【摘要】：本文主要研究在M.AVELLANEDA、A.LEVY和A.PARAS提出的不確定波動(dòng)率模型理論基礎(chǔ)上的期權(quán)定價(jià)問題。本文建立的模型主要是考慮具有路徑依賴的亞式期權(quán)在不確定波動(dòng)率模型下的定價(jià)問題。 我們假定股票價(jià)格的波動(dòng)率在兩個(gè)極值(σmin和σmax之間,但不確切知道的市場情形中衍生證券定價(jià)的計(jì)算問題。我們可以得出波動(dòng)率路徑在這樣一個(gè)界中變化的亞式期權(quán)的極值無套利價(jià)格能夠描述成一個(gè)非線性PDE(Partial Differential Equations)。在這個(gè)模型中“定價(jià)”的波動(dòng)率是根據(jù)值函數(shù)的凹凸性動(dòng)態(tài)的從兩個(gè)極值,σmin和σTmax,之間選取。本文給出基于單一股票模型的算術(shù)平均亞式期權(quán)的定價(jià)計(jì)算問題,并借助一個(gè)簡單的算法,即有限差分或三叉樹,來解這個(gè)問題。
[Abstract]:This paper mainly studies the option pricing problem based on the theory of uncertain volatility model proposed by M. AVELLANEDAA. Levy and A.PARAS. The model established in this paper mainly considers the pricing of Asian options with path dependence under the uncertain volatility model. We assume that the volatility of stock price is between two extreme values (蟽 min and 蟽 max, but not exactly known). We can conclude that the extreme value of an Asian option whose volatility path changes in such a bound can be described as a nonlinear PDE (Partial Differential Equations). In this model, the volatility of "pricing" is selected from two extremum, 蟽 min and 蟽 Tmax, according to the dynamic concave and convexity of value function. In this paper, the problem of arithmetic average Asian option pricing based on a single stock model is given, and the problem is solved by a simple algorithm, that is, finite-difference or tri-tree.
【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F224;F830.9

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本文編號：2253891