Trading Dates Research Articles

Execution Costs and Efficient Execution Frontiers

Single period risks acceptable to the market at zero cost are modeled by a convex set of random variables leading to bid and ask prices that are trade size dependent. The theory of nonlinear expectations is employed to construct dynamically consistent sequences of bid and ask unit size prices that are size and trade date contingent. We then study the optimal design of spot and forward trading to minimize execution costs. Finally we illustrate the construction of a two period execution cost frontier trading a decrease in execution costs for additional exposure to price risk.

Admissible Strategies in Semimartingale Portfolio Selection

The choice of admissible trading strategies in mathematical modeling of financial markets is a delicate issue, going back to Harrison and Kreps [J. Econom. Theory, 20 (1979), pp. 381–408]. In the context of optimal portfolio selection with expected utility preferences this question has been the focus of considerable attention over the last 20 years. We propose a novel notion of admissibility that has many pleasant features—admissibility is characterized purely under the objective measure P; each admissible strategy can be approximated by simple strategies using a finite number of trading dates; the wealth of any admissible strategy is a supermartingale under all pricing measures; local boundedness of the price process is not required; neither strict monotonicity, strict concavity, nor differentiability of the utility function is necessary; the definition encompasses both the classical mean-variance preferences and the monotone expected utility. For utility functions finite on $\mathbb{R}$, our class represents a minimal set containing simple strategies which also contains the optimizer, under conditions that are milder than the celebrated reasonable asymptotic elasticity condition on the utility function.

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 Trade Execution and Absence of Price Manipulations in Limit Order Book Models

We continue the analysis of optimal execution strategies in the model for a limit order book with nonlinear price impact and exponential resilience that was considered in Alfonsi, Schied, and Fruth (2009). We now allow for non-homogeneous resilience rates and arbitrary trading dates and consider the extended problem of optimizing jointly over trading dates and sizes. Our main results show that, under general conditions on the shape function of the limit order book, placing the deterministic trade sizes identified in Alfonsi, Schied, and Fruth (2009) at trading dates that are homogeneously spaced is optimal also within the large class of adaptive strategies with arbitrary trading dates. Perhaps even more importantly, our analysis yields as a corollary that our model does not admit price manipulation strategies in the sense of Huberman and Stanzl (2004). This latter result contrasts the recent findings of Gatheral (2008), where, in a related but different model, exponential resilience was found to give rise to price manipulation strategies when price impact is nonlinear.

Optimal Trade Execution and Absence of Price Manipulations in Limit Order Book Models

We analyze the existence of price manipulation and optimal trade execution strategies in a model for an electronic limit order book with nonlinear price impact and exponential resilience. Our main results show that, under general conditions on the shape function of the limit order book, placing deterministic trade sizes at trading dates that are homogeneously spaced is optimal within a large class of adaptive strategies with arbitrary trading dates. This extends results from our earlier work with A. Fruth. Perhaps even more importantly, our analysis yields as a corollary that our model does not admit price manipulation strategies. This latter result contrasts the recent findings of Gatheral [Quant. Finance, to appear], where, in a related but different model, exponential resilience was found to give rise to price manipulation strategies when price impact is nonlinear.

Measuring the error of dynamic hedging: a Laplace transform approach

Using the Laplace transform approach, we compute the expected value and the variance of the error of a hedging strategy for a contingent claim when trading in discrete time. The method applies to a fairly general class of models, including Black-Scholes, Merton’s jump-diffusion and Normal Inverse Gaussian, and to several interesting strategies, as the Black-Scholes delta, the Wilmott’s improveddelta and the local optimal one. With this approach, also transaction costs may be treated. The results obtained are not asymptotical approximations but exact and efficient formulas, valid for any number of trading dates. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.

Martingales and arbitrage: a new look

This paper addresses the equivalence between the absence of arbitrage and the existence of equivalent martingale measures. The equivalence will be established under quite weak assumptions since there are no conditions on the set of trading dates (it may be finite or countable, with bounded or unbounded horizon, etc.) or on the trajectories of the price process (for instance, they do not have to be right-continuous).

