Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree

In this paper, we present a natural mathematical framework to model trader behavior as a continuous time discrete event process, and derive stochastic differential equations for aggregate behavior and price dynamics by passing to diffusion limits. In particular, we model extraneous, value, momentum and hedge traders. Through analysis and numerical simulation we explore some of the effects these trading strategies have on price dynamics.     

信息优势、有限关注与知情交易者竞争交易

在具有一个风险资产的两期交易模型中,刻画了两类知情交易者:一个内部交易者和多个市场专家,内部交易者获得更精确的信息,而市场专家是有限关注的,根据投入的关注度评价获得的信息质量。通过求解线性均衡条件下关注度和市场竞争程度对订单流、流动性、期望收益和市场效率等市场微观特征的影响,结果表明:市场专家的交易强度随关注度的增大而增强,而内部交易者的交易强度随关注度的增大而减弱;市场流动性随着关注度的增大而增大;当市场专家数量较少时,市场专家的收益随着关注度的增大而增大,当市场专家数量较多时,市场专家的收益随着关注度的增大先增大然后缓慢降低。     

Does AHP help us make a choice? An experimental evaluation

In this paper, we use experimental economics methods to test how well Analytic Hierarchy Process (AHP) fares as a choice support system in a real decision problem. AHP provides a ranking that we statistically compare with three additional rankings given by the subjects in the experiment: one at the beginning, one after providing AHP with the necessary pair-wise comparisons and one after learning the ranking provided by AHP. While the rankings vary widely across subjects, we observe that for each individual all four rankings are similar. Hence, subjects are consistent and AHP is, for the most part, able to replicate their rankings. Furthermore, while the rankings are similar, we do find that the AHP ranking helps the decision makers reformulate their choices by taking into account suggestions made by AHP.     

基于做市商过度自信行为的市场均衡分析

针对做市商的过度自信行为对金融市场的影响,通过建立的数学模型对市场均衡时的价格波动、市场交易量、价格质量、市场深度以及市场参与者的利润做了相应的分析。结果表明:做市商的过度自信行为对市场的影响不同于以往研究中过度自信的信息交易者。在市场均衡时,做市商的过度自信行为使得市场交易量增大、市场深度增大、价格质量改善,同时价格波动降低,即做市商的过度自信行为提高了市场的流动性、稳定性与有效性。另外,市场中的信息交易者与噪音交易者都能从做市商的过度自信行为中获利,但同时过度自信行为会损害做市商的利益,影响其在市场中的地位。较小程度的过度自信不会使做市商退出市场,其对市场的影响得以维持;但当这种过度自信达到一定程度后,做市商就会退出市场。     

Mutual funds performance appraisal using stochastic multicriteria acceptability analysis

Mutual fund investors are concerned with the selection of the best fund in terms of performance among the set of alternative funds. This paper proposes an innovative mutual funds performance evaluation measure in the context of multicriteria decision making. We implement a multicriteria methodology using stochastic multicriteria acceptability analysis, on Greek domestic equity funds for the period 2000-2009. Combining a unique dataset of risk-adjusted returns such as Carhart’s alpha with funds’ cost variables, we obtain a multicriteria performance evaluation and ranking of the mutual funds, by means of an additive value function model. The main conclusion is that among employed variables, the sophisticated Carhart’s alpha plays the most important role in determining fund rankings. On the other hand, funds’ rankings are affected only marginally by operational attributes. We believe that our results could have serious implications either in terms of a fund rating system or for constructing optimal combinations of portfolios.     

Eliciting and mapping qualitative preferences to numeric rankings in group decision making

Group work is becoming the norm in organizations. From strategy planning committees to quality management teams, organizational members are collaborating on problem solving. One area of team support that is often desired is the scoring and ranking of decision alternatives on qualitative/subjective domains, and the aggregation of individual preferences into group preferences. In this paper we present a new conceptual approach to qualitative preference elicitation and aggregation. This approach is based on well established decision analysis techniques. It significantly advances the state of the art of group decision making by addressing four common limitations: (1) the inability to deal with vagueness of human decision makers in articulating preferences; (2) difficulties in mapping qualitative evaluation to numeric estimates; (3) problems in aggregating individual preferences into meaningful group preference; and (4) the lack of simple user friendly techniques for dealing with a large number of decision alternatives. Our approach is easy to implement in stand alone personal computers and groupware. We illustrate this with a real-world problem.     

