Economic Modelling · Principles of option pricing

Factors Affecting Option Prices: Effect on Calls and Puts

Updated 11 October 2026 · Fact-checked

Six factors drive an option's value: the underlying price, the strike, time to expiry, volatility, the risk-free interest rate and dividends. Work out each one by asking how it changes the chance and size of a payoff. Then check your direction against put-call parity and no-arbitrage bounds.

Understand Factors Affecting Option Prices

An option gives you a right, not an obligation. A call pays max(S − K, 0) at expiry. A put pays max(K − S, 0). Its price today reflects how large and how likely that payoff is.

Start with the underlying price S. A higher S makes a call more likely to finish in the money and increases its payoff. So calls rise with S. Puts fall with S. The strike K works the other way: a higher K lowers call values and raises put values.

Volatility is the cleanest idea to learn. The holder has limited loss (the premium) but unlimited or large gain. Greater volatility widens the spread of final prices. The upside gain grows while the downside is cut off at zero payoff. So both calls and puts increase in value with volatility. This holds for European and American options.

Time to expiry adds more time for price moves, so it usually raises value. For American options it always does, because a longer option contains the shorter one. For European options it is not guaranteed. A European put deep in the money can lose value with more time, because its payoff is received later and the strike is discounted. A European call on a share paying large dividends before expiry can also be worth less with more time.

Interest rates matter through discounting the strike and through the cost of carrying the share. A higher risk-free rate r lowers the present value of K. That raises call values and lowers put values. Dividends lower the share price on the ex-dividend date. So higher expected dividends reduce call values and raise put values. Remember the logic: a call holder does not receive dividends, but the share price falls when they are paid.

All of these effects assume the other factors are held constant. In the exam, state that assumption.

Key rules to remember

Call and put payoffs at expiry: Call = max(S_T − K, 0); Put = max(K − S_T, 0); The base for every directional argument.
Direction summary (European, other factors fixed): S↑: call ↑, put ↓. K↑: call ↓, put ↑. σ↑: call ↑, put ↑. r↑: call ↑, put ↓. Dividends↑: call ↓, put ↑.; Time is ambiguous for European options. It is positive for American options.
Time to expiry (American): For T₂ > T₁: C_A(T₂) ≥ C_A(T₁) and P_A(T₂) ≥ P_A(T₁); A longer American option can be exercised on every date the shorter one can.
Put-call parity (European, no dividends): C + K e^(−rT) = P + S₀; Use it to check the direction of r and K effects.
Put-call parity with known dividends: C + D + K e^(−rT) = P + S₀, where D is the present value of dividends during the life; Higher D means a lower C or a higher P.
Lower bounds, European, no dividends: C ≥ max(S₀ − K e^(−rT), 0); P ≥ max(K e^(−rT) − S₀, 0); Violation gives an arbitrage.

How to solve Factors Affecting Option Prices questions

Use this method for any question asking how a factor changes an option's value.

1Identify the option type (call or put), style (European or American) and whether the share pays dividends.
2Write the payoff at expiry and say which factor is changing, with all others held constant.
3Ask how the change alters the size and the probability of a positive payoff.
4For r, K and dividends, confirm the direction with put-call parity or the discounted strike.
5For time, state the style. American options are never worth less with more time. For European options, say the effect is ambiguous and give the case.
6State the direction clearly and give the reason in one or two sentences.
7If numbers are given, compute using parity or bounds and check the result is at or above the lower bound.

Quickest way: Direction table plus parity check

When to use it: Multiple-choice questions and short written parts asking for the direction of an effect.

Recall the pattern: calls like high S, low K, high r, low dividends. Puts are the opposite.
Volatility helps both. Say so first.
For time, check whether the option is American. If yes, longer is worth more or equal.
If unsure on r or dividends, use C − P = S₀ − D − K e^(−rT) and see how C − P moves.
Eliminate options that break a bound or a parity relationship.

