本文選題：障礙期權(quán) + 模糊數(shù)　； 參考：《中國(guó)礦業(yè)大學(xué)》2014年碩士論文

【摘要】：障礙期權(quán)是一種路徑依賴期權(quán),它的收益取決于標(biāo)的資產(chǎn)價(jià)格在持有期內(nèi)是否觸碰到障礙值.障礙期權(quán)的期權(quán)金低于歐式期權(quán),并且障礙期權(quán)合約靈活地表現(xiàn)了投資者的主觀意愿,因此深受投資者喜愛.在期權(quán)定價(jià)過程中,標(biāo)的資產(chǎn)價(jià)格的不確定性包括隨機(jī)性和模糊性,而一般的期權(quán)定價(jià)模型只考慮其隨機(jī)性,對(duì)模糊性卻研究甚少.本文建立的期權(quán)定價(jià)模型既考慮了標(biāo)的資產(chǎn)價(jià)格的隨機(jī)性,又考慮了其模糊性. 本文主要研究向下敲入、敲出看漲期權(quán)在模糊環(huán)境下的定價(jià)問題.首先,將到期日的股票價(jià)格模糊化,得到新的支付函數(shù).然后,運(yùn)用風(fēng)險(xiǎn)中性定價(jià)原理和Girsanov定理,推導(dǎo)股票價(jià)格服從幾何布朗運(yùn)動(dòng)時(shí),向下敲入、敲出看漲期權(quán)的定價(jià)公式.最后,進(jìn)一步研究股票價(jià)格服從跳擴(kuò)散過程時(shí),向下敲入、敲出看漲期權(quán)的模糊理論定價(jià).具體工作如下: (1)假設(shè)股票價(jià)格服從幾何布朗運(yùn)動(dòng),將到期日的股票價(jià)格用梯形模糊數(shù)表示,使得期權(quán)在到期日的損益模糊化.然后運(yùn)用風(fēng)險(xiǎn)中性定價(jià)原理和Girsanov定理,求解歐式看漲期權(quán)以及向下敲入、敲出看漲期權(quán)在模糊環(huán)境下的定價(jià)公式,并給出敲入、敲出期權(quán)與歐式期權(quán)價(jià)值之間的關(guān)系.最后通過數(shù)值試驗(yàn)分析期權(quán)價(jià)值與股票價(jià)格的關(guān)系以及新的定價(jià)模型的有效性,并與B-S定價(jià)公式進(jìn)行比較. (2)假設(shè)股票價(jià)格服從跳擴(kuò)散過程,運(yùn)用模糊理論將到期日的股票價(jià)格模糊化,再結(jié)合風(fēng)險(xiǎn)中性定價(jià)原理和Girsanov定理,研究歐式看漲期權(quán)以及向下敲入、敲出看漲期權(quán)在跳擴(kuò)散過程下的定價(jià)問題,得到了無窮級(jí)數(shù)形式的定價(jià)公式,并證明了該定價(jià)公式是收斂的.最后通過數(shù)值試驗(yàn)分析期權(quán)價(jià)值與股票價(jià)格的關(guān)系,并與跳擴(kuò)散過程下的一般定價(jià)公式進(jìn)行比較.
[Abstract]:Obstacle option is a path dependent option, and its income depends on whether the underlying asset price touches the barrier value in the holding period. The option gold of barrier option is lower than that of European option, and obstacle option contract flexibly expresses the subjective will of investors, so it is loved by investors. In the process of option pricing, the uncertainty of underlying asset price includes randomness and fuzziness, but the general option pricing model only considers its randomness, but there is little research on fuzziness. The option pricing model in this paper not only considers the randomness of underlying asset price, but also considers its fuzziness. This paper mainly studies the pricing of call option in fuzzy environment. Firstly, the stock price of maturity date is blurred and a new payment function is obtained. Then, by using the risk-neutral pricing principle and Girsanov theorem, the pricing formula of call option is derived when stock price is driven by geometric Brownian motion. Finally, this paper further studies the fuzzy theory pricing of call option when stock price spreads from jump to diffusion, knocks down and knocks out call options. The specific work is as follows: 1) assuming that stock price moves from geometric Brownian motion, the stock price on maturity date is expressed as trapezoidal fuzzy number, which makes the gains and losses of option on maturity date fuzzy. Then the risk neutral pricing principle and Girsanov theorem are used to solve the European call option and down knock in, and the pricing formula of call option in fuzzy environment is given, and the relationship between the value of call option and European option is given. Finally, the relationship between option value and stock price and the validity of the new pricing model are analyzed by numerical experiments, and compared with B-S pricing formula. (2) assuming the process of stock price diffusion from jump to diffusion, the stock price of maturity date is fuzzy by using fuzzy theory, and combining with risk neutral pricing principle and Girsanov theorem, the paper studies European call options and knocks down. In this paper, the pricing problem of call option in the process of jump diffusion is discussed, and the pricing formula of infinite series is obtained, and it is proved that the formula is convergent. Finally, the relationship between option value and stock price is analyzed by numerical experiments, and compared with the general pricing formula in the process of jump diffusion.
【學(xué)位授予單位】：中國(guó)礦業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F830.91;O159

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相關(guān)期刊論文 前2條

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2 韓立巖;周娟;;Knight不確定環(huán)境下基于模糊測(cè)度的期權(quán)定價(jià)模型[J];系統(tǒng)工程理論與實(shí)踐;2007年12期

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本文編號(hào)：1969363