What drives an option’s price

A call pays only if the price ends above the strike. So anything that makes a high finish more likely, or more valuable, makes the call worth more today; a put works the other way round. Six things matter: the share price, the strike, the time left, how much the price swings, interest rates and dividends.

A higher share price lifts a call and lowers a put. A higher strike does the opposite: paying more to buy makes a call worth less, and selling for more makes a put worth more. With a share at 100, the 90 call is worth more than the 110 call, and the 110 put more than the 90 put.

Picture two shares at 100: one barely moves, the other often swings 20% either way. An option on the jumpy share has more chance of a big payoff, and it can never lose more than its premium. So bigger swings raise the value of calls and puts alike. How much a price swings, as a yearly %, is its volatility.

Nobody knows how much a price will swing in future. So traders work backwards: they take an option’s market price and find the volatility that explains it. That figure is implied volatility, and options are usually quoted in it. When markets fall and fear rises, implied volatility usually jumps, so options get dearer.

More time gives the price longer to move, so a longer-dated option is usually worth more, call or put. But value grows with the square root of time, not with time itself: four times as long costs about twice as much. A one-year option is worth roughly twice a three-month one.

Higher interest rates lift calls and lower puts: a call holder pays the strike later and can earn interest meanwhile, while a put holder receives it later. A dividend does the reverse: the share price drops by the dividend when it is paid out, which hurts calls and helps puts. Both effects are small for short-dated options.

For an option struck at today’s price (at the money), a handy estimate is: value ≈ 0.4 × price × volatility × √time, with volatility as a decimal and time in years. A share at 100 with 20% volatility gives a one-year option of about 0.4 × 100 × 0.20 × 1 = 8.

The rule is a shortcut for the Black–Scholes model, the standard formula that turns the six inputs into a price; for the example above it gives 7.97 rather than 8. It assumes prices never jump and volatility never changes. Neither is true, so traders use it as a common language: they agree a volatility, and the model gives the price.

Some options, called American, can be used on any day up to expiry; European ones only at expiry. Using a call early is rarely wise: you pay the strike sooner and throw away its time value, so selling the call is better. Using it early can pay for a put deep in the money, or for a call just before a large dividend.