改变真实概率会改变期权价吗
A stock worth $ today
题目详情
A stock worth $50 today will be worth either $60 or $40 in three months, with equal probability.
The value of a three-months at-the-money (ATM) put on this stock is $4.
Does the value of the three-months ATM put increase or decrease, and by how much, if the probability of the stock going up to $60 were 75% and the probability of the stock going down to $40 were 25%?
解析
在无套利定价框架下，期权价格由风险中性测度下的期望确定，而不是由“真实世界概率”直接决定。
若标的当前价格 、上下行幅度（）以及利率（此题取 0）不变，则风险中性概率由无套利条件确定，不随真实概率改变，因此期权价格不变。
题目给出 ATM put 价格为 4，那么把“上涨概率从 50% 改为 75%”并不会改变风险中性定价：