Table 242

Gains and Losses in One Year. Original investment: purchase a one-year call option with a strike price of $105 for $15. Invest $100 in risk-free asset paying 5 percent. Total cost is $115.

What does this strategy accomplish? Once again, we will create a table to illustrate your gains and losses. Notice that in Table 24.2 your $100 grows to $105 based on a 5 percent interest rate. If you compare Table 24.2 to our previous Table 24.1, you will make an interesting discovery. No matter what the stock price is one year from now, the two strategies always have the same value in one year!

The fact that the two strategies always have exactly the same value in one year explains why they have the same cost today. If one of these strategies were cheaper than the other today, there would be an arbitrage opportunity involving buying the one that's cheaper and simultaneously selling the one that's more expensive.

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