三叉树模型下期权定价的计算
发布时间：2018-10-05 15:23
【摘要】：本文主要研究在M.AVELLANEDA、A.LEVY和A.PARAS提出的不确定波动率模型理论基础上的期权定价问题。本文建立的模型主要是考虑具有路径依赖的亚式期权在不确定波动率模型下的定价问题。 我们假定股票价格的波动率在两个极值(σmin和σmax之间,但不确切知道的市场情形中衍生证券定价的计算问题。我们可以得出波动率路径在这样一个界中变化的亚式期权的极值无套利价格能够描述成一个非线性PDE(Partial Differential Equations)。在这个模型中“定价”的波动率是根据值函数的凹凸性动态的从两个极值,σmin和σTmax,之间选取。本文给出基于单一股票模型的算术平均亚式期权的定价计算问题,并借助一个简单的算法,即有限差分或三叉树,来解这个问题。
[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.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
本文编号：2253891
[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.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
【参考文献】
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