What drives an option’s price · RiskAtoms Academy

By the end you will be able to

1Explain the effect of spot, strike, volatility, time and interest rates on an option's price.
2Explain why higher volatility raises the value of both calls and puts.
3Split an option's price into intrinsic value and time value.
4Use the drivers to predict which way a call and a put will move after market news.

Why it matters

On 16 March 2020, as markets panicked over the pandemic, the VIX, an index worked out from the prices of S&P 500 options, closed above 80, its highest close on record. Options had become very expensive. The share price is not the only thing an option's price depends on: fear itself, measured as volatility, has a price.

Core explanation

Five dials

Before expiry, an option is worth more than what it would pay right now. Its price is intrinsic value plus time value (L1.7.06). Five things set that price. Think of them as dials. Turn one, hold the rest, and the price moves in a predictable direction.

When this rises…	Call	Put	Why
Share price	↑	↓	The call's right to buy is worth more; the put's right to sell, less.
Strike	↓	↑	You pay more under a call and receive more under a put.
Volatility	↑	↑	Bigger moves, and losses are capped at the premium.
Time to expiry	↑	↑ usually	More time for a big move.
Interest rate	↑	↓	The strike, paid or received later, is worth less today.
Dividends expected	↓	↑	Dividends lower the share price on the day they are paid.

Spot and strike are the obvious ones: they set how far the option is in or out of the money. Interest rates come from parity (L1.7.08): $C - P = S_0 - PV(K)$ . Higher rates shrink $PV(K)$ , so calls gain relative to puts.

Volatility is the surprise. Volatility measures how much a price tends to move (L1.5.06), and it raises the value of calls and puts. The reason is the option's asymmetry: if the share moves your way, the payoff keeps growing; if it moves against you, you lose only the premium. Spread the possible outcomes wider and the good ones get better while the bad ones cannot get worse. Try it with three equally likely outcomes:

Spread the outcomes

How far the share can move, either way± 10

Chance 1 in 3

Share 90

call pays 0

Chance 1 in 3

Share 100

call pays 0

Chance 1 in 3

Share 110

call pays 10

Average share price100.00

Average call payoff3.33

Average put payoff3.33

Strike 100. The good outcome grows; the bad one is capped at zero.

Time works the same way: a longer life gives the share more time to make a big move. One exception: a deep in-the-money European put can lose value with more time, because its holder must wait longer to receive the strike.

Predict the move

4 cards

A company beats its profit forecast and its share price jumps.
A war scare makes traders expect much larger daily swings in the index.
The company announces a large special dividend, to be paid before the options expire.
The central bank raises interest rates unexpectedly (share price unchanged).

The formal version

Option pricing models such as Black-Scholes turn the five dials into a price. You do not need the formula yet; later levels build it. At this level one idea is enough: an option's value is the average of its possible payoffs, weighted by their chances, and discounted to today. That average is an expectation (see the Expectation Math Atom):

\text{Call value} \approx \frac{1}{(1+r)^T} \times \text{average of } \max(S_T - K,\ 0)

Each driver changes either the spread of possible prices $S_T$ (volatility, time), where they are centred (share price, rates, dividends), or the point where the payoff starts (strike). The chances used are special “risk-neutral” ones that make the share itself earn the risk-free rate on average; later levels explain why.

Try it

Behind these sliders is the Black-Scholes model, the one on the site's valuation page. Start at the money: share 100, strike 100, volatility 20%, one year, rate 5%. The call is worth 10.45 and the put 5.57. Turn one dial at a time and read the arrows. Then try a put with the share at 50, the rate at 8% and see what more time does.

Try itWhat moves the price?

Open the Black-Scholes model →

Share price, S100

Strike, K100

Volatility (a year)20%

Time to expiry (years)1.00

Interest rate (continuous)5.00%

Option

value today intrinsic value (payoff if it expired now)

Call value today

10.45

Intrinsic value0.00

Time value10.45

If this driver rises a little, the call…

Share price↑ rises
Strike↓ falls
Volatility↑ rises
Time to expiry↑ rises
Interest rate↑ rises

Worked example

Calm share, wild share

Two shares both trade at 100, and at expiry each will be at one of three prices, each with a chance of 1 in 3. The calm share moves ±10; the wild one ±30. Consider a call and a put with strike 100 on each. We ignore discounting to keep the numbers clear.

Average payoffs

Step 1 of 5

1
Average share price
Calm: (90 + 100 + 110) ÷ 3 = 100. Wild: (70 + 100 + 130) ÷ 3 = 100. On average, the two shares end in the same place.

Regulatory lens · looking ahead

The sensitivity of an option's price to each driver has a Greek letter: delta for the share price, vega for volatility, theta for time, rho for rates. Bank capital rules for market risk (FRTB, L4.3) charge capital on delta, vega and curvature risk, so these directions become numbers banks must report.

Sparks

SparkThe fear gauge

The Cboe Volatility Index, or VIX, is worked out from the prices of options on the S&P 500. It reads the volatility the market is paying for, the implied volatility. Because it jumps when investors panic, the press calls it the “fear gauge”.

SparkA Nobel prize for a price

In 1997 Myron Scholes and Robert Merton won the Nobel memorial prize in economics for their work on pricing options. Fischer Black, co-author of the 1973 formula, had died in 1995; the prize is not awarded after death, but the committee cited his contribution.

Key takeaways

Option price = intrinsic value + time value.
Higher share price: calls up, puts down. Higher strike: the reverse.
Higher volatility raises both calls and puts, because losses are capped and gains are not.
More time usually raises both. Higher rates raise calls and lower puts. Dividends lower calls and raise puts.
An option's value is a discounted average of its possible payoffs, which is what pricing models compute.

Reaction

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Glossary

Volatility: How much a price tends to move, measured as the standard deviation of its returns over a year.
Implied volatility: The volatility that, put into a pricing model, gives the option's market price. The market's view of future movement.
Time value: The part of an option's price above its intrinsic value.
Asymmetry: An option holder's losses stop at the premium, while the gains can keep growing.
Pricing model: A formula that turns the drivers into a price. Black-Scholes, from 1973, is the best known.
Expectation: The average of all possible outcomes, each weighted by its chance.

Deep Dives & Origins

Deep Dives

John C. Hull, Options, Futures, and Other Derivatives, 11th edition (Pearson, 2021), the chapter “Properties of Stock Options”, section on factors affecting option prices. Beginner.
Cboe, VIX White Paper: Cboe Volatility Index. Intermediate.

Origins

John C. Hull, Options, Futures, and Other Derivatives, 11th edition, Pearson, 2021.
Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy 81(3), 1973.
The Royal Swedish Academy of Sciences, press release for the 1997 prize in economic sciences.

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