發(fā)布時間：2018-06-16 22:59

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

【摘要】：期權定價理論是當前金融數(shù)學和金融工程學科研究和討論的前沿和熱點問題之一．美式期權相比歐式期權具有可提前執(zhí)行的特權，這導致了其定價問題難度大大增加．本文從提前執(zhí)行策略、最優(yōu)執(zhí)行邊界、期權性質等方面剖析了美式期權的價格構成原理，重點解決如何利用數(shù)值計算方法求解期權價格以及方法的實現(xiàn)． 主要研究內(nèi)容如下： 第1章系統(tǒng)介紹了有關金融衍生產(chǎn)品定價的基本概念，發(fā)展歷史及研究現(xiàn)狀，同時闡述了研究美式期權定價的理論和實際意義． 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出了美式期權定價模型，有交易成本和紅利的歐式美式期權定價模型． 第3章主要給出了幾種常用美式期權定價的數(shù)值計算方法：如樹圖方法，，有限差分法和有限元法．并借用程序設計的思路給出了詳細的計算過程和步驟． 第4章以數(shù)值算例為研究內(nèi)容，利用MATLAB軟件進行數(shù)值試驗，并從收斂性、收斂速度、計算精度及穩(wěn)定性等角度分析實驗所得結果．最后，以真實的股票價格為研究對象，討論了隨機波動率條件之下的美式期權定價問題，并利用時間序列中的有關方法，采用真實數(shù)據(jù)做波動率預測，用數(shù)值方法求出了股票期權的價格． 第5章分析匯總并給出了進一步研究的問題．
[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.
【學位授予單位】：西安工程大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：F830.91;O241.82

【參考文獻】

相關期刊論文 前1條

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

本文編號：2028402