双货币模型下几何平均亚式期货期权定价

发布时间：2018-09-01 17:00

【摘要】：本文主要研究的问题是几何平均亚式期权的定价.为了使研究的问题更具实际应用价值,此类亚式期权的标的资产假定为期货合约,即亚式期货期权. 文章采取了两种方法分别求解几何平均亚式期货期权定价问题.(一)偏微分方程方法.该方法主要是通过Δ对冲技术找到单货币市场模型下的金融衍生品价格满足的偏微分方程,并通过合理的变量替换,将求解复杂方程问题化为求解热传导方程的Cauchy问题,进而得到该金融衍生品的定价公式.本方法主要引自姜礼尚[1],但结果有所不同.(二)鞅测度分析方法.应用该方法时,要在不同的市场模型下,即单货币市场模型和双货币市场模型,分别考虑几何平均亚式期货期权的定价问题.此方法的关键就通过Girsanov定理找到一个等价鞅测度,使得标的资产价格的贴现过程在该测度下为鞅过程.然后在该测度下应用资产定价基本定理求出可交易资产的收益期望贴现.
[Abstract]:The main problem of this paper is the pricing of geometric average Asian options. In order to make the study more practical value, the underlying assets of this kind of Asian options are assumed to be futures contracts, that is, Asian futures options. In this paper, two methods are adopted to solve the geometric average Asian option pricing problem. (1) partial differential equation method. This method is mainly to find the partial differential equation of the price of financial derivatives under the single money market model by means of 螖 hedging technique, and to solve the complex equation problem into the Cauchy problem of solving the heat conduction equation by reasonable variable substitution. Then the pricing formula of the financial derivatives is obtained. This method is mainly quoted from Jiang Lieshang [1], but the results are different. (2) martingale measure analysis method. When applying this method, the pricing problem of geometric average Asian futures options should be considered under different market models, that is, single money market model and double money market model. The key of this method is to find an equivalent martingale measure by Girsanov theorem so that the discount process of the underlying asset price is a martingale process under the measure. Then the expectation discount of tradable assets is obtained by applying the basic theorem of asset pricing.
【学位授予单位】：哈尔滨师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

【共引文献】