Intrinsic value and time value
1. The idea
An option’s price, the premium of Level 1, has two parts. The intrinsic value is the option’s payoff if it expired now:
\[ \text{call: } \max(S_0 - K,\ 0), \qquad \text{put: } \max(K - S_0,\ 0), \]
where \(S_0\) is the share price today and \(K\) the strike price. It is the payoff of Level 1, with today’s share price in place of the price at expiry. The rest of the price is the time value:
\[ \text{time value} = \text{price} - \text{intrinsic value}. \]
An example. A share trades at $50, and a six-month European call with a strike price of $45 costs $7.06. Its intrinsic value is \(\$50 - \$45 = \$5\), so its time value is \(\$7.06 - \$5 = \$2.06\): what the chance of a higher share price by expiry is worth.
An option is in the money when its intrinsic value is positive, at the money when the share price equals the strike price, and out of the money when exercising would lose. An option at or out of the money has no intrinsic value: all of its price is time value. At expiry the time value is zero, and the price is the payoff.
An American option can be exercised at any time, so it is worth at least its intrinsic value: its time value is never negative. A European option can be worth less. The holder of a European put deep in the money receives the strike price only at expiry, and waiting for it costs interest. With a share at $30, a one-year European put with a strike price of $50 costs $17.12 at a 6% rate and 20% volatility, less than its $20 intrinsic value: its time value is −$2.88. An American put with the same terms is worth exactly $20, because it would be exercised at once. In the binomial trees of Level 4, an American put is exercised early at the nodes where its intrinsic value is more than the value of keeping it.
2. Try it
If an answer is wrong, we will see what went wrong and how to fix it.
3. The price on a chart
First, the put’s intrinsic value.
Now move today’s share price. The gap between the two lines is the time value: largest near the strike price, where it is least clear whether the put will end in the money, and smaller deep in or out of the money.
4. One worked example, then your turn
In the worked example, we split the price of a call in the money.
Now one with hints, one step at a time.
And one on your own.
5. Practice
Each question has new numbers. You master the skill when you get three right in a row, with at least one right answer for a call and one for a put. You can always open the solution, but then that question does not count.
6. Coming back to it
When you have mastered a skill, it comes back on the start page for a short review after 1 day. After each right answer the next review comes later: after 3, 7, 14 and then 30 days. After a wrong one, the reviews start again at 1 day.
This skill: