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Option Trading

Consider a stock priced at $30 with a standard deviation of .30. The risk-free rate is .05.
There are put and call options available at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost $2.15. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). Use this information to answer the following.


Suppose the buyer of the call sold the call two months before expiration when the stock price was $33. How much profit would the buyer make?

Suppose the investor constructed a covered call. At expiration the stock price is $27. What is the investor's profit? (3 marks)

If the transaction is closed out when the option has three months to go and the stock price is at $36, what is the investor's profit?


我觉得思路如下:
1、先用BSM模型求出到期前两个月这个时点的call option的payoff,然后结合期权费来算profit。
2、思路和上题类似,covered call为long stock+short call,所以算出stock的payoff,short call的payoff,再加上期初收入的期权费,就是整个的profit。貌似不需要BS公式了。
3、跟1一样。
不一定正确,供参考哈

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