Diversion et création d’échanges commerciaux dans le cadre du système canadien de préférences tarifaires

This paper explores in quantitative terms the potential effects on trade flows as a result of Canadian tariff preferences in favor of the developing countries instituted in 1974. The paper develops a model of trade creation and trade diversion due to preferences based on imperfect substitution, within each product category, between preference-granting, preference-receiving and non-preferred countries. This model depart from the usual assumption of the customs union theory that countries trade in perfect substitutes. The model is then applied to the 1978 trade date under BTN chapters 25 - 99 on a 4-digit classification. One major conclusion of the paper is that the assumption of perfect substitution tends to overstate the magnitude of trade creation and trade diversion, while the method based on less than perfect substitutability seems to offer more realistic estimates of the actual impact of trade preferences.

The Tracking Error Rate of the Delta-Gamma Hedging Strategy

We analyse the convergence rate of the quadratic tracking error, when a Delta-Gamma hedging strategy is used at N discrete times. The fractional regularity of the payoff function plays a crucial role in the choice of the trading dates, in order to achieve optimal rates of convergence.

Markowitz principles for multi-period portfolio selection problems with moments of any order

The multi-period portfolio selection problem is formulated as a Markowitz mean–variance optimization problem in terms of time-varying means, covariances and higher-order and intertemporal moments of the asset prices. The crux lies in expressing the number of shares of any particular asset to be transacted on any future trading date, which is a non-anticipative process, as a polynomial of the changes in the discounted prices of all the risky assets. This results in the expected return of the portfolio being dependent on not only the means of the asset prices, but also the higher-order and intertemporal moments, and its variance being dependent on not only the second-order moments, but also the higher-order and intertemporal moments. As illustrations, we study the portfolio selection problems including the discrete version of the Merton problem. It is shown numerically that the efficient frontier obtained from Markowitz's discrete multi-period formulation coincides with that from Merton's continuous-time formulation when the number of rebalancing periods is ‘large’. The effects of dynamic trading, in particular volatility pumping, in comparison with a static single-period model are measured by a non-dimensional number, Dyn( P ) ( P , number of trading periods), which quantifies the relative gain due to dynamic trading. It is sufficient to rebalance the portfolio a few times in order to get more than 95% of the gain due to continuous trading.

Valuation of Bond Illiquidity

In this article, the authors present an easily applicable option-theoretical approach to quantifying liquidity spreads of bonds. Following Longsta [1995], they describe the value of liquidity as that of exotic options. After valuing these lookback options in a framework with interest rate uncertainty, this approach yields liquidity spreads for bonds that cannot be traded continuously. The liquidity spreads show plausible properties: they are humped-shaped functions of the maturity and increase with the interest rate volatility. Liquidity spreads depend on the distribution of possible trading dates but are independent of the short rate. Regarding German Jumbo Pfandbrief market data, they find several parallels between theoretical and empirical liquidity spreads, while credit risk has nearly no explanatory power. <b>TOPICS:</b>Legal and regulatory issues for structured finance, options, statistical methods

The Impact of Increased Accounting Disclosure on Information Asymmetry: A Case of Implementing New Auditing Standards in Emerging Markets

In this paper, I investigate the association between increased accounting disclosures and bid-ask spreads in an emerging market (China). I hypothesize that the implementation of new auditing standards in emerging markets would result in increased disclosures and a subsequent reduction in information asymmetry. I report the following primary findings. First, I find that adverse selection component accounts for about 37% of the total relative spread, indicating that information asymmetry cost is substantial in the emerging market. Second, after controlling for various firm characteristics and other market liquidity variables, I find in the cross-sectional analysis that Chinese companies experienced significant reduction in bid-ask spread subsequent to their adoption of new auditing standards. The sensitivity test shows that these results remain significant for the first set of auditing when the simultaneous effects of disclosure on trading volume and price volatility is considered. Third, after controlling for the concurrent effects of trading volume and price volatility, time-series intervention analyses show that the reductions in bid-ask spreads were significant and permanent. A sensitivity test of dummy events introduced on the first trading date of the fourth quarter of each year yields substantially different results, indicating that the significant downward interventions in bid-ask spreads are not driven by any systematic changes in the market microstructure. In addition, I find that the B-share market, where international auditing standards had been applied, experienced significantly less changes in the bid-ask spreads than A-share market. The results have implications for the standard-setters and regulators in emerging markets.

