發(fā)布時(shí)間：2018-12-15 21:42

【摘要】：期權(quán)是重要的衍生工具之一,期權(quán)的核心問(wèn)題是期權(quán)的定價(jià)問(wèn)題.近年來(lái),為了與金融市場(chǎng)實(shí)際情況更好的吻合,滿(mǎn)足更多投資者的需求,人們逐步放寬了Black-Scholes模型最初的假設(shè).許多學(xué)者考慮了在期權(quán)有效期內(nèi)標(biāo)的資產(chǎn)有紅利支付的歐式期權(quán)的定價(jià)公式,但相關(guān)的美式期權(quán)的定價(jià)研究較少.本文考慮當(dāng)標(biāo)的資產(chǎn)在期權(quán)有效期內(nèi)有離散紅利支付時(shí),美式看漲期權(quán)的定價(jià)公式. 首先,為了給出美式看漲期權(quán)的解析公式,引入了三種模型.模型1假設(shè)凈紅利股票價(jià)格,即股票價(jià)格減去未來(lái)紅利的現(xiàn)值,服從幾何布朗.模型2假設(shè)累積紅利股票價(jià)格,即股票價(jià)格加上己付紅利的現(xiàn)值,服從幾何布朗運(yùn)動(dòng).模型3是利用泰勒展開(kāi)把離散紅利近似轉(zhuǎn)化為連續(xù)紅利率,從而使得在到期日的股票價(jià)格服從對(duì)數(shù)正態(tài)分布. 其次,研究利率是常數(shù),且標(biāo)的資產(chǎn)在期權(quán)有效期內(nèi)有離散紅利支付時(shí),美式看漲期權(quán)的價(jià)格.利用風(fēng)險(xiǎn)中性測(cè)度定價(jià)原理得到了價(jià)格的解析公式. 最后,討論當(dāng)利率服從Vasicek模型時(shí),相應(yīng)的美式期權(quán)的定價(jià)公式.利用等價(jià)鞅測(cè)度變換及Girsanov定理得到價(jià)格的解析公式.
[Abstract]:Option is one of the important derivatives, the core problem of option is option pricing. In recent years, in order to better match the actual situation of financial markets and meet the needs of more investors, people have gradually relaxed the initial assumptions of the Black-Scholes model. Many scholars have considered the pricing formula of European option with dividend payment of the underlying asset during the term of validity of the option, but there is little research on the pricing of the American option. This paper considers the pricing formula of American call option when the underlying asset has discrete dividend payment during the period of validity of the option. Firstly, in order to give the analytic formula of American call option, three models are introduced. Model 1 assumes the net dividend stock price, that is, the stock price minus the present value of the future dividend, from geometric Brown. Model 2 assumes that the cumulative dividend stock price, that is, the stock price plus the present value of the pay-as-you-go dividend, is governed by geometric Brownian motion. Model 3 uses Taylor expansion to approximate the discrete dividend to a continuous red interest rate, so that the stock price at maturity date from the logarithmic normal distribution. Secondly, we study the price of American call option when interest rate is constant and the underlying asset has discrete dividend payment during the term of option. The analytical formula of price is obtained by using the pricing principle of risk neutral measure. Finally, the pricing formula of American option is discussed when interest rate is based on Vasicek model. By means of equivalent martingale measure transformation and Girsanov theorem, the analytical formula of price is obtained.
【學(xué)位授予單位】：河北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：F832.5;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 蔡華;苗杰;;隨機(jī)利率下有紅利支付的跳擴(kuò)散模型的期權(quán)定價(jià)[J];昌吉學(xué)院學(xué)報(bào);2007年03期

2 李莉英,張q，

本文編號(hào)：2381339