Options course · Lesson 5 of 10
Time decay speeds up as expiration gets near.
An option loses value every day, and the loss gets faster at the end. Volatility moves the price too, and it can move it without any change in the stock.
The clock costs more near the end
| Days to expiration | 100 call | 110 call | Theta of the 100 call, per contract a day |
|---|---|---|---|
| 90 | $5.43 | $1.89 | -$3.27 |
| 60 | $4.36 | $1.11 | -$3.90 |
| 30 | $3.02 | $0.35 | -$5.30 |
| 14 | $2.03 | $0.05 | -$7.52 |
| 7 | $1.42 | $0.00 | -$10.41 |
| 1 | $0.53 | $0.00 | -$26.65 |
The table holds the stock at $100 and changes only the time. The 100 call loses $1.07 a share in its first 30 days, from 90 days to 60. It loses $3.02 in its last 30 days. The cost of time is almost three times larger at the end.
Time value grows with the square root of time, not in proportion to it. So each day near the end costs more than a day far from it. With one day left, theta is -$26.65 a contract, against -$3.27 with 90 days left.
Options out of the money go to zero
The 110 call costs $1.89 with 90 days left. With 14 days left and the stock still at $100, it is worth $0.05. With 7 days left, its price rounds to $0.00.
Volatility sets the price
| Implied volatility | 100 call | 110 call |
|---|---|---|
| 15% | $3.47 | $0.49 |
| 25% | $5.43 | $1.89 |
| 35% | $7.39 | $3.63 |
| 45% | $9.35 | $5.50 |
A rise in volatility from 25% to 35% adds $1.96 to the 100 call, which is 36%. The same change adds $1.74 to the 110 call, which is 92%. In percent, options out of the money react more to volatility.
The reverse is also true. If implied volatility falls from 35% to 25%, the 100 call loses $1.96 with no change in the stock. A buyer can lose money on a call even when the stock does not fall.
The expected move
Volatility also tells you how far the stock can move. A one standard deviation move over 90 days is the stock price, times the volatility, times the square root of the time in years. For our stock, that is $100 times 25% times the square root of 90/365, or $12.41.
In the model, the stock ends within $12.41 of $100 in 68% of cases. So a larger move happens in about one case in three.
Key points
- Time decay is slow at first and fast at the end.
- A rise in implied volatility helps the buyer. A fall helps the seller.
- In percent, options out of the money lose value fastest and react most to volatility.
Sources
- Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 1973, for the model that gives every price in this course.