本文選題：美式期權(quán) + 自由邊界��； 參考：《西安工程大學(xué)》2012年碩士論文

【摘要】：期權(quán)定價(jià)理論是當(dāng)前金融數(shù)學(xué)和金融工程學(xué)科研究和討論的前沿和熱點(diǎn)問(wèn)題之一．美式期權(quán)相比歐式期權(quán)具有可提前執(zhí)行的特權(quán)，這導(dǎo)致了其定價(jià)問(wèn)題難度大大增加．本文從提前執(zhí)行策略、最優(yōu)執(zhí)行邊界、期權(quán)性質(zhì)等方面剖析了美式期權(quán)的價(jià)格構(gòu)成原理，重點(diǎn)解決如何利用數(shù)值計(jì)算方法求解期權(quán)價(jià)格以及方法的實(shí)現(xiàn)． 主要研究?jī)?nèi)容如下： 第1章系統(tǒng)介紹了有關(guān)金融衍生產(chǎn)品定價(jià)的基本概念，發(fā)展歷史及研究現(xiàn)狀，同時(shí)闡述了研究美式期權(quán)定價(jià)的理論和實(shí)際意義． 第2章完整的給出了Black-Scholes模型，并借鑒類似的方法分別推導(dǎo)出了美式期權(quán)定價(jià)模型，有交易成本和紅利的歐式美式期權(quán)定價(jià)模型． 第3章主要給出了幾種常用美式期權(quán)定價(jià)的數(shù)值計(jì)算方法：如樹圖方法，，有限差分法和有限元法．并借用程序設(shè)計(jì)的思路給出了詳細(xì)的計(jì)算過(guò)程和步驟． 第4章以數(shù)值算例為研究?jī)?nèi)容，利用MATLAB軟件進(jìn)行數(shù)值試驗(yàn)，并從收斂性、收斂速度、計(jì)算精度及穩(wěn)定性等角度分析實(shí)驗(yàn)所得結(jié)果．最后，以真實(shí)的股票價(jià)格為研究對(duì)象，討論了隨機(jī)波動(dòng)率條件之下的美式期權(quán)定價(jià)問(wèn)題，并利用時(shí)間序列中的有關(guān)方法，采用真實(shí)數(shù)據(jù)做波動(dòng)率預(yù)測(cè)，用數(shù)值方法求出了股票期權(quán)的價(jià)格． 第5章分析匯總并給出了進(jìn)一步研究的問(wèn)題．
[Abstract]:Option pricing theory is one of the frontier and hot issues in the research and discussion of financial mathematics and financial engineering. Compared with European option, American option has the privilege to execute ahead of time. This leads to a great increase in the difficulty of pricing problems. This paper analyzes the pricing principle of American options from the aspects of early execution strategy, optimal execution boundary, option nature, and so on. The main contents of this paper are as follows: chapter 1 systematically introduces the basic concepts of pricing of financial derivatives. In chapter 2, the Black-Scholes model is given, and the American option pricing model is derived by using similar methods. European American option pricing model with transaction costs and dividends. Chapter 3 mainly gives several numerical calculation methods of American option pricing in common use, such as tree graph method, The finite difference method and finite element method are used to give the detailed calculation process and procedure. Chapter 4 takes numerical example as the research content, carries on the numerical experiment with MATLAB software, and from the convergence, the convergence speed, Finally, taking the real stock price as the research object, the problem of American option pricing under the condition of random volatility is discussed, and the relevant methods in time series are used. The real data is used to predict volatility and the price of stock options is calculated by numerical method.
【學(xué)位授予單位】：西安工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F830.91;O241.82

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 王小群;金融數(shù)學(xué)介紹[J];系統(tǒng)工程;1999年06期

本文編號(hào)：2028402