I recommend using the “Pricing of American Options on Non-Dividend Paying Stocks spreadsheet I uploaded earlier today to help you solve Problem Set 8. It would also be worthwhile to spend a few minutes reviewing the Early Exercise of American Call and Put Options on Non-Dividend Paying Stocks lecture note before working on this problem set.
Upon opening the spreadsheet, you will likely see the following security alert due to the spreadsheet’s embedded Visual Basic code. If you trust the source of this file (hopefully you do! :-)), you will enable macros to proceed any further:
Since no dividends are considered in any of these spreadsheets, you’ll obtain the not-surprising result that the value of the American call is the same as that of the European call in all three cases. However, in-the-money American puts may have higher values than otherwise identical European puts.
Feel free to use this spreadsheet when you are working on problem set 8, but DON’T turn the spreadsheet in as part of your PDF; instead, explain the reasons for the results you obtain in plain English. You can solve both Problems 1 and 2 using the 2-period put worksheet that is included in this spreadsheet. The trial-and-error aspect of Problem 2 can be accomplished by using Solver.
Lastly, I would like to note that it is also feasible to solve Problem 2 analytically – no calculus – just basic algebra. Extra credit will be awarded to anyone who successfully does so.