题目

这道金融题怎么算?
A financial market consists of just two instruments,a stock and a cash bond.The model has 3 time steps,in which over each time step the stock price either increases by $20 or decreases by $10.The initial price of the stock is $120.If interest rates are zero,what is the cost of an American put with a maturity at the end of last period and a strike price of $132?What would be the cost of a European put with a maturity at the end of last period and a strike price of $132?Which of these two options is more expensive?Explain why.

提问时间：2021-04-01

答案

either ...or...在这里似乎代表两种情况发生的概率都是50％,否则无法计算.但貌似只能代表二者必有其一,概率不能确定吧?
但对于这道题目,必须用前面的解释.
然后就很简单了.只比前一道题目多了2步而已,无风险收益率是0,不用考虑货币时间价值.
初始股价120,第一期末股价到140和110的概率都是50％,第二期末股价到160的概率是25％、130的概率是50％、100的概率是10％,第三期末股价到180的概率是1/8、到150的概率是3/8、到120的概率是3/8、到90的概率是1/8.
权证到期日都是第三期末.
欧式权证只能在到期日行权,期初价格取决于第三期末的预期收益：3/8*（132-120）+1/8*（132-90）＝39/4.
美式权证可以在任意时间行权,期初价格取决于各时点预期收益最大值,对于该题,需要计算3个时点,即一、二、三期期末.容易算出第一期期末收益最大,为11；第二期期末最小,为9.
所以,美式权证期初价格为11.
美式权证贵.