证券市场正反馈交易与收益自相关

正反馈交易是非理性投资者的一种交易策略,正反馈交易者通常依据证券前一期收益的高低决定其当期买卖行为。在正反馈交易存在的情况下,证券市场收益会表现出不同于有效市场假设所假定的特征,使证券市场表现出超常的波动性。本文建立了一个正反馈交易者和理性交易者参与的市场模型,分析了该市场中证券收益时间序列呈现出的正自相关性。     

基于交易量的最优指令提交策略模型

构建了两个价位的指令驱动市场模型.交易者根据自己的估值选择提交限价指令或市价指令.假设交易量作为交易者的禀赋,可在一个连续区间上任意取值,从而提出限价收益曲线的概念,并结合该曲线给出基于交易量的最优指令提交策略时.最优指令提交策略不仅依赖于交易者的私人估值、市场深度和价差,同时依赖于交易者所持交易量.模型揭示以下几点微观特征:1.私人估值偏离证券基本价值较大的交易者倾向于提交市价订单,而私人估值接近证券基本价值的交易者倾向于提交限价订单;2.当市场深度较小时,交易者倾向于限价单;而市场深度较大时,交易者倾向于提交市价单;3.随价差的增加,交易者更倾向于提交限价订单.     

A limit order book model for latency arbitrage

We consider a single security market based on a limit order book and two investors, with different speeds of trade execution. If the fast investor can preempt the slower investor, we show that this allows the fast trader to obtain risk free profits, but that these profits cannot be scaled. We derive the fast trader??s optimal behaviour when she has only distributional knowledge of the slow trader??s actions, with few restrictions on the possible prior distributions. We also consider the slower trader??s response to the presence of a fast trader in a market, and the effects of the introduction of a ??Tobin tax?? on financial transactions. We show that such a tax can lead to the elimination of profits from preemptive strategies. Consequently, a Tobin tax can both increase market efficiency and attract traders to a market.     

Rationality,emotion and preference change Drama-theoretic models of choice

Traditional models of “rational choice”, such as those based on Game Theory and Decision Theory tend to work on the assumption that aims/preferences can be specified prior to the decision process, and remain fixed during it. Other approaches, by contrast, stress the dynamics of preference change and problem re-formulation. In the context of conflict and cooperation analysis, we have recently attempted to bridge these two traditions by introducing drama-theoretic models. This paper reviews some theories about preference change from this standpoint, some concerning individual preferences (including the role of emotions), others introducing group and organisational dimensions. We suggest that it possible to build dynamic models of choice which use the paradoxes of rational choice to link and systematise research both on the strategic role of emotions and on the strategic use of argumentation.     

Robust multi-criteria ranking with additive value models and holistic pair-wise preference statements

We consider a problem of ranking alternatives based on their deterministic performance evaluations on multiple criteria. We apply additive value theory and assume the Decision Maker’s (DM) preferences to be representable with general additive monotone value functions. The DM provides indirect preference information in form of pair-wise comparisons of reference alternatives, and we use this to derive the set of compatible value functions. Then, this set is analyzed to describe (1) the possible and necessary preference relations, (2) probabilities of the possible relations, (3) ranges of ranks the alternatives may obtain, and (4) the distributions of these ranks. Our work combines previous results from Robust Ordinal Regression, Extreme Ranking Analysis and Stochastic Multicriteria Acceptability Analysis under a unified decision support framework. We show how the four different results complement each other, discuss extensions of the main proposal, and demonstrate practical use of the approach by considering a problem of ranking 20 European countries in terms of 4 criteria reflecting the quality of their universities.     

Learning about preferences in electronic negotiations – A volume-based measurement method

To create an integrative solution in a bargaining problem, negotiators need to have information about each other’s preferences. Empirical negotiation research therefore requires methods to measure the extent to which information about preferences is available during a negotiation. We propose such a method based on Starr’s domain criterion, which was originally developed for sensitivity analysis in decision making. Our method provides indices for the amount of preference information that can be inferred both in negotiations reaching an agreement and negotiations where an agreement was not (yet) reached. To test the external validity of our proposed measures, we conduct an empirical study which shows that the proposed measures exhibit positive relationships to the success of negotiations as well as to the efficiency of outcomes that would be expected according to negotiation theory.     

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.     

A portfolio model for performance assessment: the <Emphasis Type="Italic">Financial Times</Emphasis> MBA ranking

The ranking of MBA programmes by newspapers and magazines is common and usually controversial. This paper discusses the use of the most popular method of making these rankings via a multicriteria model which uses the weighted sum of a number of performance measures to give an overall score on which selection or ranking may be based. The weights are a quantitative model of the preferences of those making the evaluation. Many methods are available to obtain weights from preference statements so that for any set of preferences a number of different weight sets can be found depending on the method used. Cognitive limits lead to inconsistency in preference judgements so that weights may be subject both to uncertainty and to bias. It is proposed that choosing weights to minimize discrimination between alternatives (not weights) guards against unjustified discrimination between alternatives. Applying the method to data collected by the Financial Times shows the effect of varying the level of discrimination between weights and also the effect of using a reduced data set made necessary by the partial publication of information.     

