本文選題：Black-Scholes公式　切入點(diǎn)：回望期權(quán)　出處：《吉林大學(xué)》2017年碩士論文

【摘要】：隨著“中國(guó)經(jīng)濟(jì)新常態(tài)”的提出,金融市場(chǎng)將面臨一個(gè)新的機(jī)遇和挑戰(zhàn).作為中國(guó)金融市場(chǎng)上的短板,金融衍生品的發(fā)展對(duì)于穩(wěn)定金融市場(chǎng)運(yùn)行、擴(kuò)展金融市場(chǎng)都是至關(guān)重要的,更會(huì)關(guān)系到于實(shí)體經(jīng)濟(jì)的風(fēng)險(xiǎn)管理.自從1973年4月初,第一次在芝加哥期權(quán)交易所開始交易期權(quán)以來,我們發(fā)現(xiàn)期權(quán)市場(chǎng)的發(fā)展勢(shì)頭十分高歌猛進(jìn).在期權(quán)合約中,我們可以明顯知道,期權(quán)價(jià)格——是唯一一個(gè)會(huì)隨市場(chǎng)“供求關(guān)系”波動(dòng)變化的自變量.因此,期權(quán)的價(jià)格會(huì)直接影響在合約中買賣雙方的收益情況,這也導(dǎo)致期權(quán)定價(jià)問題成為了金融衍生品市場(chǎng)中最核心的問題.近年來,在國(guó)內(nèi)外的金融衍生品交易市場(chǎng)的交易合約中,除了我們最熟悉的歐式期權(quán)、美式期權(quán)這些普通期權(quán)之外,還活躍著大量由標(biāo)準(zhǔn)期權(quán)派生出的更為個(gè)性化的奇異期權(quán).它們的產(chǎn)生,是衍生品設(shè)計(jì)者為滿足投資者更加個(gè)性化的投資偏好,迎合市場(chǎng)需求構(gòu)造出的新組合.回期期權(quán)就是新型期權(quán)中備受歡迎的一種.由于最大收益可能且遺憾最小的特點(diǎn),回望期權(quán)的價(jià)格也就變得相對(duì)貴一些,所以如何更準(zhǔn)確地對(duì)回望期權(quán)進(jìn)行定價(jià),這是一個(gè)具有重大意義的研究方向.隨著我們對(duì)期權(quán)定價(jià)問題的深入研究很容易發(fā)現(xiàn),期權(quán)價(jià)格所依賴的金融環(huán)境,非常復(fù)雜且具有模糊性.這其中包含著主觀和客觀兩方面的影響因素:主觀上,受投資者的風(fēng)險(xiǎn)偏好影響,不一而足;客觀上,受政策及市場(chǎng)等非隨機(jī)不確定性影響.雖然主觀因素?zé)o法避免,但是為了處理這些可解決的客觀上的非隨機(jī)不確定性,我們可以在期權(quán)定價(jià)的模型中,引入模糊數(shù)學(xué)理論.這也是最近幾年才涌現(xiàn)的金融領(lǐng)域中的一個(gè)新的方向.本文基于傳統(tǒng)的Black-Scholes期權(quán)定價(jià)模型[2],通過總結(jié)升華國(guó)內(nèi)外知名學(xué)者的研究經(jīng)驗(yàn),決定嘗試以三角模糊數(shù)和擴(kuò)張?jiān)淼裙ぞ?創(chuàng)新性地把模糊數(shù)學(xué)理論引入到回望期權(quán)的定價(jià)中,得到回望期權(quán)的模糊期權(quán)價(jià)格.并構(gòu)造最優(yōu)化問題,采用二分法算法求解,得到期權(quán)模糊價(jià)格的最大可信度.我們知道,這一模糊價(jià)格無疑是更貼合實(shí)際環(huán)境.最終投資者可通過判斷是否能接受可信度,選擇是否能接受這一期權(quán)價(jià)格,并最終做出投資選擇.本文在模型的選擇方面,主要考慮了具有浮動(dòng)敲定價(jià)的歐式回望期權(quán)的模糊定價(jià)模型,并可由此一般推論到具有固定敲定價(jià)的歐式回望期權(quán)的定價(jià)模型和部分回望期權(quán)的定價(jià)模型.
[Abstract]:With the proposal of "the new normal state of China's economy", the financial market will face a new opportunity and challenge. As a short board in the Chinese financial market, the development of financial derivatives will stabilize the operation of the financial market. Expansion of financial markets is vital, and more relevant to risk management in the real economy. Since early April 1973, when options were first traded on the Chicago options Exchange, We find that the development of the option market is very dynamic. In the option contract, we can clearly know that the option price is the only independent variable that fluctuates with the "supply and demand" of the market. The price of options directly affects the income of both parties in the contract, which leads to the issue of option pricing becoming the core problem in the financial derivatives market. In recent years, in the domestic and foreign financial derivatives trading market, In addition to the European options, American options, which we are most familiar with, ordinary options are also active in a large number of more personalized exotic options derived from standard options. It is a new combination created by derivatives designers to satisfy investors' more individualized investment preferences and cater to market demands. Backdated options are one of the most popular options in the new type. The price of the option becomes more expensive, so how to price the option more accurately is a significant research direction. With the in-depth study of option pricing, it is easy to find out. The financial environment on which the option price depends is very complex and fuzzy. It contains both subjective and objective factors: subjective, influenced by investors' risk preference, and objectively, Affected by non-random uncertainties such as policy and market. Although subjective factors can not be avoided, in order to deal with these resolvable objective non-random uncertainties, we can use the option pricing model. The theory of fuzzy mathematics is introduced. This is also a new direction in the field of finance which has just emerged in recent years. Based on the traditional Black-Scholes option pricing model [2], this paper summarizes the research experience of famous scholars at home and abroad through summing up and sublimating the research experience of famous scholars at home and abroad. It is decided to introduce the fuzzy mathematics theory into the pricing of the lookback option innovatively by means of triangular fuzzy number and expansion principle, and to obtain the fuzzy option price of the lookback option, and to construct the optimization problem, and to solve the problem by using the dichotomy algorithm. Get the maximum credibility of an option's fuzzy price. We know that this fuzzy price is undoubtedly more appropriate to the actual environment. Finally, investors can decide whether they can accept the credibility and choose whether they can accept the option price. In this paper, we mainly consider the fuzzy pricing model of European lookback option with floating knock pricing. The pricing model of European lookback option with fixed knock pricing and the pricing model of partial lookback option can be deduced.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F830.9

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本文編號(hào)：1687475