【摘要】：Black和Scholes在1973年提出的期權(quán)定價模型作為最經(jīng)典的歐式期權(quán)定價方法被研究者和投資者廣范使用。該模型的一個重要假設(shè)是標(biāo)的股票市場流動性充分,任何數(shù)量的股票均可以立即買進(jìn)或賣出,也就是說任何數(shù)量的股票交易均不會引起價格發(fā)生變化。然而,以往大量的研究成果表明：投資者的頭寸規(guī)模與交易行為將影響交易價格,甚至在流動性非常好的市場中,短時間內(nèi)的大規(guī)模訂單仍會導(dǎo)致交易價格的逆向變化。B-S模型認(rèn)為投資者能夠根據(jù)標(biāo)的股票的價格和到期日的長短完全復(fù)制期權(quán)合約的現(xiàn)金流,并且能夠隨著股票價格的變化及時調(diào)整股票頭寸,使得在任一股票價格下投資者都“恰好”持有均衡頭寸,但是如果流動性不充分,投資者的復(fù)制行為本身將引起標(biāo)的股票價格變化,產(chǎn)生新的均衡頭寸,投資者按照變化前的價格建立的頭寸已經(jīng)不能產(chǎn)生和期權(quán)合約相同的現(xiàn)金流,所以在流動性充分基礎(chǔ)上建立的期權(quán)定價模型必然與合理的期權(quán)價值存系統(tǒng)性偏差。本文根據(jù)無套利均衡原理,在標(biāo)的資產(chǎn)服從的幾何布朗運(yùn)動中加入復(fù)制期權(quán)產(chǎn)生的流動性溢價,推導(dǎo)出流動性修正的期權(quán)定價微分方程,同時借助前人的研究本文證明了該方程的解析解是存在的,并且是唯一的。對解的性質(zhì)的分析發(fā)現(xiàn)流動性不足改變了標(biāo)的股票收益的波動率,進(jìn)而改變了期權(quán)的內(nèi)在價值,修正的期權(quán)價格依然滿足平價公式。與B-S模型不同,流動性修正的期權(quán)定價模型不能得到顯式解析解,本文使用有限差分方法求解修正模型的數(shù)值解,并且證明該方法及其改進(jìn)算法是穩(wěn)定的。為了比較流動性修正的期權(quán)定價模型是否優(yōu)于傳統(tǒng)B-S模型,本文對香港指數(shù)期權(quán)市場上不同價外程度,不同到期日期歐式期權(quán)合約進(jìn)行了實(shí)證研究。研究表明:所有合約的修正價格都比B-S模型價格更接近實(shí)際市場價格,說明修正模型精確;對于期權(quán)合約多頭.流動性修正的期權(quán)定價模型具有較高的估值能力,對于期權(quán)合約空頭而言,修正模型改進(jìn)程度較�。簭暮霞s的角度看,考慮流動性沖擊的期權(quán)定價模型的修正效果隨價外程度的增加而變大；模型對看漲期權(quán)的修正優(yōu)于看跌期權(quán)。本文的的理論意義是流動性因素被合理的引入到期權(quán)定價過程中,并且推導(dǎo)出期權(quán)定價的均衡模型；實(shí)踐意義是本文構(gòu)建的流動性修正的期權(quán)定價模型可以作為相對準(zhǔn)確的期權(quán)估值工具,為投資者提供衡量期權(quán)價格高低的標(biāo)尺。
[Abstract]:The option pricing model proposed by Black and Scholes in 1973 is widely used by researchers and investors as the most classical European option pricing method. An important assumption of the model is that the underlying stock market is sufficiently liquid, and any number of stocks can be bought or sold immediately, that is to say, any amount of stock trading will not cause a change in price. However, a large number of previous studies have shown that the size and behavior of investors' positions will affect trading prices, even in very liquid markets. Large orders within a short period of time can still lead to adverse changes in the transaction price. B-S model assumes that investors can completely replicate the cash flow of the option contract based on the price of the underlying stock and the length of the maturity date. And the ability to adjust stock positions in time as stock prices change, so that investors "happen" to hold equilibrium positions at any stock price, but if liquidity is inadequate, The investor's copying behavior itself will cause the underlying stock price to change, creating a new equilibrium position, and the investor's position at the pre-change price can no longer produce the same cash flow as the option contract. Therefore, the option pricing model established on the basis of sufficient liquidity must have a systematic deviation from the reasonable option value. Based on the principle of no-arbitrage equilibrium, this paper adds the liquidity premium generated by replicating options to the geometric Brownian motion of underlying assets, and deduces a liquidity modified option pricing differential equation. At the same time, it is proved that the analytical solution of the equation is unique. By analyzing the nature of the solution, it is found that the lack of liquidity changes the volatility of the underlying stock return, and then changes the intrinsic value of the option, and the revised option price still meets the parity formula. Unlike B-S model, the liquidity modified option pricing model can not get an explicit analytical solution. In this paper, the finite difference method is used to solve the numerical solution of the modified model, and it is proved that the method and its improved algorithm are stable. In order to compare whether the liquidity modified option pricing model is superior to the traditional B-S model, this paper makes an empirical study on the European option contracts with different maturity dates in the Hong Kong index options market. The results show that the modified price of all contracts is closer to the actual market price than that of B-S model, which shows that the modified model is accurate. The liquidity modified option pricing model has higher valuation ability, and the modified model is less improved for short options contracts: from the point of view of contract, The modified effect of the option pricing model considering liquidity shock increases with the increase of the degree of extravalency. The model modifies call options better than put options. The theoretical significance of this paper is that liquidity factors are reasonably introduced into the process of option pricing and the equilibrium model of option pricing is derived. The practical significance is that the liquidity modified option pricing model constructed in this paper can be used as a relatively accurate option valuation tool to provide investors with a yardstick to measure the price of options.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F224;F830.9

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本文編號：2423923