They could be classified as call options , put options , american options , european options , financial options , real options and so on according to different benchmarks 按不向标准，期权可分为看涨期权和看跌期权、美式期权和欧式期权、金融期权和实物期权等。
The article detailedly researches the characters of the american option and the principle of forming its value , and offers a new , very fast and accurate numerical pricing method of the american put option ? " fft " method 本文深入剖析了美式期权特点及其价值形成机理，提出了一种新的快速的高精度的美式看跌期权定价的数值方法?快速傅里叶变换法。
Furthermore , i also research on the problem of american option pricing when there being no transact cost using the property of martingale process . and i give correspondent buying price , selling price and some conclusions 另外，本文还利用鞅过程的性质讨论了当不存在交易成本时美式期权的定价问题，并给出了相应的买价和卖价公式以及相关的一些结论。
Just because of these reasons , cox , ross and rubinstein put forward the foundation of the algorithm , solving the pricing problem of the american option , which is significant to the development of the pricing theory of the option and option products 正是因为这些原因， 1979年， cox , ross和rubinstein发表了《期权定价：一种简化方法》的论文，提出算法的基础，解决了美式期权的定价问题，对期权定价理论和期权产品的发展具有重要意义。
In the 3rd section we introduce how to use mathematical model to study financial problems , whose assets running on mixed jump - diffusion process , first we get the famous non - linear feynman - kac formula by fbsde , then let the solution of the bsde be a investor ' s utility function , and it ' s the so - called recurse utility function . second , we can prove that this utility function is a continue viscosity solution of the variation inequality which we get above , and we get the comparison theory . third we can use the result to financial market to study the optimal consumption and portfolio problem or evaluate the american option 第三章介绍了利用金融资产价格运行基于复合跳跃? ?扩散过程的数理模型来研究金融经济问题，通过结合运用正倒向随机微分方程，推导得到著名的非线性feynman - - kac公式，并且将相应的倒向随机微分方程的解记为投资者的值函数，这也就是通常所说的效用值函数；接着我们可以证明此效用值函数为某一偏微积分变差不等式的连续粘性解，并且得到了比较原则；这些结果可以应用到金融领域用于消费投资组合的选择或是美式期权的估值。
Chapter two analyses the problems that fixes the convertible bond price in our country . many listed companies generally use european option price at the formula , namely black - scholes model . because of the multiple option nature and the american option nature contained in the transferable bond , black - scholes model ca n ' t be applied mechanically to fix the price of the convertible bond 第二章分析了可转换债券定价在我国所存在的问题，即从我国上市公司发行可转换债券的公告来看，一般都使用欧洲期权定价公式，这是由1973年fischerblack和myronscholes在其《期权和公司负债定价》的著名论文中所建立起的欧式期权定价解析表达式，即black - scholes模型而成。
