有交易费用和红利的若干类欧式期权的定价研究

发布时间：2018-07-09 22:04

本文选题：期权定价 + 交易费用　；参考：《延安大学》2012年硕士论文

【摘要】：金融数学所研究的的对象包括未定权益的定价问题，其涉及到现代金融数学的许多知识，如数学中的随机分析以及优化理论，以及资产定价理论和投资组合理论等学科。要想对风险进行有效的预测和规避，这就需要对金融衍生证券进行正确的估价和评估。如何有效快速的准确的确定金融衍生证券的相对公平价格，这是他们能够存在与健康正常发展的关键所在。本文主要讨论欧式期权定价的相关问题。是在有交易费用和红利基础上，认为标的资产服从混合过程，得到标的资产服从混合过程的期权定价方程，以及它的彩虹期权定价方程和多因素期权定价方程；并且给出了欧式期权二叉树模型，和欧式期权二叉树模型的矩阵形式算法。首先，通过改变Black-Scholes模型的基本假设，研究既有交易费用，又有红利的欧式期权定价，且认为标的资产是服从混合过程。运用证券组合模拟期权收益等方法，，得到有交易费用和红利的标的资产服从混合过程的期权定价方程，并推导出有交易成本和红利的标的资产服从混合过程的欧式期权定价模型；同时也得到有交易成本和红利的标的资产服从混合过程的彩虹期权定价方程，以及多因素期权定价方程。其次，也是在有交易费用和红利的基础上，我们考虑有红利和交易成本的欧式期权的二叉树图法。分别从已知红利率和交易成本和已知红利数额和交易成本数额两方面，给出了欧式期权二叉树模型；按已知红利率支付红利和按交易额的固定比例收取交易成本,以及按已知红利数额支付红利和交易成本数额收取交易成本两种情况进行讨论,给出了欧式期权二叉树模型的矩阵形式算法。
[Abstract]:The object of financial mathematics is the pricing of undetermined equity, which involves a lot of knowledge of modern financial mathematics, such as stochastic analysis and optimization theory in mathematics, asset pricing theory and portfolio theory and so on. In order to predict and avoid risks effectively, it is necessary to evaluate and evaluate financial derivatives correctly. How to determine the relative fair price of derivative securities effectively, quickly and accurately is the key to their existence and healthy development. This paper mainly discusses the European option pricing issues. On the basis of transaction costs and dividends, it is considered that the underlying asset service follows the hybrid process and obtains the option pricing equation of the underlying asset service from the hybrid process, as well as its rainbow option pricing equation and multi-factor option pricing equation. The matrix algorithm of European option binary tree model and European option binary tree model is also given. Firstly, by changing the basic assumptions of Black-Scholes model, we study the pricing of European options with both transaction costs and dividends, and consider that the underlying asset is a hybrid process. By using the method of portfolio simulation, the option pricing equation of the underlying asset with transaction costs and dividends is obtained. The European option pricing model of the underlying asset with transaction cost and dividend is derived, and the rainbow option pricing equation of the underlying asset with transaction cost and dividend is obtained. And multi-factor option pricing equation. Secondly, on the basis of transaction cost and dividend, we consider the binary tree method of European option with dividend and transaction cost. From two aspects of known red interest rate and transaction cost and the amount of known dividend and transaction cost, the paper gives the binary tree model of European option, pays dividends according to known red interest rate and collects transaction cost according to the fixed proportion of transaction amount. The paper also discusses the two cases of paying dividends according to known dividend amount and collecting transaction cost according to the amount of transaction cost, and gives the matrix algorithm of European option binary tree model.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

【相似文献】