On Method for Uncertain Multiple Attribute Decision Making Problems with Uncertain Multiplicative Preference Information on Alternatives

The uncertain multiple attribute decision making (UMADM) problems are investigated, in which the information about attribute weights is known partly and the attribute values take the form of interval numbers, and the decision maker (DM) has uncertain multiplicative preference information on alternatives. We make the decision information uniform by using a transformation formula, and then establish an objective-programming model. The attribute weights can be determined by solving the developed model. The concept of interval positive ideal point of alternatives (IPIPA) is introduced, and an approach based on IPIPA and projection to ranking alternatives is proposed. The method can avoid comparing and ranking interval numbers, and can reflect both the objective information and the DMs subjective preferences.     

A fuzzy ranking method with range reduction techniques

For ranking alternatives based on pairwise comparisons, current analytic hierarchy process (AHP) methods are difficult to use to generate useful information to assist decision makers in specifying their preferences. This study proposes a novel method incorporating fuzzy preferences and range reduction techniques. Modified from the concept of data envelopment analysis (DEA), the proposed approach is not only capable of treating incomplete preference matrices but also provides reasonable ranges to help decision makers to rank decision alternatives confidently.     

Multicriteria decision support using rules that represent rough-graded preference relations

The approach described in this paper aims to support multicriteria choice and ranking of actions when the input preference information acquired from the decision maker is a graded comprehensive pairwise comparison (or ranking) of reference actions. It is based on decision-rule preference model induced from a rough approximation of the graded comprehensive preference relation among the reference actions. The set of decision rules applied to a new set of actions provides a graded fuzzy preference relation, which can be exploited by weighted-fuzzy net flow score or lexicographic-fuzzy net flow score procedure to obtain a final recommendation in terms of the best choice or of the ranking.     

Target setting in the general combined-oriented CCR model using an interactive MOLP method

The traditional data envelopment analysis (DEA) model does not include a decision maker’s (DM) preference structure while measuring relative efficiency, with no or minimal input from the DM. To incorporate DM’s preference information in DEA, various techniques have been proposed. An interesting method to incorporate preference information, without necessary prior judgment, is the use of an interactive decision making technique that encompasses both DEA and multi-objective linear programming (MOLP). In this paper, we will use Zionts-Wallenius (Z-W) method to reflecting the DM’s preferences in the process of assessing efficiency in the general combined-oriented CCR model. A case study will conducted to illustrate how combined-oriented efficiency analysis can be conducted using the MOLP method.     

Locating a waste treatment facility by using stochastic multicriteria acceptability analysis with ordinal criteria

In this paper we describe a real-life application of an ordinal multicriteria method in the context of choosing a location for a waste treatment facility near Lappeenranta in South-Eastern Finland. The associated environmental impact assessment (EIA) procedure is briefly described. The application was characterized by two interesting properties: no preference information was available, and only ordinal measurements for the criteria were available. The large amount of data obtained was then analyzed using the SMAA-O method – Stochastic Multicriteria Acceptability Analysis with Ordinal criteria designed for this problem setting. SMAA-O converts ordinal information into cardinal data by simulating all possible mappings between ordinal and cardinal scales that preserve the given rankings. As with the basic SMAA-method, the decision makers' (DMs) unknown or partly known preferences are at the same time simulated by choosing weights randomly from appropriate distributions. The main results of the analysis are acceptability indices for alternatives describing the variety of preferences that could make each alternative the best choice. Based on these and additional considerations, the DMs made the final choice for the location of the plant.     

Mean field game of controls and an application to trade crowding

In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a mean field game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader facing a “background noise” (or “mean field”). In standard frameworks, the interactions between the large trader and the price are a temporary and a permanent market impact terms, the latter influencing the public price. In this paper the trader faces the uncertainty of fair price changes too but not only. He also has to deal with price changes generated by other similar market participants, impacting the prices permanently too, and acting strategically. Our MFG formulation of this problem belongs to the class of “extended MFG”, we hence provide generic results to address these “MFG of controls”, before solving the one generated by the cost function of optimal trading. We provide a closed form formula of its solution, and address the case of “heterogenous preferences” (when each participant has a different risk aversion). Last but not least we give conditions under which participants do not need to instantaneously know the state of the whole system, but can “learn” it day after day, observing others’ behaviors.