某个股票现价为$40。有连续2个时间步,每个时间步的步长为3个月,每个单位二叉树的股价或者上涨10%或者下跌10%。无风险年利率为12%(连续复利)。执行价格为$42的6个月期限的欧式看跌期权的价值为多少?
正确答案:
由题意可得,![](https://img.274949.com/Images/2020-04/08/i8jaj9tr.jpg)
则风险中性概率![](https://img.274949.com/Images/2020-04/08/urj446o7.jpg)
计算股价二叉树图的结果如下:
![](https://img.274949.com/Images/2020-04/08/t9mchxo0.jpg)
如上图,当到达中间终节点时,期权的损益为42-39.6=2.4;在最低的节点处,期权的损益为42-32.4=9.6。
欧式期权的价值为:
![](https://img.274949.com/Images/2020-04/08/i8jaj9tr.jpg)
则风险中性概率
![](https://img.274949.com/Images/2020-04/08/urj446o7.jpg)
计算股价二叉树图的结果如下:
![](https://img.274949.com/Images/2020-04/08/t9mchxo0.jpg)
如上图,当到达中间终节点时,期权的损益为42-39.6=2.4;在最低的节点处,期权的损益为42-32.4=9.6。
欧式期权的价值为:
![](https://img.274949.com/Images/2020-04/08/u5nn344r.jpg)
答案解析:有
![](/editor/images/201705/qrcode_for_gh_573e2a458573_258.jpg)
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