weshow that arbitrage bounds cannot be tightened based on efficiencywithout restricting preferences or endowments. We observe commoninvestment strategies becoming inefficient with market frictionsand others rationalized by them.     

Extreme spillovers of VIX fear index to international equity markets

This study analyzes the impact of VIX spillovers on market activities during extreme market conditions in 42 international equity markets from 1998 to 2014. Specifically, tail cross-dependence suggests that a small change in VIX significantly influences global market activities during extreme market conditions. The impact of VIX is asymmetric, which is more pronounced in bearish, highly volatile, and low trading volume markets. Moreover, VIX spillovers exhibit a stronger impact on returns in developed markets and on volatility in emerging markets. In terms of geographical location, the impact of VIX spillovers is more pronounced on returns in Europe and on volatility in Latin America. These findings indicate that international investors can potentially benefit from international portfolio diversification and can serve as useful guidance to policymakers in designing appropriate policies.

     

The effectiveness of position limits: Evidence from the foreign exchange futures markets

This study considers the effects of the relative size of hedger and speculator open interests and the potential impact of implementing position limits on the price discovery process in both JPY–USD and EUR–USD futures markets. Hedging trading exerts a negative impact, regardless of its size, on price discovery in futures markets. Hedgers are less likely to be information motivated, so their trading uniformly delays the price discovery process. However, there is a positive and nonlinear impact of speculators’ trade size on price discovery, the contribution of which depends on the relative size of the speculative open interest. Contrary to conventional wisdom among regulators, speculative trading does not harm the market in terms of market efficiency; as long as the percentage of speculators’ open interest is below an endogenously determined threshold (approximately 20% for EUR–USD and 16.3% for JPY–USD), speculative trading even improves futures market efficiency.     

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.     

Heterogeneous real-time trading strategies in the foreign exchange market

The foreign exchange (FX) market is worldwide, but the dealers differ in their geographical locations (time zones), working hours, time horizons, home currencies, access to information,transaction costs, and other institutional constraints. The variety of time horizones is large: from intra-day dealers, who close their positions every evening, to long-term investors and central banks. Depending on the constraints, the different market participats need different strategies to reach their goal, which is usually maximizing the profit, or rather a utility function including risk. Different intra-day trading strategies can be studied only if high-density data are available. Oslen & Associates (O & A) has collected and analysed large amounts of FX quotes by market makers around the clock (up to 5000 non-equally spaced prices per day for the German mark against US$). Based on these data, a set of real-time intra-day trading models has been developed. These models give explicit trading recommendations under realistic constraints. They are allowed to trade only during the opening hours of a market, depending on the time zone and local holidays. The models have been running real-time for more than three years, thus leading to an ex ante test. The test results, obtained with a risk-sensitive performance measure, are presented. All these trading models are profitable, but they differ in their risk behaviour and dealing frequency. If a certain profitable intra-day algorithm is tested with different working hours, its success can considerably change. A systematic study shows that the best choice of working hours is usually when the most important markets for the particular FX rate are active. All the results demonstrate that the assumption of a homogeneous 24-hour FX market with identical dealers, following an identical ‘rational expectation’, is far from reality. To explain the market dynamics, a heterogeneous model of the market with different types of dealers is more appropriate.     

Trading gap in holidays and price transmission: Evidence from cross-listed stocks on the A-share and H-share markets

Chinese public holidays of differing durations celebrated in mainland China and Hong Kong provide a unique trading gap when the A-share markets are closed but the H-share market is not. In this study, we examine how these non-overlapping trading gaps caused by holidays affect price transmission between cross-listed stocks in the A-share and H-share markets. We find that the price movements of H-shares during trading gaps are positively associated with post-holiday drifts in the A-share markets. This positive association is stronger when the length of non-overlapping holidays is longer, and when firms have a weaker connection to Hong Kong market. Moreover, our evidence reveals that investor distraction rather than sentiment during holiday periods may be the reason for this positive association. Finally, our results show that a portfolio trading strategy based on our findings can be profitable, indicating the economic magnitude of our findings.     

Price discovery in the U.S. stock and stock options markets: A portfolio approach

Option prices vary with not only the underlying asset price, but also volatilities and higher moments. In this paper, we use a portfolio of options to seclude the value change of the portfolio from the impact of volatility and higher moments. We apply this portfolio approach to the price discovery analysis in the U.S. stock and stock options markets. We find that the price discovery on the directional movement of the stock price mainly occurs in the stock market, more so now than before as an increasing proportion of options market makers adopt automated quoting algorithms. Nevertheless, the options market becomes more informative during periods of significant options trading activities. The informativeness of the options quotes increases further when the options trading activity generates net sell or buy pressure on the underlying stock price, even more so when the pressure is consistent with deviations between the stock and the options market quotes. JEL Classification C52, G10, G13, G14     

Arbitrage and Viability in Insurance Markets

Insurance markets are subject to transaction costs and constraints on portfolio holdings. Therefore, unlike the frictionless asset markets case, viability is not equivalent to absence of arbitrage possibilities. We use the concept of unbounded arbitrage to characterize viable prices on a complete and an incomplete insurance market. In the complete market, there is an insurance contract for every possible event. In the incomplete market, risk can be insured through proportional and excess of loss like insurance contracts. We show how the the structure of viable prices is affected by the portfolio constraints, the transaction costs, and the structure of marketed contracts.     

On derivatives with illiquid underlying and market manipulation

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework to construct optimal trading strategies under market impact in a multi-player framework by introducing strategic interactions into the model of Almgren [Appl. Math. Finance, 2003, 10(1), 1–18]. Specifically, we consider a financial market model with several strategically interacting players who hold European contingent claims and whose trading decisions have an impact on the price evolution of the underlying. We establish the existence and uniqueness of equilibrium results for risk-neutral and CARA investors and show that the equilibrium dynamics can be characterized in terms of a coupled system of possibly nonlinear PDEs. For the linear cost function used by Almgren, we obtain a (semi) closed-form solution. Analysing this solution, we show how market manipulation can be reduced.