离散分红下障碍期权的间接级数展开定价方法

Indirect Series Expansion Method for Pricing Barrier Options with Discrete Dividend Payments

人们投资股票市场的最大动力,除了从股票本身的升值中获利,还包括收益分红.提出了带有离散分红的障碍期权的一种新型的近似方法,以向上敲出看涨障碍期权为例,固定分红的次数,通过泰勒级数展开得到关于关键变量的仿射函数,给出了一个只带有一维积分的定价公式,提高了计算速度.该方法还可以用于回望期权等其它衍生品的定价,对在市场上进行期权交易有一定指导意义.

The incentive for people to invest in stock market is receiving dividend payments,in addition to gaining appreciation of the stock value itself.A new approach has been presented for pricing barrier options with discrete dividend payments,which take up-and-out call option as an example and fix the amount of the discrete dividend.An affine function of key variables is obtained through Taylor series expansion.A new approximation formula with only one-dimensional integrals involved has been derived.The method improves computing speed and can be applied to pricing other derivatives,such as look-back options and so on,which has instructional significance for trading options in real markets.