A parallel genetic algorithm for optimization of trading strategies

An approach to optimization of trading strategies (algorithms) is described based on indicators of financial markets and on evolutionary computations. A parallel genetic algorithm is presented for searching optimal parameters of trading strategies aimed at profit maximization.     

Optimal execution with weighted impact functions: a quadratic programming approach

In this paper, we develop optimal trading strategies for a risk averse investor by minimizing the expected cost and the risk of execution. Here we consider a law of motion for price which uses a convex combination of temporary and permanent market impact. In the special case of unconstrained problem for a risk neutral investor, we obtain a closed form solution for optimal trading strategies by using dynamic programming. For a general problem, we use a quadratic programming approach to get approximate dynamic optimal trading strategies. Further, numerical examples of optimal execution strategies are provided for illustration purposes.     

A sample-path approach to optimal position liquidation

We consider the problem of optimal position liquidation where the expected cash flow stream due to transactions is maximized in the presence of temporary or permanent market impact. A stochastic programming approach is used to construct trading strategies that differentiate decisions with respect to the observed market conditions, and can accommodate various types of trading constraints. As a scenario model, we use a collection of sample paths representing possible future realizations of state variable processes (price, trading volume etc.), and employ a heuristical technique of sample-path grouping, which can be viewed as a generalization of the standard nonanticipativity constraints.     

基金投资行为与投资绩效实证研究

本文主要研究2000年末到2004年6月国内基金投资行为与投资绩效。我们将基金交易行为分为:新进入、完全退出和对仓位进行调整3类,并分别研究其投资行为。研究结果显示,我国基金交易频率很高,近90%的基金采用动量投资策略,基金新进入股票时动量效应最强。价值型基金更易采取动量投资策略,高动量组收益高于低动量组收益。     

A model for optimal execution of atomic orders

Atomic Orders are the basic elements of any algorithm for automated trading in electronic stock exchanges. The main concern in their execution is achieving the most efficient price. We propose two optimal strategies for the execution of atomic orders based on minimization of impact and volatility costs. The first considered strategy is based on a relatively simple nonlinear optimization model while the second allows re-optimization at some time point within a given execution time. In both cases a combination of market and limit orders is used. The key innovation in our approach is the introduction of a Fill Probability function which allows a combination of market and limit orders in the two optimization models we are discussing in this paper. Under certain conditions the objective functions of both considered problems are convex and therefore standard optimization tools can be applied. The efficiency of the resulting strategies is tested against two benchmarks representing common market practice on a representative sample of real trading data.     

CO2 emissions trading planning in combined heat and power production via multi-period stochastic optimization

The EU emissions trading scheme (ETS) taking effect in 2005 covers CO₂ emissions from specific large-scale industrial activities and combustion installations. A large number of existing and potential future combined heat and power (CHP) installations are subject to ETS and targeted for emissions reduction. CHP production is an important technology for efficient and clean provision of energy because of its superior carbon efficiency. The proper planning of emissions trading can help its potential into full play, making it become a true “winning technology” under ETS. Fuel mix or fuel switch will be the reasonable choices for fossil fuel based CHP producers to achieve their emissions targets at the lowest possible cost. In this paper we formulate CO₂ emissions trading planning of a CHP producer as a multi-period stochastic optimization problem and propose a stochastic simulation and coordination approach for considering the risk attitude of the producer, penalty for excessive emissions, and the confidence interval for emission estimates. In test runs with a realistic CHP production model, the proposed solution approach demonstrates good trading efficiency in terms of profit-to-turnover ratio. Considering the confidence interval for emission estimates can help the producer to reduce the transaction costs in emissions trading. Comparisons between fuel switch and fuel mix strategies show that fuel mix can provide good tradeoff between profit-making and emissions reduction.     

Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer

From the point of view of a price-taking hydropower producer participating in the day-ahead power market, market prices are highly uncertain. The present paper provides a model for determining optimal bidding strategies taking this uncertainty into account. In particular, market price scenarios are generated and a stochastic mixed-integer linear programming model that involves both hydropower production and physical trading aspects is developed. The idea is to explore the effects of including uncertainty explicitly into optimization by comparing the stochastic approach to a deterministic approach. The model is illustrated with data from a Norwegian hydropower producer and the Nordic power market at Nord Pool.     

Mean–Variance Optimal Adaptive Execution

Abstract

Electronic trading of equities and other securities makes heavy use of ‘arrival price’ algorithms that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean–variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substantial improvement is possible by using dynamic trading strategies and that the improvement is larger for large initial positions.

We develop a technique for computing optimal dynamic strategies to any desired degree of precision. The asset price process is observed on a discrete tree with an arbitrary number of levels. We introduce a novel dynamic programming technique in which the control variables are not only the shares traded at each time step but also the maximum expected cost for the remainder of the program; the value function is the variance of the remaining program. The resulting adaptive strategies are ‘aggressive-in-the-money’: they accelerate the execution when the price moves in the trader's favor, spending parts of the trading gains to reduce risk.     

Insider Trading in Convergent Markets

Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints.     

基于技术分析指标组合的程序化交易模型研究

程序化交易的兴起对技术分析方法的发展提供了新机遇,利用常见技术分析指标,建立基于指标组合的交易策略,并从统计分析角度讨论了交易策略的理论基础,最后通过实证分析验证了该策略的稳定表现和可观收益,以期为程序化交易模型研究提供新思路.     

Modeling Capital Gains Taxes for Trading Strategies of Infinite Variation

In this article, we show that the payment flow of a linear tax on trading gains from a security with a semimartingale price process can be constructed for all càglàd and adapted trading strategies. It is characterized as the unique continuous extension of the tax payments for elementary strategies w.r.t. the convergence “uniformly in probability.” In this framework, we prove that under quite mild assumptions dividend payoffs have almost surely a negative effect on investor’s after-tax wealth if the riskless interest rate is always positive. In addition, we give an example for tax-efficient strategies for which the tax payment flow can be computed explicitly.     

Derivatives trading for insurers

We investigate optimal strategies for a constant absolute risk aversion (CARA) insurer to manage its business risk through not only equity investment and proportional reinsurance but also trading derivatives of the equity. We obtain the optimal strategies in closed-form and quantify the value of derivatives trading by means of certainty-equivalence. Some numerical examples and sensitivity analysis are presented to illustrate our theoretical results. Our numerical results show that, unlike standard CRRA investors, the gain from trading derivatives to a CARA insurer is small and the insurer needs to expose itself to a relatively large position to fully enjoy the gain.     

Strong asymptotic arbitrage in the large fractional binary market

We study, from the perspective of large financial markets, the asymptotic arbitrage (AA) opportunities in a sequence of binary markets approximating the fractional Black–Scholes model. This approximating sequence was introduced by Sottinen and named fractional binary market. The large financial market under consideration does not satisfy the standard assumptions of the theory of AA. For this reason, we follow a constructive approach to show first that a strong AA (SAA) exists in the frictionless case. Indeed, with the help of an appropriate version of the law of large numbers and a stopping time procedure, we construct a sequence of self-financing trading strategies leading to the desired result. Next, we introduce, in each small market, proportional transaction costs, and we show that a slight modification of the previous trading strategies leads to a SAA when the transaction costs converge fast enough to 0.     

Simplified mean-variance portfolio optimisation

We propose a simplified approach to mean-variance portfolio problems by changing their parametrisation from trading strategies to final positions. This allows us to treat, under a very mild no-arbitrage-type assumption, a whole range of quadratic optimisation problems by simple mathematical tools in a unified and model-independent way. We provide explicit formulas for optimal positions and values, connections between the solutions to the different problems, two-fund separation results, and explicit expressions for indifference values.     

