How options are priced: intrinsic value, time value, and the basics of Black-Scholes

In short

A friend of mine once bought a call option and was puzzled when it cost more than the gain he could cash in that very day. He had every right to be puzzled. If you are holding an option, or thinking about one, the price you see has two parts. One part is what the option is worth right now if used. The other part is a price paid for time and uncertainty. The first part is called intrinsic value. The second is called time value. A famous formula called Black Scholes puts a number on the whole price using five inputs. The formula is a guide to how prices are built, not a promise of what will happen. Knowing the parts lets you read an option quote the way a farmer reads the sky.

The whole of it

What it is

I once watched a neighbor haggle over a small lot he did not yet want to buy. The seller agreed to hold it for him for a fee. That fee, paid for a choice and not an obligation, is the heart of an option. An option is a contract that gives the holder the right, but not the duty, to buy or sell a stock at a set price before a set date. The set price is the strike price. The set date is the expiration. A call option gives the right to buy. A put option gives the right to sell.

The price of that contract is called the premium. The premium splits into two pieces, and a good deal of confusion melts away once you see them apart. Intrinsic value is what the option would be worth if it were used this very moment. Time value is whatever is left over. In plain terms, the premium equals intrinsic value plus time value.

Take a call with a strike of $50 on a stock trading at $58. The holder could buy at $50 something worth $58, so the intrinsic value is $58 minus $50, which is $8. A call with a strike of $60 on that same $58 stock has no intrinsic value, because nobody would pay $60 for what sells at $58. Its intrinsic value is $0. Intrinsic value never drops below zero. That is a quiet kindness built into the contract.

How it works

You have probably wondered why an option that is worth nothing today can still cost real money. The answer is time and the chance of change. A stock moves. Between now and expiration, it might climb or fall. The holder of a call gains if it climbs a good way and loses only the premium if it falls. That lopsided deal has value, and the market charges for it. That charge is time value.

Time value shrinks as expiration draws near, because there is less time left for the stock to move. This is often called time decay. It is a bit like a block of ice on a summer porch. The melting speeds up toward the end. Two things lift time value. More time left lifts it. A stock that swings more widely lifts it too, since a bigger swing means a bigger chance of a big payoff.

Now, about Black Scholes. In 1973, Fischer Black and Myron Scholes published a paper in the Journal of Political Economy titled The Pricing of Options and Corporate Liabilities. Robert Merton added important work around the same time. Their formula gives a fair price for a European option, which can be used only at expiration. It rests on five inputs. They are the current stock price, the strike price, the time left, the risk free interest rate, and the volatility of the stock. Volatility is a measure of how widely the stock price swings.

The formula assumes a few tidy things. It assumes the stock moves in a smooth, random way. It assumes volatility stays steady and that no dividends are paid. Real markets are messier. So the formula is a fine map, but a map is not the ground.

The numbers, and where to find yours

Most of the inputs sit in plain view. The stock price and the strike price are on any option quote. The time left is the number of days to expiration, turned into a fraction of a year. The risk free rate is usually taken from the yield on a Treasury security of matching length, and the U.S. Department of the Treasury publishes daily yield curve rates on its website. The tough one is volatility.

There are two kinds. Historical volatility looks backward at how much the stock actually moved. Implied volatility works backward from the option price itself, asking what swing the market must be expecting. Brokerage platforms commonly display implied volatility beside each option. When the stock price, strike, time, and rate are known, and the premium is known, implied volatility is the one number that makes the formula match the market.

For the rules that shape how options trade, the Options Clearing Corporation publishes the contract terms, and the Cboe Global Markets site explains how listed options work. Each standard equity option contract usually covers 100 shares. Your own broker lists the contract size on every quote, so check there for yours.

A worked example

Let me tell you about a woman named Marguerite. She is a schoolteacher who likes to understand a thing before she touches it. She looks at a call option on a stock trading at $40. The strike is $35, and the option has 60 days left. The premium is quoted at $6.20.

First she finds the intrinsic value. The stock is at $40 and the strike is $35, so $40 minus $35 is $5. The intrinsic value is $5.

Next she finds the time value. The premium is $6.20 and the intrinsic value is $5, so $6.20 minus $5 is $1.20. The time value is $1.20 per share.

Because one contract covers 100 shares, she multiplies. The intrinsic value of one contract is 100 times $5, which is $500. The time value of one contract is 100 times $1.20, which is $120. The full premium for one contract is 100 times $6.20, which is $620. Check it: $500 plus $120 is $620. It adds up.

Now she watches the clock. Suppose the stock sits still at $40 and 30 days pass. Intrinsic value stays at $5. But the time value, with half the time gone, might shrink to something like $0.70. The premium would then be $5 plus $0.70, which is $5.70. She would be down $0.50 per share, or $50 per contract, though the stock did not move at all. That small, steady loss is time decay at work, and Marguerite was glad to see it on paper before it showed up in her account.

I chose $0.70 only to show the idea. A real figure depends on volatility and the other inputs, and the formula would give the exact number.

Where it goes wrong

A neighbor of mine used to say that every tool has a place where it slips. Black Scholes slips in a few places, and knowing them is a form of respect for the tool.

The formula assumes volatility holds steady, but real volatility changes by the day. When a company reports earnings, implied volatility often jumps beforehand and drops after. A buyer can be right about the stock's direction and still lose, because the volatility fell and pulled the time value down with it. It stings.

The formula also treats the stock as moving smoothly. Real stocks sometimes gap on sudden news. It assumes no dividends, but many stocks pay them, and dividends change the price. Most listed stock options in the United States are American style, meaning they can be used before expiration, and the original formula was built for European style. Adjusted versions exist for that.

Then there are the costs outside the formula. The gap between the bid and the ask price is a real cost every time. Commissions, where they apply, add more. And an option can expire worth nothing. The premium paid is then gone in full. That is the plain arithmetic of the contract, and no formula softens it.

Questions to answer before you leave this page

Can you say, in your own words, what the difference is between intrinsic value and time value, and why time value never goes below zero while an option still has time left? If an option has a strike of $45 and the stock sits at $50, can you work out the intrinsic value of a call and see that it is $5 per share and $500 per contract? Do you know the five inputs to the Black Scholes formula, and which one is the hardest to know ahead of time? Have you thought about why an option can lose value even when the stock does not move? Can you find the contract size, the expiration date, and the implied volatility on a quote from your own broker? And when you read the words time decay, can you picture the ice block melting faster as the days run short?