Common mistakes in Factors Affecting Option Prices

Saying higher volatility lowers put values because a put is a bearish bet.
Confusing risk to the holder with option value. Students think volatility is bad.
Fix: The put payoff is capped below at zero. More spread raises the expected payoff, so puts rise with volatility too.
Saying a higher interest rate raises put values.
Students link rates to higher cost of everything.
Fix: A higher r reduces the present value of the strike a put holder receives, so puts fall. Calls rise. Check with parity.
Saying dividends raise call values because the share is more attractive.
Mixing up the share holder with the option holder.
Fix: The option holder gets no dividend. The share price drops when it is paid, so calls fall and puts rise.
Stating that more time always increases a European option's value.
Over-generalising from American options.
Fix: Say it is true for American options. For European options the effect is usually positive but not guaranteed, for example a deep in-the-money put or a call with a large dividend before expiry.
Giving a direction without stating other factors are held constant.
Students treat the factors as moving together.
Fix: Start each answer with 'holding all else constant'. It is also needed for the marks.
Treating a higher strike as raising both call and put values.
Mixing strike and price level.
Fix: A higher K reduces call payoffs and increases put payoffs. Draw the payoff to confirm.

Worked examples

Example 1

A non-dividend-paying share has price ₹100. A European call with strike ₹95 expires in 1 year. The risk-free rate is 5% per year continuously compounded. Find the lower bound for the call price, and explain how the bound and the call price change if r rises to 8%.

Show the solution

The lower bound is max(S₀ − K e^(−rT), 0).
At r = 5%: K e^(−0.05) = 95 × 0.951229 = 90.367.
Bound = 100 − 90.367 = ₹9.63 (to 2 decimals).
At r = 8%: K e^(−0.08) = 95 × 0.923116 = 87.696.
Bound = 100 − 87.696 = ₹12.30.
The discounted strike is lower when r is higher, so the bound rises. The call price must stay at or above this bound, so it rises.

Answer: The lower bound is about ₹9.63 at 5%. It rises to about ₹12.30 at 8%, so higher interest rates raise European call values (other factors constant).

Example 2

A European call and put on the same non-dividend share have strike ₹200 and expire in 6 months. The share price is ₹210, r = 6% per year continuously compounded and the call costs ₹24. Find the put price. Then explain what happens to the put if volatility rises.

Show the solution

Use C + K e^(−rT) = P + S₀.
K e^(−rT) = 200 × e^(−0.03) = 200 × 0.970446 = 194.089.
P = C + K e^(−rT) − S₀ = 24 + 194.089 − 210 = 8.089.
So the put is about ₹8.09.
If volatility rises, the put payoff max(K − S, 0) has the same floor at zero but a bigger chance of large payoffs. Its value rises. The call rises too, and parity still holds.

Answer: The put price is about ₹8.09. A rise in volatility increases the put's value, other factors constant.

Exam tips

Always state 'holding other factors constant' before giving any direction.
For time to expiry, name the option style. This single point separates full marks from partial marks.
Use put-call parity to justify r, K and dividend effects. It shows you understand why.
In multiple-choice questions, volatility is usually the trap. Both calls and puts increase with it.
Quote exp(−rT) with continuous compounding unless the question states otherwise, and show the discounting step.

Practice questions from Principles of option pricing

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?

Both rise with volatility. The holder's loss is limited to the premium, while larger price swings increase the chance of a large payoff. This applies to European and American options.

How do interest rates affect option prices?

A higher risk-free rate reduces the present value of the strike. This raises call values and lowers put values, other factors constant. Put-call parity shows it directly.

How do dividends affect option prices?

The share price falls when a dividend is paid, and the option holder does not receive it. Higher expected dividends therefore lower call values and raise put values.

Does a longer time to expiry always increase an option's value?

For American options, yes, because the longer option includes all rights of the shorter one. For European options it usually does, but not always. A deep in-the-money put or a call before a large dividend can be worth less.