Transaction costs and efficiency of portfolio strategies

Some recent results for frictionless economies show that popular dynamic portfolio strategies such as stop-loss and lock-in are inefficient. I.e for each of these strategies there exists an alternative portfolio strategy that gives the same final payoff distribution at lower initial costs. However, the alternative strategies require considerably more active trading than the simple strategies. The results rely heavily on the assumption of no transaction costs. Under this assumption the initial investment required is a linear function of the prices of the contingent claims that build the final payoff distribution. In this paper we demonstrate that, even for modest levels of transaction costs, the efficient strategies are more costly than the simple strategies, i.e. a strategy that replicates the final payoff distribution of an efficient strategy is excessively costly due to the transaction costs and the heavy trading involved. Since the initial investment is no longer a linear function of the contingent claims, the optimization problems to find the most efficient strategy are complicated combinatorial optimization problems which can only be solved for trees with a small number of steps. In a world without transaction costs, options are redundant instruments, since all payoff distributions can be replicated by trading in stocks and bonds. In the second half of this paper we show that the use of options in a world with transaction costs enables investors to realize final value distributions at lower initial costs than would be possible with trades in stocks an bonds only. Hence, although in theory options do not give rise to other portfolio strategies, they do in a more restrictive setting with transaction costs.     

机构投资者的最优变现策略

在投资、变现等大宗交易过程中,资产交易价格与交易策略密切相关,因此,交易的完成过程需要很高的技巧.文章讨论了机构投资者的最优变现策略问题,假设证券价格服从几何布朗运动,以均值方差效用为目标函数,得到了最优变现策略所满足的二阶微分方程,并由差分法得到其数值解.最后,由参数的敏感性分析知:最优变现策略与瞬时冲击、市场波动率及风险厌恶系数等参数有关,但与永久冲击无关,且最优变现策略对市场波动率和瞬时冲击的变化较敏感.     

基于均线交易系统的非特定时间动态VaR研究

为使交易产生稳定持续的收益, 使用基于一定交易规则的交易系统进行交易成为越来越多的投资者和投资机构使用的方法。如能把VaR引入交易系统,进行风险管理,将具有重要的意义。本文以5-60日均线交易系统为研究对象,建立了非特定时间动态VaR模型。经过检验,验证了模型的准确性。在基于模型进行交易策略优化后,得出了有意义的结果。本文使VaR在非特定时间度量方面实现了应用,研究结果对交易系统的风险控制,具有较大的应用价值。     

Calibrated American option pricing by stochastic linear programming

Abstract

We propose an approach for computing the arbitrage-free interval for the price of an American option in discrete incomplete market models via linear programming. The main idea is built replicating strategies that use both the basic asset and some European derivatives available on the market for trading. This method goes under the name of calibrated option pricing and it has given significant results for European options. Here, we extend the analysis to American options showing that the arbitrage-free interval can be characterized in terms of martingale measures and that it gets significantly reduced with respect to the non-calibrated case.     

A successive SDP-NSDP approach to a robust optimization problem in finance

The robustification of trading strategies is of particular interest in financial market applications. In this paper we robustify a portfolio strategy recently introduced in the literature against model errors in the sense of a worst case design. As it turns out, the resulting optimization problem can be solved by a sequence of linear and nonlinear semidefinite programs (SDP/NSDP), where the nonlinearity is introduced by the parameters of a parabolic differential equation. The nonlinear semidefinite program naturally arises in the computation of the worst case constraint violation which is equivalent to an eigenvalue minimization problem. Further we prove convergence for the iterates generated by the sequential SDP-NSDP approach.     

Option pricing with hedging at fixed trading dates

We introduce trading restrictions in the well known Black-Scholes model and Cox-Ross-Rubinstein model, in the sense that hedging is only allowed at some fixed trading dates. As a consequence, the financial market is incomplete in both modified models. Applying Schweizer's (and Schäl's) variance-optimal criterion for pricing and hedging general claims, we first analyse the dynamic consistency of the strategies which minimize the variance of the total loss due to hedging a given claim. Then we establish some convergence results, when the number of trading dates is either kept fixed or increases to infinity.