發(fā)布時(shí)間：2018-01-07 05:28

  本文關(guān)鍵詞：歐式籃子期權(quán)定價(jià)研究綜述和數(shù)值分析　出處：《清華大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 籃子期權(quán) Black-Scholes模型 綜述分析 數(shù)值模擬

【摘要】：由于交易市場的多樣性、客戶需求的差異性、金融衍生品市場的不斷完善和金融理論研究的發(fā)展，金融機(jī)構(gòu)會設(shè)計(jì)各式各樣的新型期權(quán)。籃子期權(quán)是新型期權(quán)中的一種，它是多資產(chǎn)期權(quán)，通常在多種外國貨幣的交易中使用，利用它來套期保值。多個(gè)標(biāo)的資產(chǎn)價(jià)格的加權(quán)平均決定籃子期權(quán)的到期收益。通常，由投資組合理論可知，一籃子標(biāo)的資產(chǎn)的波動(dòng)率相對比較小，這就導(dǎo)致籃子期權(quán)的價(jià)格要比單個(gè)標(biāo)的資產(chǎn)期權(quán)價(jià)格的總和小，在費(fèi)用上效率更高。已有許多學(xué)者基于不同的市場假設(shè)，，建立不同模型，選用不同方法，對籃子期權(quán)定價(jià)進(jìn)行了探索和研究�；诨@子期權(quán)定價(jià)的理論意義和現(xiàn)實(shí)意義，本文將對籃子期權(quán)的定價(jià)模型、定價(jià)方法以及定價(jià)公式進(jìn)行綜述分析，以便在實(shí)際交易中更好地進(jìn)行應(yīng)用。 一方面，在Black-Scholes模型下，對歐式籃子期權(quán)定價(jià)研究進(jìn)行綜述分析。對于幾何平均籃子期權(quán)，基于幾何平均籃子期權(quán)定價(jià)可以轉(zhuǎn)化為一維問題，通過引進(jìn)組合自變量直接求解多資產(chǎn)Black-Scholes方程，得到幾何平均籃子期權(quán)定價(jià)公式；對于算術(shù)平均籃子期權(quán)，對國內(nèi)外相關(guān)研究文獻(xiàn)進(jìn)行整理，列出五種不同的解析近似定價(jià)公式，并就部分公式作一些理論證明推導(dǎo)。 另一方面，對Black-Scholes模型的假設(shè)進(jìn)行放松，綜述分析不同市場假設(shè)下的歐式籃子期權(quán)定價(jià)。在標(biāo)的資產(chǎn)價(jià)格變化模式放松的基礎(chǔ)上，基于不同的解析近似法，分別給出跳躍擴(kuò)散模型和分?jǐn)?shù)布朗運(yùn)動(dòng)下的歐式籃子期權(quán)定價(jià)公式；在對常數(shù)波動(dòng)率假設(shè)放松的基礎(chǔ)上，整理出Heston隨機(jī)波動(dòng)率模型下兩個(gè)資產(chǎn)的籃子期權(quán)的近似定價(jià)公式；在對無違約風(fēng)險(xiǎn)假設(shè)放松的基礎(chǔ)上，給出有違約風(fēng)險(xiǎn)的幾何平均籃子定價(jià)模型和公式；在對無摩擦市場假設(shè)放松的基礎(chǔ)上，利用無風(fēng)險(xiǎn)對沖原理推導(dǎo)出支付交易費(fèi)用的籃子期權(quán)定價(jià)模型。 本文還對Black-Scholes模型下的歐式看漲籃子期權(quán)定價(jià)進(jìn)行數(shù)值模擬�；诖髷�(shù)定理，利用蒙特卡羅方法(Monte Carlo method)進(jìn)行大量模擬，估計(jì)歐式算術(shù)平均看漲籃子期權(quán)價(jià)格，同時(shí)采用減小方差技術(shù)中的控制變量法來提高模擬效率，以及用低偏差Halton和Faure序列來縮減取樣范圍，即擬蒙特卡羅法(Quasi-MonteCarlo method)進(jìn)行模擬。
[Abstract]:Because of the diversity of trading market, the difference of customer demand, the continuous improvement of financial derivatives market and the development of financial theory research. Financial institutions design a variety of new options. Basket options are one of the new types of options. They are multi-asset options and are usually used in transactions involving a variety of foreign currencies. It is used to hedge. The weighted average of multiple underlying asset prices determines the maturity return of basket options. Usually, from portfolio theory, the volatility of a basket of underlying assets is relatively small. As a result, the price of basket options is smaller than the sum of individual underlying asset options, and the cost efficiency is higher. Many scholars have established different models and different methods based on different market assumptions. Based on the theoretical and practical significance of basket option pricing, this paper will summarize and analyze the pricing model, pricing methods and pricing formulas of basket options. In order to be better used in actual transactions. On the one hand, under the Black-Scholes model, the research on European basket option pricing is reviewed and analyzed. Based on the geometric mean basket option pricing can be transformed into a one-dimensional problem, the geometric average basket option pricing formula is obtained by introducing portfolio independent variables to solve the multi-asset Black-Scholes equation directly. For arithmetic average basket option, the relevant literatures at home and abroad are sorted out, five kinds of analytical approximate pricing formulas are listed, and some formulas are proved theoretically. On the other hand, the hypothesis of Black-Scholes model is relaxed, and the European basket option pricing under different market assumptions is summarized and analyzed. Based on different analytical approximations, the jump diffusion model and the pricing formula of European basket options under fractional Brownian motion are given respectively. On the basis of relaxing the assumption of constant volatility, the approximate pricing formula of basket options for two assets under Heston stochastic volatility model is put forward. On the basis of loosening the assumption of non-default risk, the geometric average basket pricing model and formula with default risk are given. On the basis of loosening the assumption of frictionless market, a basket option pricing model for payment of transaction costs is derived by using the risk-free hedging principle. In this paper, the pricing of European call basket options under Black-Scholes model is numerically simulated, based on the theorem of large numbers. Monte Carlo method is used to carry out a large number of simulations to estimate the price of European arithmetic average call basket option. At the same time, the control variable method in the variance reduction technique is used to improve the simulation efficiency, and the low deviation Halton and Faure sequences are used to reduce the sampling range. Quasi-Monte Carlo method is used to simulate.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F830.9;F224

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