Six factors that move an option's value

Which factors drive an option’s value, and which way?

Six factors set an option’s value: the value of the underlying , the exercise price , the time to expiration , the risk-free interest rate , the volatility of the underlying , and any income from the underlying or carrying costs of owning it. The exam asks for the direction of each. This is the most tested table in the topic.

Increase in…	Call value	Put value	Why, in one line
Underlying price S	↑	↓	calls pay S − X, puts pay X − S
Exercise price X	↓	↑	same payoffs, other side
Time to expiration	↑	usually ↑ (can ↓)	more time, more chance of a big move; but a deep in-the-money (ITM) put waits longer to receive X
Risk-free rate r	↑	↓	higher r lowers the present value (PV) of X, written PV(X): good for the payer of X (call), bad for the receiver (put)
Volatility	↑	↑	more upside, downside still capped at the premium
Income (dividends, coupons, convenience yield)	↓	↑	the option holder does not receive it; the asset’s price drops when paid
Carrying costs (storage, insurance)	↑	↓	owning the asset is costlier, so the right to buy later is worth more

An increase in a factorall else equal, European options

• Opposite effect on calls and puts Memorize one gains, the other loses
  • Underlying price Memorize call up, put down
  • Exercise price Memorize call down, put up
  • Risk-free rate Memorize call up, put down
  • Income on the underlying Memorize call down, put up
  • Carrying costs Memorize call up, put down
• Same effect on calls and puts Memorize both gain
  • Volatility Memorize both up, for certain
  • Time to expiration Memorize call up; put usually up, can fall when deep ITM with high rates

Exam tip Anchor on S and X: a call likes a high S and a low X, and a put is the mirror. Then ask whether each other factor acts like a higher S for the call (rate, carrying costs) or like a lower S (income).

Why do the underlying and the exercise price push calls and puts in opposite ways?

A call pays S − X and a put pays X − S, so a higher S helps the call and hurts the put, and a higher X does the opposite. Unlike a forward, the option’s value is not a straight line in S. The more likely exercise is, the more sensitive the value is to S. A forward changes one-for-one with the underlying at every price.

Why does volatility help both calls and puts?

Memorize

Volatility of the underlying measures how widely the price may spread. A wider spread raises the chance of a large payoff, while the bad outcomes cost the holder nothing extra: the option just expires worthless. So both calls and puts gain, and a rise in volatility raises time value.

How does the risk-free rate move option values?

The rate works through the present value of the exercise price. A higher r lowers PV(X). A call’s exercise value, S − PV(X), rises. A put’s exercise value, PV(X) − S, falls. The rate does not directly change time value.

When does more time not help a put?

Memorize

More time usually raises both options, because there is more chance of a big move and the holder keeps only the favorable side. A call on an asset with no income always gains from more time: the upside is unlimited and the downside is the premium.

A European put is the exception. Its payoff, close to X − S, is received only at expiration, so a longer wait lowers the present value of that payoff. For a deep-in-the-money put at a high interest rate, that effect can win and a longer life lowers the value.

How do income and carrying costs affect options?

The owner of the underlying receives income (dividends, coupons, convenience yield); the owner of an option does not. Income lowers the underlying’s price when paid and so lowers a call’s value and raises a put’s value. Carrying costs such as storage and insurance work the other way: owning the asset costs more, so the right to buy it later is worth more and the right to sell it is worth less.

Go deeper Why the exercise value term carries the interest rate effect

The risk-free rate is the opportunity cost of holding the asset instead of cash. In the exercise value it appears only inside PV(X). Income and carrying costs enter the same way they do in forward pricing: income lowers the cost of carry, and storage costs raise it. A call behaves like a long forward on the upside, so whatever raises the forward price raises the call and lowers the put.

Go deeper Implied volatility

Of the six factors, volatility is the only one you cannot observe. Traders therefore take an option’s market price and work backward to the volatility it implies. That implied volatility is the market’s read on future risk, and it feeds back into how options are quoted.