Time Value And Option Decay
All other things being equal, an option value decays in time. Consider an out-of-the-money OEX call with strike price 650 when the OEX is 630. Taking a nominal implied volatility of 25% and using an interest rate of 5%, the value of this call declines as expiration approaches. Following is a table showing this option’s value for trading days to expiration ranging from 60 down to 0:
| Trading Days |
Value |
|---|---|
| 60 | $25.20 |
| 50 | $21.98 |
| 40 | $18.54 |
| 30 | $14.85 |
| 20 | $0.58 |
| 10 | $5.50 |
| 0 | $0 |
At an OEX price of 630, this call has an intrinsic value of 0, so the above are also the time values (theoretical value minus intrinsic value) of the call at various times to expiration. Over the 10 days from day 60 to day 50, the call loses $4.22 in value, or about 42 cents per day. Over the last 10 days of the call’s life, from day 10 to expiration, it loses $5.50 in value, or about 55 cents per day. So over the final period it loses value faster than over an earlier period of the same length.
Every option, whatever the strike, whether it is in-the-money or out-out-the-money, exhibits this same pattern: the closer to expiration, the faster it decays. And it decays fastest in the final days, which aren’t shown here. Below is a table showing the values for an in-the-money call with strike price 600, together with the time values:
| Trading Days |
Value | Time Value |
|---|---|---|
| 60 | $51.95 | $21.95 |
| 50 | $48.87 | $18.87 |
| 40 | $45.57 | $15.57 |
| 30 | $42.01 | $12.01 |
| 20 | $38.03 | $8.03 |
| 10 | $33.65 | $3.65 |
| 0 | $30.00 | $0.00 |
With the OEX at 630 and a strike price of 600, this option has an intrinsic value of $30.00, and the time value shown at each time to expiration is just the theoretical value less $30.00. During days 60 to 50, this call loses $2.88 in value (and in time value), about 29 cents per day. And during the last 10 days, it loses $3.65 in value, about 35 cents or 36 cents per day, again at a rate greater than in the earlier period.
These option values are, of course, theoretical values and not prices. To say this another way, these values assume an implied volatility of 25%, remaining constant across the 60-day time period, and an OEX value of 600, remaining constant across the 60 day time period. Neither of these is even remotely probable. So the variability of the OEX and of the implied volatility must both be considered. Every trader is familiar with the variability of the OEX, either intuitively or by using a volatility measure. The variability of the implied volatility is, however, less understood and I will discuss that at greater length in future commentaries and articles.