本文關(guān)鍵詞：Esscher變換與期權(quán)定價　出處：《湖南師范大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 期權(quán)定價 Esscher變換 Esscher鞅測度 鞅方法

【摘要】：隨著中國經(jīng)濟(jì)的騰飛,中國金融業(yè)也在市場改革和對外開放中蓬勃發(fā)展,期權(quán)交易作為金融市場最重要的交易手段之一,它在中國金融市場上發(fā)揮的作用也越來越大,那么期權(quán)定價的重要性也就毋庸置疑. 關(guān)于對期權(quán)定價的求解有著很多不同的方法,而由于鞅方法的簡潔方便,利用鞅方法求解期權(quán)定價問題一直是人們研究的重點. Esscher變換是一個經(jīng)典的精算學(xué)計算工具,但自1994年Gerber-Shiu將其由精算領(lǐng)域引入數(shù)理金融領(lǐng)域以來,由于其方法簡單明了,應(yīng)用范圍廣泛,能夠很好地解決各類期權(quán)定價問題；同年他又引入了Esscher鞅測度,結(jié)合鞅方法能夠得出一些復(fù)雜模型的期權(quán)定價的解. 本文在前人的基礎(chǔ)上,對這兩種方法進(jìn)行了合理的提取,歸納,總結(jié)；從金融市場的角度綜述了鞅的概念和性質(zhì),利用Esscher變換和鞅方法研究了多個期權(quán)定價模型,并對上述的兩種方法采取了不同的模型進(jìn)行對比,得出了各自方法的優(yōu)劣性比較.最后利用Esscher鞅測度和鞅方法,計算出了幾個特殊的由Levy過程驅(qū)動的期權(quán)定價模型的顯示解.
[Abstract]:With the rapid development of Chinese economy, Chinese financial industry is booming in market reform and opening to the outside world. Option trading is one of the most important trading methods in financial market. As it plays an increasingly important role in China's financial markets, the importance of option pricing is beyond doubt. There are many different methods to solve the option pricing problem. Because of the simplicity and convenience of the martingale method, it is always the focus of people to solve the option pricing problem by using the martingale method. Esscher transform is a classical actuarial calculation tool, but since Gerber-Shiu introduced it into the field of mathematical finance in 1994, its method is simple and clear. It has a wide range of applications and can solve all kinds of option pricing problems. In the same year, he also introduced Esscher martingale measure, which combined with martingale method can obtain the option pricing solutions of some complex models. In this paper, on the basis of predecessors, the two methods of reasonable extraction, induction, summary; This paper summarizes the concept and properties of martingale from the perspective of financial market, studies several option pricing models by using Esscher transform and martingale method, and compares the two methods with different models. Finally, by using Esscher martingale measure and martingale method, the display solutions of several special option pricing models driven by Levy process are calculated.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F224;F832.5

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本文編號：1404926