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Strategies & Market Trends : The Final Frontier - Online Remote Trading
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To: Dan Duchardt who wrote (11100)1/7/2004 9:45:12 PM
From: Ira Player  Read Replies (1) of 12617
 
I did miss one thing in my post. Dividends. My analysis is done assuming no dividends. If there are dividends, there is incentive to exercise the option to capture the dividend stream. It is obvious that it will lower the value of the option relative to the dividend paying stock. Also, since the option must be exercised to obtain the stock and capture the dividend, the strike price will play a role in the value of the option. I do not have time to look at that issue now.

"In other words, the premium becomes a function of the probability of the option having intrinsic value someday instead of within a definite period of time."

The problem is, what is the premium for a time period of infinity?

Condition: There is a stock trading at 1 and you have 2 options that can never expire. One has a Strike Price (SP) of 0.50 and the other has a SP of 1.50. Since you own them, you cannot be forced out of the position. You always have them or can pass them on to your kids and their kids and ... infinity is a long time.

Choose your stocks ability to rise:

5% up per year for 94.38729 years stock is worth 100
4% up per year for 117.4170 years stock is worth 100
3% up per year for 155.7971 years stock is worth 100
2% up per year for 232.5535 years stock is worth 100
1% up per year for 462.8157 years stock is worth 100

All of these times are significantly less than Infinite. Is there any significant advantage to the option with a 0.5 SP over the one having a 1.5 SP?

1% after at least 94 years is not that great an advantage.

If you think 1% is significant, then how about looking at 1% up per year for 925.6316 years and the stock is worth 10000. Now it's only 0.01% different...

Obviously, at infinite time, the options with a 0.5 strike and the option with a 1.5 strike are identical and must have the same value.

If they have the same value, what is that value?

I'd argue that it is the value of the normally most advantageous SP, ZERO. An option to buy a stock at a SP of ZERO has no time premium because there is no leverage in the investment. There is no capital to put to other uses while you wait to exercise. You can exercise at any time without further payment. That's equivalent to owning the stock so the premium is equal to the stock price.

Ira
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