Option value: intrinsic value, time value and implied volatility

What you will learn

• How to calculate intrinsic value and time value for calls and puts
• Which factors raise or lower an option's price
• What implied volatility (IV) is and how it differs from historical volatility
• How to turn implied volatility into a rough expected price range

Explanation

An option premium has two parts: Premium = intrinsic value + time value.

Intrinsic value is what the option would be worth if exercised now:

• Call: max(S − K, 0)
• Put: max(K − S, 0)

Here S is the underlying price and K the strike. Intrinsic value is never negative. Only in-the-money options have intrinsic value.

Time value (also called extrinsic value) is the rest: premium − intrinsic value. It is what buyers pay for the chance that the option becomes more valuable before expiry. Out-of-the-money options consist only of time value. At expiry time value is zero.

What drives the premium

Time value is usually largest for at-the-money options, because their outcome is most uncertain. Deep in-the-money and far out-of-the-money options have little time value.

Implied versus historical volatility

Volatility measures how strongly a price fluctuates, expressed as an annualised standard deviation of returns. Historical volatility is calculated from past prices. Implied volatility is the volatility number that, put into an option pricing model such as the Black-Scholes model, reproduces the current market price of the option. IV is therefore the market's price for uncertainty, not a measurement of the past and not a guaranteed forecast.

Traders often compare options by IV instead of by euro price, because IV removes the effect of different strikes and expiries. A high IV means options are expensive relative to the model. IV often rises before known events such as earnings reports and often falls sharply after them (sometimes called "IV crush"). A buyer can be right about the direction and still lose because IV falls.

From IV to an expected range

A common rule of thumb for a one standard deviation move:

Expected move ≈ S × IV × √T, with T = time in years.

Under the simplified model assumption of normally distributed returns, the price stays inside this range about 68% of the time. Real markets have more extreme moves than this model assumes, so treat the range as an estimate.

Worked example

Hypothetical example: a share trades at €100. Options expire in 3 months (T = 0.25). The quoted premiums below were calculated with a pricing model at 25% IV and zero interest, and rounded. No fees.

The ATM call has the highest time value (€5.00). With a multiplier of 100, it costs €500, all of which is time value and disappears if the share is exactly at €100 at expiry.

Expected move: €100 × 0.25 × √0.25 = €100 × 0.25 × 0.5 = €12.50. The rough one standard deviation range for the next 3 months is €87.50 to €112.50. The market is pricing a move of this size; it is not saying in which direction.

Common mistake

Practice activity

Hypothetical: a share trades at €40. One month to expiry. Premiums: put K = €45 at €5.40; call K = €35 at €5.25; call K = €45 at €0.40. IV = 40%.

1. Calculate intrinsic value and time value for each option.
2. Which option contains only time value?
3. Estimate the one standard deviation expected move over one month (T = 1/12) and the resulting range.

Key takeaways

• Premium = intrinsic value + time value; time value is zero at expiry.
• At-the-money options usually carry the most time value.
• Implied volatility is the market's price of uncertainty, backed out of option prices.
• Expected move ≈ S × IV × √T gives a rough range, not a prediction of direction.

Next step

In the next lesson you will draw the payoff profiles of long and short calls and puts at expiry and read maximum profit, maximum loss and break-even from them.