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  本文關鍵詞：不確定環(huán)境下的脆弱期權(quán)定價研究　出處：《華南理工大學》2013年碩士論文　論文類型：學位論文

  更多相關文章： 脆弱期權(quán) 信用風險 三維三叉樹 Lévy過程 模糊數(shù)

【摘要】：期權(quán)作為一種金融衍生產(chǎn)品，在金融市場上扮演著十分重要的角色。因而，對其進行準確有效的定價就顯得異常重要。Black和Scholes于20世紀70年代提出了著名的B-S期權(quán)定價模型。該模型對交易員如何定價和對沖期權(quán)產(chǎn)生了深遠的影響，并對金融工程領域的發(fā)展起到了巨大的促用。然而，隨著金融市場的快速發(fā)展，這一模型所固有的缺陷開始顯露出來，并制約了期權(quán)市場的進一步發(fā)展。其中表現(xiàn)比較明顯的是期權(quán)交易過程中的信用風險。所以，如何調(diào)整期權(quán)的價格來反映交易對手的信用風險就成為一個亟待解決的問題。這一問題也就是通常所說的脆弱期權(quán)定價問題。本文在定價脆弱期權(quán)的結(jié)構(gòu)模型的基礎上，主要從以下三個方面對美式脆弱期權(quán)和歐式脆弱期權(quán)的定價進行了研究。 首先， Klein（2010）基于Hull和White（1995）提出的三維二叉樹方法的思想，將其運用到美式脆弱期權(quán)定價研究中，為了得到更加準確有效的美式脆弱期權(quán)價格，本文引入三叉樹代替二叉樹對標的股票價格及交易對手資產(chǎn)價值進行刻畫，在此基礎上構(gòu)建了定價美式脆弱期權(quán)的三維三叉樹模型。根據(jù)這一模型，我們給出了一些數(shù)值例子，這些數(shù)值例子很好地分析了美式脆弱期權(quán)的性質(zhì)。 其次，本文在考慮運用幾何Lévy過程描述標的股票價格波動的基礎上，依據(jù)Klein（1996）提出的定價歐式脆弱期權(quán)的模型框架，構(gòu)建了一個基于Lévy過程的定價歐式脆弱期權(quán)的修正模型�？紤]到金融市場的時常波動性和市場投資者所面臨的信息的非完全準確性所導致的市場參數(shù)的不確定性，本文在修正的脆弱期權(quán)定價模型的基礎上，進一步引入模糊集理論，通過假定無風險利率、波動率、平均跳躍強度以及資產(chǎn)收益率為三角模糊數(shù)，得到了模糊環(huán)境下基于Lévy過程的歐式脆弱期權(quán)定價模型。同時，本文通過一些數(shù)值例子對修正模型和Klein（1996）模型進行了比較分析。 最后，Xu（2012）在假定股票價格和交易對手的資產(chǎn)價值均服從跳躍擴散過程的情況下，給出了定價脆弱期權(quán)的模型�？紤]到影響金融市場的因素較多所導致的市場參數(shù)的不確定性，本文在Xu（2012）的基礎上，引入模糊集理論，通過假定無風險利率，波動率以及其平均跳躍強度為三角模糊數(shù)，，運用Wu（2004）提供的模糊數(shù)運算法則，得到了定價歐式脆弱期權(quán)的模糊跳躍擴散模型，并最終給出了模型的相應算法步驟。運用該模型算法，投資者不僅可以根據(jù)自己滿意的隸屬度選擇相應的期權(quán)進行投資，而且還可以計算給定期權(quán)價格所對應的隸屬度。同時，本文針對新模型給出了一些數(shù)值例子，并通過這些數(shù)值例子對模糊模型、Xu（2012）模型以及Klein（1996）模型進行了比較分析。 數(shù)例結(jié)果表明，本文提出的定價脆弱期權(quán)的方法，能夠更加準確有效地對脆弱期權(quán)進行定價，從而可以引導金融投資者們更加有效地進行決策。
[Abstract]:As a financial derivative, option plays a very important role in the financial market. Black and Scholes put forward the famous B-S option pricing model in 1970s. Punching options have had a profound impact. It has greatly promoted the development of financial engineering. However, with the rapid development of financial markets, the inherent defects of this model began to show. It also restricts the further development of the option market. Among them, the more obvious performance is the credit risk in the process of option trading. How to adjust the price of options to reflect the credit risk of counterparty is an urgent problem to be solved. On... The pricing of American fragile options and European fragile options is studied from the following three aspects. First of all, Klein 2010) is based on the idea of three-dimensional binary tree proposed by Hull and White 1995, and applies it to the study of American fragile option pricing. In order to get more accurate and effective American fragile option price, this paper introduces tri-tree instead of binary tree to describe the underlying stock price and counterparty asset value. On the basis of this, we construct a three dimensional triple tree model for pricing American fragile options. According to this model, we give some numerical examples, which give a good analysis of the properties of American fragile options. Secondly, on the basis of considering the geometric L 茅 vy process to describe the volatility of the underlying stock price, this paper proposes a model framework for pricing European fragile options according to Klein's 1996. A modified model of pricing European fragile options based on L 茅 vy process is constructed. Considering the frequent volatility of financial markets and the incomplete accuracy of information faced by market investors, the market parameters are not satisfied. Certainty. On the basis of the modified fragile option pricing model, this paper further introduces the fuzzy set theory, which assumes that the risk-free interest rate, volatility, average jump intensity and return rate of assets are triangular fuzzy numbers. A European vulnerable option pricing model based on L 茅 vy process in fuzzy environment is obtained. At the same time, the modified model and Kleinnberg 1996) model are compared and analyzed by some numerical examples. Finally, Xue Xue (2012) assumes that both the stock price and the asset value of the counterparty are subject to the jump diffusion process. The model of pricing vulnerable options is given. Considering the uncertainty of market parameters caused by many factors affecting financial market, fuzzy set theory is introduced on the basis of Xuan2012). Based on the assumption that the risk-free interest rate, volatility and its average jump intensity are triangular fuzzy numbers, the fuzzy number algorithm provided by Wuwei 2004 is used. The fuzzy jump diffusion model for pricing European fragile options is obtained, and the corresponding algorithm steps are given. Investors can not only select the corresponding options according to their own satisfactory membership degree, but also calculate the corresponding membership degree of a given option price. At the same time, this paper gives some numerical examples for the new model. These numerical examples are used to compare and analyze the fuzzy model Xujia2012) and the Kleinfen 1996) model. The results of several examples show that the method proposed in this paper can price fragile options more accurately and effectively, thus leading financial investors to make more effective decisions.
【學位授予單位】：華南理工大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F224;F830.9

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