FRM Exam Part I · Properties of Options

Factors Affecting Option Prices: Effect on Calls and Puts

Updated 11 October 2026 · Fact-checked

Six factors drive option prices: stock price, strike price, time to expiry, volatility, risk-free rate and dividends. Calls gain when the stock rises; puts gain when it falls. Higher volatility raises both. Higher rates help calls and hurt puts. Dividends hurt calls and help puts. Time usually helps, except for some European options.

Understand Factors Affecting Option Prices

An option's value has two parts: intrinsic value (what you would get if you exercised now) and time value (the extra you pay for the chance of a better outcome). Each factor changes one or both parts.

Start with the stock price and strike. A call pays max(S − K, 0), so it gains when S rises or K falls. A put pays max(K − S, 0), so it gains when S falls or K rises. That is why the two move in opposite directions for these two factors.

Volatility is different. An option holder keeps the upside but is protected from the downside, because the payoff cannot go below zero. A wider range of outcomes therefore adds value to both calls and puts. Volatility raises both.

Time to expiry gives more chance for the stock to move. For American options, a longer life never lowers value, since the holder can exercise early anyway. For European options it is usually true, but not always. A deep in-the-money European put can be worth less with more time, because you must wait for the strike to be paid. A European call on a stock paying a large dividend before the shorter expiry can also be worth less with more time.

The risk-free rate and dividends work through the stock's forward price. Higher rates raise the expected growth of the stock and lower the present value of the strike. That helps calls and hurts puts. Dividends lower the stock price on the ex-dividend date, which hurts calls and helps puts. Think of both as pushing the forward price up (rates) or down (dividends).

Key formulas to remember

Call payoff at expiry: c = max(S_T − K, 0); Rises with S, falls with K.
Put payoff at expiry: p = max(K − S_T, 0); Falls with S, rises with K.
Direction table (increase in the factor): S: European call ↑, put ↓ | K: call ↓, put ↑ | σ: call ↑, put ↑ | r: call ↑, put ↓ | Dividends: call ↓, put ↑; Memorise this. For time T: American call and put ↑; European usually ↑ but can fall.
Time to expiry, American options: C(longer T) ≥ C(shorter T); P(longer T) ≥ P(shorter T); Holds because the longer option can be exercised whenever the shorter one can.
European lower bound, call, no dividends: c ≥ max(S₀ − K·e^(−rT), 0); Shows why a higher r raises the call's lower bound.
European lower bound, put, no dividends: p ≥ max(K·e^(−rT) − S₀, 0); Shows why a higher r lowers the put's lower bound.
Dividend-adjusted put-call parity (European): c + D + K·e^(−rT) = p + S₀; D is the present value of dividends during the option's life.

How to solve Factors Affecting Option Prices questions

Use this routine for any 'what happens to the option price if…' question.

1Identify whether the option is a call or a put, and whether it is European or American.
2Name the factor that changes and its direction (up or down).
3Check the payoff: does the change make the option more likely to finish in the money, or raise the payoff?
4Apply the direction table from memory: S, K, σ, r, dividends, time.
5For time, check the exceptions: American options never lose value with more time; European options may.
6If numbers are given, confirm with put-call parity or the lower bound formula.
7Pick the answer that matches both the option type and the style, and watch for words like 'must', 'always' or 'may'.

Quickest way: Forward-price shortcut

When to use it: Use when the question asks about rates, dividends or stock price on a plain European option.

Treat calls as 'bullish on the forward' and puts as 'bearish on the forward'.
Anything that raises the forward (higher S, higher r) helps calls and hurts puts.
Anything that lowers the forward (higher dividends) hurts calls and helps puts.
For K, reverse the logic: higher K helps puts and hurts calls.
Volatility always helps both, so choose 'increases' for both when the question mentions it.

Common mistakes in Factors Affecting Option Prices

Saying higher volatility lowers put values because puts are a bearish bet.
Students link 'puts' with 'risk' and assume risk hurts them.
Fix: Remember the payoff floor at zero. More volatility widens the upside for both calls and puts, so both increase.
Claiming a higher interest rate raises both options.
Students think a higher rate means 'more value everywhere'.
Fix: A higher rate lowers the present value of the strike. That helps calls and hurts puts.
Stating that longer maturity always increases a European option.
It is true for American options, and students over-generalise.
Fix: Write 'usually'. Deep in-the-money European puts, or calls on stocks with large dividends, can lose value with more time.
Getting dividend effects backwards.
Students think dividends are good for stock holders, so good for calls.
Fix: The stock price falls by about the dividend on the ex-date. The option holder does not receive it. So calls fall and puts rise.
Mixing up the strike direction.
Students associate a higher number with a higher price.
Fix: A higher strike means the call pays less and the put pays more. Calls fall with K, puts rise with K.

Worked examples

Example 1

A European call and a European put on the same non-dividend stock have S₀ = $50, K = $50, T = 1 year and r = 4% (continuous). Volatility rises. What happens to each, and which options bound does not change?

Show the solution

Volatility widens the range of possible terminal prices.
Payoff is floored at zero for both options, so extra upside is not offset by extra downside.
Both the call and the put increase in value.
The call lower bound is S₀ − K·e^(−rT) = 50 − 50 × e^(−0.04) = 50 − 48.04 = 1.96, which does not depend on σ.
The put lower bound is max(48.04 − 50, 0) = 0, also independent of σ.

Answer: Both the call and the put increase. The lower bounds (1.96 for the call, 0 for the put) are unchanged.

Example 2

A European call on a stock has c = $6.00. S₀ = $100, K = $100, T = 1 year, r = 5% (continuous), and the present value of dividends is $2. Using put-call parity, find the put price. Then say what happens to the put if the dividend is higher.

Show the solution

Parity: c + D + K·e^(−rT) = p + S₀.
Compute K·e^(−rT) = 100 × e^(−0.05) = 100 × 0.951229 = 95.1229.
Left side: 6.00 + 2.00 + 95.1229 = 103.1229.
p = 103.1229 − 100 = 3.1229.
If D rises, with c unchanged the left side would rise, so p would rise. Economically, a higher dividend lowers the stock and lowers the call and raises the put.

Answer: p ≈ $3.12. A higher dividend raises the put and lowers the call.

Exam tips

Memorise the direction table and be able to recite it for calls and puts, European and American.
Watch for 'always' and 'must': exceptions exist for time to expiry on European options.
Treat dividends and rates as a pair: they have opposite effects on the forward price, so opposite effects on options.
For numerical questions, use put-call parity and continuous discounting e^(−rT) unless told otherwise.
Hull's table for these factors is the usual source of questions, so expect a direct 'which statement is correct' format.

Practice questions from Properties of Options

Factors Affecting Option Prices in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Factors Affecting Option Prices: frequently asked questions

How does volatility affect call and put prices?

Higher volatility increases both call and put values. The payoff cannot go below zero, so extra upside adds value while extra downside costs the holder nothing more.

How does the interest rate affect call and put values?

A higher risk-free rate raises call values and lowers put values. The present value of the strike falls, which helps a call buyer and hurts a put buyer.

What is the effect of dividends on option prices?

Dividends reduce the stock price on the ex-dividend date. Calls become less valuable and puts more valuable. Larger dividends increase these effects.

Does more time to expiry always raise an option's price?

For American options, yes, since a longer option can do everything the shorter one can. For European options it is usually true but not always, for example for deep in-the-money puts.