Voyage of discoveries [transporting LNG

As more and more nations switch to cleaner fuels in a bid to hit Kyoto commitments, transporters of liquefied natural gas (LNG) are reaping the benefits. Natural gas is supplied to around 40 reception terminals in energy consuming countries. International LNG trade dates back to 1964, and, since then, more than 80,000 LNG carrier voyages have taken place, covering more than 100 million miles, without major accidents or safety problems. While this sounds impressive, it is the recent onslaught of technology development in LNG carriers that has really turned heads. While the demand for cleaner fuels has spurred on the transportation of liquefied natural gas, it may also be accelerating the development of new, exciting tanker technologies. The article discusses developments such as the successful use of dual-fuel engines (diesel engines designed to use gas fuel), the surge in diesel-electric carriers, on-board liquefaction and the increasing use of electronic control of marine engines.

Adviser “client notice and consent” for principal trades and the impact of “real‐time” reporting

Broker/dealers and investment managers that trade municipal securities on behalf of their clients are preparing for the shift from “end‐of‐the‐day batch” trade reporting to “real‐time” transaction reporting. In January 2005, the Municipal Securities Rulemaking Board (“MSRB”) will be initiating its Real‐time Transaction Reporting System (the “RTRS”). Amended MSRB Rule G‐14 now requires dealers to report transactions in municipal securities within 15 minutes of the time of trade execution, instead of by midnight on trade date. Rule G‐12(f) was amended to require municipal securities dealers to submit inter‐dealer transactions to the Central Comparison System within the same time frame. Investment advisers that engage in principal transactions with their clients or that are dually‐registered as, or affiliated with, broker/dealers that trade securities as principals on behalf of investment adviser clients generally must comply with the client notice and consent requirements set forth under Section 206(3) of the Investment Advisers Act of 1940 (the “Advisers Act”). In light of the acceleration of the MSRB’s trade reporting requirement, investment advisers should consider the extent to which these new requirements impact their obligation to notify clients of the fact that a principal trade is being processed and to secure each client’s approval prior to the completion of each transaction. At the very least, the implementation of the RTRS should prompt advisers to confirm, in fulfillment of their best execution obligations, that each broker/dealer that is executing their municipal securities trades complies with the new 15‐minute reporting window.

Valuation of Bond Illiquidity: An Option-theoretical Approach

We present an easily applicable option-theoretical approach to quantifying liquidity spreads of bonds. Following Longstaff (1995), we describe the value of liquidity as that of exotic options. After valuing these lookback options in a framework with interest rate uncertainty, this approach yields liquidity spreads for bonds that cannot be traded continuously. The liquidity spreads show plausible properties: they are humped-shaped functions of the maturity and increase with the interest rate volatility. Liquidity spreads depend on the distribution of possible trading dates but are independent of the short rate. Regarding German Jumbo Pfandbrief market data, we find several parallels between theoretical and empirical liquidity spreads.

Local Expected Shortfall-Hedging in Discrete Time *

This paper proposes a self-financing trading strategy that minimizes the expected shortfall locally when hedging a European contingent claim. A positive shortfall occurs if the hedger is not willing to follow a perfect hedging or a superhedging strategy. In contrast to the classical variance criterion, the expected shortfall criterion depends only on undesirable outcomes where the terminal value of the written option exceeds the terminal value of the hedge portfolio. Searching a strategy which minimizes the expected shortfall is equivalent to the iterative solution of linear programs whose number increases exponentially with respect to the number of trading dates. Therefore, we partition this complex overall problem into several one-period problems and minimize the expected shortfall only locally, i.e., only over the next trading period. This approximation is quite accurate and the number of linear programs to be solved increases only linearly with respect to the number of trading dates.

