Prices and sensitivities of Asian options: A survey

Asian options are hard to price both analytically and numerically. Even though they have been the focus of much attention in recent years, there is no single technique which is widely accepted to price Asian options for all choices of market parameters. For hedging purposes, the estimation of the price sensitivities is often as important as the evaluation of the prices themselves. This paper provides a survey of current methods for pricing Asian options and computing their sensitivities to the key input parameters. The methods discussed include: Monte Carlo simulation, the finite difference approach and various quasi analytical approaches and approximations. We discuss practical numerical issues that arise in implementing these methods. The paper compares the accuracy and efficiency of the different approaches and offers some general conclusions.     

具限制投资组合和交易费用的博弈未定权益的保值

博弈期权是由kifer(2000)提出的,但就其本质而言,仍是美式期权的一种,只是增加了卖方中止合约的权利.本文主要对连续市场模型中具交易费用和限制投资组合的博弈未定权益的保值问题进行了研究,给出了买卖双方的保值价格和一个无套利区间.     

NUMERICAL ANALYSIS ON BINOMIAL TREE METHODS FOR AMERICAN LOOKBACK OPTIONS

1　IntroductionLookback options are path-dependent options whose payoffs depend on the maximumor the minimum of the underlying asset price during the life of the options( see[6] [1 0 ][1 4] ) .Here the maximum or minimum realized asset price may be monitored either con-tinuously or discretely.An American lookback call( put) option allows to be exercised atany time prior to expiry and gives the holder the rightto buy( sell) atthe historical mini-mum( maximum) of the underlying asset price on ex…     

The Pietra term structures of financial assets

This paper explores an elemental connection between call options-the most commonly tradable financial derivatives, implied volatility term structures-critical “market information” emanating from call-option prices, and the Pietra index-a quantitative economic measure of societal egalitarianism. Our study: (i) unveils an intrinsic “Pietra structure” of call-option prices; (ii) introduces the notion of the “Pietra term structures” of financial assets; (iii) describes the probabilistic meaning of the Pietra term structures; (iv) establishes an explicit nonlinear one-to-one mapping between the Pietra term structures and the implied volatility term structures of financial assets. The results presented in this paper provide a deep insight into the econophysics of call options and implied volatility term structures.     

Timing and eco(nomic) efficiency of climate-friendly investments in supply chains

Emission trading schemes such as the European Union Emissions Trading System (EUETS) attempt to reconcile economic efficiency with ecological efficiency by creating financial incentives for companies to invest in climate-friendly innovations. Using real options methodology, we demonstrate that under uncertainty, economic and ecological efficiency continue to be mutually exclusive. This problem is even worse if a climate-friendly project depends on investing in of a whole supply chain. We model a sequential bargaining game in a supply chain where the parties negotiate over implementation of a carbon dioxide (CO₂) saving investment project. We show that the outcome of their bargaining is not economically efficient and even less ecologically efficient. Furthermore, we show that a supply chain becomes less economically efficient and less ecologically efficient with every additional chain link. Finally, we make recommendations for how managers or politicians can improve the situation and thereby increase economic as well as ecological efficiency and thus also the eco-efficiency of supply chains.     

Cooperative advertising models in supply chain management: A review

This paper reviews articles on cooperative advertising, a topic which has gained substantial interest in the recent years. Thereby, we first briefly distinguish five different definitions of cooperative advertising which can be found in operations research literature. After that, we concentrate on vertical cooperative advertising, which is the most common object of investigation and is understood as a financial agreement where a manufacturer offers to pay a certain share of his retailer’s advertising expenditures. In total, we identified 58 scientific papers considering mathematical modeling of vertical cooperative advertising. These articles are then analyzed with regard to their general model setting (e.g., the underlying supply chain structure and design of the cooperative advertising program). After that, we explain the different demand and cost functions that are employed, whereupon we distinguish between static and dynamic models. The last dimension of our review is dedicated to the game-theoretic concepts which are mostly used to reflect different forms of distribution of power within the channel.     

On the core of cost-revenue games: Minimum cost spanning tree games with revenues

In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net revenues that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a nonempty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a nonempty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost).     

Competition through capacity investment under asymmetric existing capacities and costs

This paper discusses the way that different operational characteristics including existing capacity, scale economies, and production policy have an important influence on the capacity outcomes when firms compete in the market place. We formulate a game-theoretical model where each firm has an existing capacity and faces both fixed and variable costs in purchasing additional capacity. Specifically, the firms simultaneously (or sequentially) make their expansion decisions, and then simultaneously decide their production decisions with these outputs being capacity constrained. We also compare our results with cases where production has to match capacity. By characterizing the firms’ capacity and production choices in equilibrium, our analysis shows that the operational factors play a crucial role in determining what happens. The modeling and analysis in the paper gives insight into the way that the ability to use less production capacity than has been built will undermine the commitment value of existing capacity. If a commitment to full production is not possible, sinking operational costs can enable a firm to keep some preemptive advantage. We also show that the existence of fixed costs can introduce cases where there are either no pure strategy equilibrium or multiple equilibria. The managerial implications of our analysis are noted in the discussion. Our central contribution in this paper is the innovative integration of the strategic analysis of capacity expansion and well-known (s,S)$(s\text{,}S)$ policy in operations and supply chain theory.     

A three-dimensional voting system in Hong Kong

The voting system of the Legislative Council of Hong Kong (Legco) is sometimes unicameral and sometimes bicameral, depending on whether the bill is proposed by the Hong Kong government. Therefore, although without any representative within Legco, the Hong Kong government has certain degree of legislative power – as if there is a virtual representative of the Hong Kong government within the Legco. By introducing such a virtual representative of the Hong Kong government, we show that Legco is a three-dimensional voting system. We also calculate two power indices of the Hong Kong government through this virtual representative and consider the C-dimension and the W-dimension of Legco. Finally, some implications of this Legco model to the current constitutional reform in Hong Kong will be given.     

Optimal cost sharing for capacitated facility location games

We consider cost sharing for a class of facility location games, where the strategy space of each player consists of the bases of a player-specific matroid defined on the set of resources. We assume that resources have nondecreasing load-dependent costs and player-specific delays. Our model includes the important special case of capacitated facility location problems, where players have to jointly pay for opened facilities. The goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability. We investigate two classes of protocols: basic protocols guarantee the existence of at least one pure Nash equilibrium and separable protocols additionally require that the resulting cost shares only depend on the set of players on a resource. We find optimal basic and separable protocols that guarantee the price of stability/price of anarchy to grow logarithmically/linearly in the number of players. These results extend our previous results (cf. von Falkenhausen & Harks, 2013), where optimal basic and separable protocols were given for the case of symmetric matroid games without delays.