本文關(guān)鍵詞： 模糊 跳擴(kuò)散 交易費(fèi)用 期權(quán)定價(jià)　出處：《華中科技大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：由于金融市場(chǎng)的波動(dòng)性,許多金融數(shù)據(jù)不能用確定的數(shù)來表示,例如市場(chǎng)無風(fēng)險(xiǎn)利率,波動(dòng)率等,通常利率為5%左右,波動(dòng)率為3%左右等等這些具有模糊性的數(shù)據(jù),為了描述這些數(shù)據(jù)模糊數(shù)學(xué)被引入到金融理論中.一方面,市場(chǎng)中標(biāo)的資產(chǎn)的價(jià)格波動(dòng)往往有跳躍發(fā)生,因此,在期權(quán)定價(jià)中標(biāo)的資產(chǎn)的運(yùn)動(dòng)模型中應(yīng)含有跳躍項(xiàng);另一方面,由于證券交易需要支付交易費(fèi)用,因此,為了能更好的估計(jì)期權(quán)價(jià)值,交易費(fèi)用應(yīng)是一個(gè)急需考慮的問題.本文將在Merton跳擴(kuò)散過程基礎(chǔ)上考慮模糊環(huán)境中帶有交易費(fèi)用的期權(quán)定價(jià)問題. 本文主要分為四個(gè)部分.第一部分,介紹期權(quán)定價(jià)理論的產(chǎn)生與發(fā)展,包括三方面：跳擴(kuò)散模型下的期權(quán)定價(jià)理論研究現(xiàn)狀,帶有交易費(fèi)用的期權(quán)定價(jià)研究現(xiàn)狀以及模糊環(huán)境下的期權(quán)定價(jià)研究現(xiàn)狀.第二部分,主要利用等價(jià)鞅測(cè)度方法和概率方法得到跳擴(kuò)散模型下帶有交易費(fèi)用的歐式看漲期權(quán)的定價(jià)公式.第三部分,將模糊理論引入到期權(quán)定價(jià)中.首先,推導(dǎo)出在置信水平a下的期權(quán)的價(jià)格區(qū)間,即投資者在滿意度為a的情形下可以選擇的期權(quán)價(jià)格范圍;其次,利用優(yōu)化理論推導(dǎo)出模糊期權(quán)價(jià)格的隸屬度,即給定任意期權(quán)價(jià)格得到其置信水平a,其經(jīng)濟(jì)含義為投資者對(duì)期權(quán)價(jià)格C的滿意度為a;最后,為了方便統(tǒng)一定價(jià)給出模糊期權(quán)的模糊期望.第四部分,在前面所做的工作的基礎(chǔ)上,對(duì)具體的股票進(jìn)行數(shù)值分析.給出模糊對(duì)期權(quán)定價(jià)的影響,并且得到交易費(fèi)用對(duì)期權(quán)價(jià)格的影響,也說明了本文研究的合理性.
[Abstract]:Because of the volatility of financial markets, many financial data can not be expressed in certain numbers, such as market risk-free interest rate, volatility, etc., usually interest rate is about 5%. In order to describe the fuzzy data, the volatility is about 3% and so on. In order to describe these data, fuzzy mathematics is introduced into the financial theory. On the one hand, the price volatility of the assets in the market often jumps, so. Jumping items should be included in the motion model of the assets in which the option is priced. On the other hand, in order to better estimate the value of options, because of the transaction costs to be paid for securities trading. Transaction cost should be an urgent problem. This paper will consider the option pricing problem with transaction cost in fuzzy environment on the basis of Merton jump diffusion process. This paper is divided into four parts. The first part introduces the emergence and development of option pricing theory, including three aspects: the current situation of option pricing theory under the jump-diffusion model. The present situation of option pricing with transaction costs and the current situation of option pricing in fuzzy environment. Part two. This paper mainly uses the equivalent martingale measure method and the probability method to get the pricing formula of European call option with transaction cost under jump diffusion model. In the third part, the fuzzy theory is introduced into option pricing. The price range of options under confidence level a is derived, that is, the price range of options that investors can choose when their satisfaction is a. Secondly, the membership degree of the fuzzy option price is deduced by using the optimization theory, that is, given arbitrary option price to obtain its confidence level a, its economic meaning is that the investor's satisfaction with option price C is a; Finally, in order to facilitate the unified pricing of fuzzy options to give the fuzzy expectations. 4th, on the basis of the previous work, the specific stock numerical analysis, and give the impact of fuzzy options pricing. And the influence of transaction cost on option price is obtained, which also shows the rationality of this study.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F830;F224

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本文編號(hào)：1489560