Pricing, Hedging and Measuring Risk in Markets with Transaction Costs

用交易成本定价、对冲和衡量市场风险

• 批准号: 1007938
• 负责人: Birgit Rudloff
• 金额: $ 18万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007938&HistoricalAwards=false
• 关键词: Pricing; Hedging; Measuring; Risk; Markets

The objective of this project is to solve problems of hedging and pricing in markets where transaction costs are present. Closely related is the question on how to measure risk in these markets. The difficulty lies in the fact that transaction costs lead in a natural way to set-valued constructions. Set-valued risk measures for random solvency cones are studied. An example is the superhedging price of a multivariate claim under transaction costs. This link makes it possible to study price bounds that are more reasonable from a practical point of view like good deal bounds and indifference prices, which have already proven to be a powerful pricing mechanism in frictionless incomplete markets. Another goal is to solve a hedging problem in markets with transaction costs when the risk of falling short a contingent claim is evaluated by a set-valued risk measure. The above problems are solved by means of a recent convex duality theory, particularly designed for set-valued functions. Especially, dual problems for the main set-valued problem and its subproblems are established and conditions for strong duality will be studied. The chosen model itself, a set-valued optimization problem, as well as the proposed solution methods are new in mathematical finance andbeyond: The approach also extends concepts from optimization theory.Models for markets with transaction costs are more realistic than frictionless models. The finance industry benefits from research in hedging, pricing and risk managing techniques as there is a need to cope with bid-ask-spreads for traded assets caused by transaction costs. In complex market situations it is an advantage to have flexible tools for risk evaluation in terms of more than one currency and corresponding risk managing techniques. Thus, this research project leads to a better understanding of multivariate risks.

本项目的目标是解决存在交易成本的市场中的套期保值和定价问题。 与此密切相关的问题是如何衡量这些市场的风险。 困难在于，交易成本以一种自然的方式导致集值构造。研究了随机偿付能力锥的集值风险度量。 一个例子是交易费用下的多元索赔的超套期保值价格。 这种联系使得研究从实际角度来看更合理的价格界限成为可能，比如好交易界限和无差异价格，它们已经被证明是无摩擦不完全市场中强大的定价机制。 另一个目标是解决有交易费用的市场中的套期保值问题时，短期或有索赔的风险是由一个集值风险度量评估。 上述问题的解决，通过最近的凸对偶理论，特别是集值函数设计。 特别地，建立了主集值问题及其子问题的对偶问题，并研究了强对偶的条件。 所选择的模型本身，一个集值优化问题，以及所提出的解决方法是新的数学金融和超越：该方法还扩展了优化理论的概念。有交易成本的市场模型比无摩擦模型更现实。 金融业从对冲、定价和风险管理技术的研究中受益，因为需要应对交易成本导致的交易资产的买卖价差。 在复杂的市场情况下，拥有灵活的多种货币风险评估工具和相应的风险管理技术是一个优势。 因此，该研究项目导致更好地理解多元风险。