Mathematical Finance Question: Verify the results in Example 10.7. Erample 10.7.
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Question
Mathematical Finance Question:
Verify the results in Example 10.7.
Erample 10.7. We price an American call option on such a dividend-paying stock. Suppose there are inputs S(0,0) 100, D1-0, D2-1, D3-0 and D4 Thus, with 1, R = exp(0.01), u = exp(oVit) = exp(0.15), d = 1/u. 0 D2 = 0.81873075 Do R2 D2 =-= 0.90483742 D, D2 =0 D1 = 0. The American call price is $45.67. In this case notice that the European and American call prices are the same, and there is no early exercise. With 134 10 Dividends an American put option, there are always situations where it is optimal to exercise early; with the American call, as here, there may not be optimal choices to exercise early.Explanation / Answer
Thank you for the question.
Going by the scenario, If you are confident that the stock is going to grow up continuously, it is ideal to wait. But, If you think the stock has touched its peak, then shorting the stock in the open market platform seems to be the best bet. However, if the shorted stock continues to climb, you can always use the call option to cover your position.
Now let us assume what will happen if the stock price falls below your strike price, then the best option for you will be to let the option expire and cover your position.
The ability to choose the buying price (strike vs market) when covering a short sale that makes the option valuable. Fortunately, you can do the same thing with a European option.
To end, American option gives you no added value over the European option. So, there is no benefit to exercising an American call option early.