本文選題：二叉樹期權(quán)定價(jià)模型 + 維納過程　； 參考：《西安建筑科技大學(xué)》2012年碩士論文

【摘要】：在過去的30年，金融的衍生產(chǎn)品變得越來越重要。當(dāng)今，隨著我們的知識的增加，對金融產(chǎn)品理解的加深，期權(quán)交易在全球的諸多交易所都逐漸受歡迎。我們經(jīng)常接觸到的金融衍生產(chǎn)品之一就是期權(quán)，它的用途非常廣泛，常常被用于公司的高層管理員的報(bào)酬、或者用于資本項(xiàng)目投資中、或是轉(zhuǎn)移股票風(fēng)險(xiǎn)等等。投資者常常會關(guān)注長期的期權(quán)價(jià)格，而交易者則會關(guān)注短期的期權(quán)價(jià)格的變化。期權(quán)是一種選擇權(quán)，它是股票交易雙方之間簽訂的一份協(xié)議，，這份協(xié)議允許期權(quán)購買者在將來的某個(gè)特定日或這個(gè)日子之前，按照已經(jīng)規(guī)定好的價(jià)格買賣一定數(shù)量的標(biāo)的物品的權(quán)利，并且不承擔(dān)任何義務(wù)。當(dāng)買方?jīng)Q定執(zhí)行期權(quán)合約時(shí)，賣方就必須賣出或買進(jìn)合約中規(guī)定的標(biāo)的物。市場具有動態(tài)性，所以我們對期權(quán)價(jià)格行為變化的正確理解是非常有必要的。本文主要介紹的是關(guān)于美式股票期權(quán)，而美式期權(quán)又有提前執(zhí)行的情況，所以對于股票期權(quán)買方或賣方而言，如何判斷最有利的時(shí)間點(diǎn)執(zhí)行期權(quán)合約，使得投資者“風(fēng)險(xiǎn)最小化，利益最大化”成為我們討論的焦點(diǎn)。 本文首先介紹了期權(quán)的定義、分類、影響因素等，并且利用軟件OP-EVAL4對股票期權(quán)進(jìn)行定價(jià)，并且通過比較計(jì)算結(jié)果分析每種因素是如何影響股票期權(quán)價(jià)值的。然后簡述已有的幾種美式期權(quán)定價(jià)的數(shù)值方法，如：Black-Scholes期權(quán)定價(jià)模型、期權(quán)定價(jià)的二叉樹定價(jià)模型、期權(quán)定價(jià)的三叉樹定價(jià)模型、蒙特卡羅模擬法、有限差分法。已有的定價(jià)模型未考慮股息支付的情況，在此基礎(chǔ)上，本文以美式看漲期權(quán)的定價(jià)問題為研究對象，引入了股票交易過程中存在的股息支付，根據(jù)隨機(jī)誤差校正的思想，結(jié)合美式看漲權(quán)的具體情況，考慮用lnS代替S來模擬股票價(jià)格，建立帶有支付股息的新型二叉樹期權(quán)定價(jià)模型。以美式看漲期權(quán)為例進(jìn)行數(shù)據(jù)分析及檢驗(yàn)，并且將計(jì)算結(jié)果與Black-Scholes期權(quán)定價(jià)模型的計(jì)算結(jié)果、不帶股息支付的二叉樹定價(jià)模型進(jìn)行對比研究。
[Abstract]:Over the past 30 years, financial derivatives have become increasingly important.Today, as our knowledge grows and our understanding of financial products deepens, option trading is gaining popularity on many exchanges around the world.One of the financial derivatives we often come into contact with is option, which is used in a wide range of applications. It is often used in the remuneration of top executives of a company, or in capital account investments, or in transferring stock risks, etc.Investors tend to focus on long-term option prices, while traders focus on short-term price changes.An option is an option, an agreement between the two parties to a stock exchange that allows the buyer of an option to buy an option on or before a particular day in the future.The right to buy and sell a certain quantity of the subject matter at a specified price and without any obligation.When the buyer decides to execute the option contract, the seller must sell or buy the subject matter specified in the contract.The market is dynamic, so it is necessary to understand the change of option price behavior correctly.This article mainly introduces the American stock option, and American option has the situation of early execution, so for the buyer or seller of the stock option, how to judge the most favorable time point to execute the option contract,Make investor "risk minimization, profit maximization" become the focus of our discussion.This paper first introduces the definition, classification, influencing factors and so on of options, and makes use of software OP-EVAL4 to price stock options, and analyzes how each factor affects the value of stock options by comparing the results of calculation.Then several numerical methods of American option pricing are introduced, such as: Black-Scholes option pricing model, binomial tree pricing model, triple-tree pricing model, Monte Carlo simulation method and finite difference method.The existing pricing model does not take dividend payment into account. On this basis, the pricing problem of American call options is taken as the research object, and the dividend payment existing in the course of stock trading is introduced, according to the idea of random error correction.Considering the specific situation of American bullish power, we consider using lnS instead of S to simulate stock price and establish a new pricing model of binomial tree option with dividend payment.Taking American call option as an example, the data are analyzed and tested, and the results are compared with the results of Black-Scholes option pricing model and the binary tree pricing model without dividend payment.
【學(xué)位授予單位】：西安建筑科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F224;F830.91

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