本文關(guān)鍵詞：雙貨幣模型下資產(chǎn)價(jià)格帶跳的期權(quán)定價(jià)　出處：《哈爾濱師范大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 跳躍模型 泊松過(guò)程 Girsanov定理 等價(jià)鞅測(cè)度 △-對(duì)沖

【摘要】：本文主要研究雙幣種模型下資產(chǎn)價(jià)格帶跳的期權(quán)定價(jià)問(wèn)題,當(dāng)金融市場(chǎng)中風(fēng)險(xiǎn)資產(chǎn)的價(jià)格出現(xiàn)跳躍的時(shí)候,原有的Black-Scholes模型已經(jīng)不再適用.文中討論了歐式期權(quán)及美式期權(quán)的定價(jià). 本文中歐式期權(quán)的定價(jià)是在風(fēng)險(xiǎn)資產(chǎn)價(jià)格的跳躍服從Poisson過(guò)程且跳躍幅度為常數(shù)的假定條件下,利用多因子的Girsanov定理及資產(chǎn)價(jià)格帶跳的Girsanov定理,構(gòu)造出與原市場(chǎng)測(cè)度P等價(jià)的測(cè)度Q并且證明了測(cè)度Q是風(fēng)險(xiǎn)中性的,進(jìn)而運(yùn)用期權(quán)定價(jià)的鞅方法,得出模型下歐式期權(quán)定價(jià)的顯示表達(dá)式. 美式期權(quán)的定價(jià)則不能得到顯式表達(dá)式,為計(jì)算簡(jiǎn)便,模型與歐式期權(quán)相比稍有變化,但本質(zhì)相同.由于單個(gè)風(fēng)險(xiǎn)資產(chǎn)的跳躍對(duì)于整個(gè)市場(chǎng)的影響是微乎其微的,因此,需要討論資產(chǎn)價(jià)格的跳躍風(fēng)險(xiǎn)是否被計(jì)算在期權(quán)價(jià)格之中,進(jìn)而采取不同的-對(duì)沖策略,通過(guò)期權(quán)定價(jià)的偏微分方法,得到美式期權(quán)價(jià)格所滿足的自由邊界問(wèn)題. 當(dāng)資產(chǎn)價(jià)格發(fā)生跳躍或其他突發(fā)事件發(fā)生時(shí),可以用此模型來(lái)對(duì)沖風(fēng)險(xiǎn),具有一定的現(xiàn)實(shí)意義.
[Abstract]:This paper mainly studies the option pricing problem of asset price with jump under the dual currency model, when the price of risky assets jumps in the financial market. The original Black-Scholes model is no longer applicable. The pricing of European and American options is discussed in this paper. In this paper, the pricing of European options is under the assumption that the price of risky assets jumps from the Poisson process and the jump amplitude is constant. By using the Girsanov theorem of multiple factors and the Girsanov theorem of asset price with jump, we construct measure Q which is equivalent to the original market measure P and prove that measure Q is risk-neutral. Then, using the martingale method of option pricing, the display expression of European option pricing under the model is obtained. The pricing of American option can not get an explicit expression. In order to calculate easily, the model is slightly different from that of European option. However, the essence is the same. Because the jump of individual risk assets has little effect on the whole market, it is necessary to discuss whether the jump risk of asset price is calculated in the option price. Then we adopt different hedging strategies and obtain the free boundary problem of American option price by using the partial differential method of option pricing. This model can be used to hedge the risk when the asset price jumps or other emergencies occur, which has certain practical significance.
【學(xué)位授予單位】：哈爾濱師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.9;F224

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本文編號(hào)：1367243