A comparison of two data mining techniques to predict abnormal stock market returns

Two data mining techniques were compared for their ability to improve the prediction of abnormal returns using insider stock trading data. The two were neural networks (NN) and Multivariate Adaptive Regressive Splines (MARS). In the comparison, both analyzed abnormal stock market returns from the same 343 companies over the identical 4\frac{1}{2} year period (1/93-6/97). The major findings were: 1) both NN and MARS generally identified the same industries that had the most predictive abnormal stock returns 2) both found that predictions further in the future (12 and 9 months ahead) were more accurate than predictions closer to the trading date (6 and 3 months ahead) 3) both obtained better predictive accuracy using four - rather than two - months of back aggregated stock data 4) NN identified a substantially greater percentage of stocks in the group with the highest explained variance than did MARS 5) data from small and midsize companies led to higher predictive accuracy than data from large size (S&P 500) companies using NN, but not MARS. The findings illustrate that the very complex interaction between insider trading data and abnormal stock returns can be systematically analyzed using non-linear techniques. Of the two assessed, NN led to comparatively more accurate predictions than did MARS.

途上国産一次産品のアンフェア・トレードの分析枠組

Based on the recognition that the current dominant trade never alleviates the poverty of small producers in developing countries, fair trade (FT) which intends to support producers has been developed.Though some recent studies have gone into a discussion of methods to evaluate FT by the absolute criteria of ‘fairness’, this study attempts to relatively evaluate whether or not FT can improve ‘unfairness’ of the current dominant trade, which will be clarified by this paper.As far as primary commodities are concerned, theoretical studies on the ‘unfairness’ of the trade date from the theory of the North-South problem in the 1960s. This paper is written with the aim of advancing a framework for analysis of unfair trade of primary commodities produced in developing countries by adoption of various theories such as the North-South problem, the World-System, the Food-System and the pricing mechanism for agricultural products. What is more, a part of results of the case study (Tanzanian coffee) from within the framework and an evaluation example of FT will be shown.

Generalized Markowitz mean–variance principles for multi–period portfolio–selection problems

The multi–period portfolio–selection problem is formulated as a Markowitz mean–variance optimization problem. It is shown that the single–period Markowitz quadratic programming algorithm can be used to solve the multi–period asset–allocation problem with suitable modifications in the covariance and linear constraint matrices. It is assumed that the number of shares invested in risky assets is deterministic and the amount of money invested in the risk–free asset is random at future trading dates when short sales on assets are allowed. The general covariance matrix in the multi–period setup contains intertemporal correlations between assets, in addition to correlations between assets at all trading dates. Analytical solutions for the optimal trading strategy, which is linear in the risk–aversion parameter, are obtained. The efficient frontier is a straight line in the expected return/standard deviation of the portfolio space. When the dynamics of the risky assets follow geometric Brownian motion, it is shown that the time–zero allocations to the risky assets coincide with those obtained by Merton in the continuous–time framework. When short sales are not allowed on assets, the values of the portfolio at future trading dates may not be conserved. In the modified Markowitz mean–variance formulation, the value of the portfolio at future trading dates is conserved in the expected sense, and the optimal trading strategy is selected so that the deviation is minimized in the least–square sense. The efficient frontier is a parabola in the expected return/total variance space when short–sales are allowed and when the portfolio consists of risky assets only. When short sales are not allowed, it is shown that finding the optimal trading strategy is equivalent to solving the single–period Markowitz quadratic programming problem, with suitable modifications in the covariance and linear constraint matrices. By solving the Karush–Kuhn–Tucker conditions, analytical solutions are obtained for a two–period two–assets case, and the Markowitz mean–variance principle is illustrated by solving a test problem numerically using the revised simplex method.

Projective system approach to the martingale characterization of the absence of arbitrage

The equivalence between the absence of arbitrage and the existence of an equivalent martingale measure fails when an infinite number of trading dates is considered. By enlarging the set of states of nature and the probability measure through a projective system of perfect measure spaces, we characterize the absence of arbitrage when the time set is countable.