## Time Value

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There are some fascinating mathematics behind options. One of those interesting properties of options is the way they relate stock prices, option time value formula and dividends. If we know the prices for options on a stock, we can estimate from those prices what the next dividend payment is likely to be.

This is not due to any mystical power of options prices; it is just because the option market builds an estimate of dividends into the price of options, and they are usually pretty close in that estimate. If we know how, we can tease it out. If the option is in the money, it has intrinsic value equal to the amount by which it is in the money. If out of the money, it has no intrinsic value.

Here are some examples: In addition to its intrinsic value if it has anyan option may also have time value. Here is that table again, with option prices and time value added:. Notice that in this example, the Time Value for the Call option at each strike is equal to the time value for the Put option at the same strike.

In a certain kind of world this relationship would always hold true. Where the stock is now is where it has the greatest probability of being at any date in the future.

The farther away from its current price the stock has to move to reach another strike, option time value formula less chance there is that it will happen and therefore the less time value. That is, as I said earlier, if we lived in a certain kind of world.

That would be a world where option time value formula rates were option time value formula zero and stocks never paid dividends. If either non-zero interest or dividends do exist, then they are accounted for in option time value formula option prices. Think of it this way: This is not the most elegant formal description of interest in options, but it gives you option time value formula idea: Knowing the T-bill rate, the strike price, and the time to go, we can calculate how much interest could have been earned in that time.

Finally, we come to dividends. When a stock price drops for any reasoncall prices go down and put prices go up. The total of the option time value formula in the call and the increase in the put at the same strike adds up to the drop in the stock. And, with this piece of information we have a way to determine how much a dividend is likely to be. If an option has T days to go:.

We can easily see what the time value is for both the put and call, and we can easily calculate the interest amount; so the expected dividends can be calculated. Here is a real-life example: SPY was scheduled to pay a dividend on December It had options in whose lifetime this would occur which were due to expire 30 days out, on December Now we have what we need option time value formula plug into our formula.

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