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At the same time , the innovation of this paper is to work out the three kinds of pricing formulas of barrier options of the geometric average assets .

同时，本文的创新之处是将上式三个障碍期权的定价公式推广到资产几何平均情况下时的期权定价公式。

In Chapter 4, the pricing of Asian geometric average option under stochastic interest rates is studied, assuming CIR model for the interest rates. Asian option is strongly dependent with path, usually have a long duration, the movement of interest rates becomes more important in pricing such long-dated options. The CIR interest rate model not only considered the interest rate behavior has mean-reverting but also take into account that the fluctuation rate is direct proportion with the square root of its interest rate. Finally, the method of finite difference for the Asian geometric average option under CIR interest rate model is given.

第四章在利率满足CIR利率模型的假设下，研究了几何亚式期权的定价公式，亚式期权是强路经依赖性期权，通常有效期较长，在进行较长时期的投资时，利率的变化是非常重要的，CIR利率模型不仅考虑了利率行为具有均数回归的现象，而且还考虑其波动性的大小与利率大小的平方根成正比，最后给出了CIR利率模型下的几何亚式期权定价的有限差分法。

4Based on a fact that the price formula of Asian options can be transformed into that of vanilla European option when the time to maturity is less than or equal to the length of average, we skillfully obtain the analytical price formula for the option on the minimum or the maximum of two geometric average prices and generalize it to obtain the price formula of several average prices for the first time. We also apply the method of [121], which approximates the arithmetic average by the geometric average, to the pricing of opitons on the minimum or the maximum of two arithmetic average prices to obtain Its approximated price formula. Numerical results show that the approximated price is relatively accurate when the riskless interest rate is large or the option is in the money and the volatility of two underlying assets are high and its accuracy is a little reduced but still good when the dividends are considered. However, it is hardly affected by the sampling number.

我们基于观察到的一个事实即当离到期时间小于或等于平均期间时亚洲期权的价格可变换成普通的欧式期权的价格，从而巧妙地得到了两个几何平均价格的最小或最大值期权价格的解析公式，通过简单地推广，首次得到了多个几何平均时的价格公式；将[121]用于算术平均亚洲期权的定价方法推广到两个算术平均价格的最小或最大值期权，从而得到它的渐进公式，数值结果表明：渐进价格的准确性在无风险利率较大或期权为实值且两标的资产的波动率较小时较好，抽样的个数对它没有影响，但考虑红利时它稍有下降但仍较好。

Specially, we primary deals with the option pricing of Black-Scholes model with continuous dividend payments then get the call option and put option formulas: And the model of geometric average Asian options with fixed strike price then we get the call option formula: The relevant formulas about call option and put option,which are all identical with the classical ones.

其中，特别是对连续支付红利的欧式Black-Scholes期权定价模型求得其买权和卖权的定价公式分别为：此外，还对具有固定敲定价格的几何平均亚式期权的模型给出买权的定价公式：所得结果与用经典解法求得的定价公式完全一致。

3We obtain the analytical price formulas for vanilla, forward-start and in-progress fixed-strike and floating-strike continuous geometric average Asian options and a put-call parity under generalized Black-Scholes with time-dependent parameters by risk neutral valuation and properties of stochastic integration.

在依赖时间参数的推广的Black-Scholes模型下，利用风险中性定价及随机积分的性质，得到平凡、远期开始和进展中的固定和浮动执行价格的连续几何平均欧式亚洲期权价格的解析公式和一个平价关系。

N }' t+} Q+% l0 \5 0 E Similarly, Bridge and Belletti are much our more attacking full back options, and although I would normally advocate Cole and Ferreira in a Premiership game, we will need width if things get congested in the middle.

" {8 V3 d， o9 w， ^" F7 Q$ J； a 同样的，尽管我一般都提议让阿什利科尔和费雷拉打英超联赛，布里奇和贝莱蒂作为边后卫助攻能力要更强一些。

Do not file for bankruptcy without trying out the other options to get rid off your debts.

不立案试行破产无其他选择甩掉脱下自己的债务。

"It's very hard for me to sit on the bench, especially after what I've achieved and what I've done for the club," said Gilberto. If I'm still not playing much by Christmas, then there might be other options for me to look at seriously.

坐在板凳上对我来说是一件困难的事，特别是考虑到我已经取得的成就和为俱乐部所做的一切"，吉尔伯托表示，"如果到圣诞节的时候我还没有获得很多的出场机会，那我应该慎重考虑一下其它的选择了。

Gilding and putting it refers to the model options anodized and gilding on speed, temperature, pressure and other factors.

烫金适性，是指电化铝的型号选择以及烫金速度、温度、压力等因素之间匹配。

Scientific research in the field of anti-aging continues to give rise to new and promising treatment options.

在抗衰老方面的科学研究能持续的为这方面提供最新的、具有保障性的治疗方案。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。