A Beginner’s Guide to Option Pricing
Part 2 – Implied Volatility: One of the Most Commonly Misunderstood Numbers in Options
Options Are Really About Uncertainty
At the end of Part 1, we saw that pricing models estimate what an option should be worth using factors like stock price, strike price, time, and volatility.
But one of those inputs is much harder to pin down than the others: nobody knows how much a stock will actually move between now and next week, next month, or six months from now. So how does a pricing model come up with a number for something nobody can know?
The answer lies in one of the most misunderstood concepts in investing: implied volatility, often abbreviated as IV. The confusion begins because investors naturally think of options primarily as bets on direction—a call as a bet that the stock will rise and a put as a bet that it will fall. But option pricing is not based simply on predicting which direction the stock will go. It must also account for how large the stock’s movements might be. Implied volatility addresses that second question: how much movement and uncertainty the market is building into the option’s price.
Thinking about options in directional terms isn’t wrong. If you buy a call, you may well be betting that the stock will rise; if you buy a put, you may well be betting that it will fall. Professional traders take directional views constantly—that’s the entire reason strategies like bull call spreads or bearish put positions exist.
But direction is the trader’s view. When estimating theoretical value, a pricing model doesn’t know or care whether you personally think the stock is going up. When it comes to volatility, the model is addressing a different question: how much might this stock move, in either direction, before the option expires?
That’s a question about magnitude—how far, not which way—and the answer doesn’t depend on whether the person trading the option is bullish, bearish, or has no directional opinion at all.
Imagine two companies, both trading at exactly $100. The first hardly ever moves, rising or falling by only a dollar or two most weeks. The second is wildly unpredictable, capable of gaining or losing $20 in a single week. Which company’s options should be more expensive?
Almost everyone would answer the second one, because there’s much more uncertainty about how far the stock might travel — regardless of which direction it goes. A call option on that stock has a much greater chance of becoming very valuable, and so does a put. Both calls and puts become more expensive when future price movements become more uncertain, independent of whether the market leans bullish or bearish.
That’s the key shift: a trader can have a strong directional opinion and still be paying for uncertainty about the size of the stock’s possible movement. Understanding the distinction between what you believe will happen and the uncertainty already reflected in the option’s price is one of the biggest conceptual leaps for new option investors.
Direction determines which option or strategy may benefit from the move, but the expected magnitude of that movement is a major part of what determines how much an option costs to buy in the first place, largely through its time value. That cost matters because the stock’s move has to be large enough to overcome it before a buyer actually profits. A trader can correctly predict the stock’s direction and still lose money if the move isn’t large enough to make up for what was paid — a distinction we’ll return to later in this series when we look at breakeven prices and the cost of time itself.
Every Option’s Price Has Two Separate Ingredients
Before we go further, we need to split an option’s price into two pieces — one of the most useful things to know about options. Every option’s price is made up of intrinsic value and time value (also called extrinsic value).
Intrinsic value is the simple part: it’s how much the option would be worth if you had to exercise it right now, today, this second. Suppose a stock is trading at $105, and a call option with a strike price of $100 lets its owner buy the stock for $100. Since the stock is worth $105, that right is worth at least $5 right now. That $5 is intrinsic value — it doesn’t depend on the future at all, it’s simply today’s stock price compared with the strike price.
Now suppose that same option is trading for $7. Where did the other $2 come from? That’s time value — the price of possibility, representing the uncertainty about where the stock might go before the option expires. An option with a lot of time remaining, on a stock that moves around a great deal, will typically carry a lot of time value; an option about to expire, on a stock that barely moves, will carry very little.
When we talked earlier about uncertainty driving option prices, we were talking specifically about time value. Intrinsic value tracks the stock, while time value is the part of the price that reflects uncertainty — and it’s the part that shrinks as expiration approaches, a process called “time decay.”
An option can also have no intrinsic value at all. If our $100 strike call existed while the stock was trading at $95, exercising it would mean paying $100 for something worth $95 — nobody would do that, so the intrinsic value in that case is zero.
Yet the option would still have a price, because there’s still time left before expiration and the stock could still rise back above $100 before then. That entire price would be time value: pure uncertainty, with nothing else behind it.
This matters because implied volatility is a statement about time value, not intrinsic value. Implied volatility is the market’s way of pricing uncertainty, and uncertainty is exactly what time value measures. Like every other market price, implied volatility emerges from buyers and sellers negotiating with one another. What they’re really trading is their collective estimate of how much uncertainty the stock deserves before the option expires.
Imagine You’re the Insurance Company
Here’s an analogy that makes implied volatility more concrete. Imagine you’re in the business of selling homeowners insurance, and two houses are worth exactly the same amount — one sits beside a quiet lake in a peaceful neighborhood, the other sits halfway up an active volcano. Would you charge both homeowners the same premium? Of course not. The volcano house carries much greater uncertainty — you don’t know whether it will erupt, but you know there’s a greater chance something dramatic could happen, so you charge more, not because you know something will happen, but because you can’t rule it out.
Options work the same way: the marketplace prices in more for a stock that could erupt than for one that typically stays quiet.
Volatility Is Not the Same as Risk
This is another point that confuses many beginners: when professionals talk about volatility, they aren’t making a judgment about whether a company is good or bad. Volatility simply measures how much prices tend to move — a wonderful company can have volatile stock, and a struggling company can have relatively stable stock. Volatility isn’t measuring quality; it’s measuring movement.
Think of driving: a straight interstate highway may be perfectly safe and predictable, while a winding mountain road may be just as safe but demand far more steering. The mountain road simply has greater variability. Stocks are the same way — some travel relatively smooth paths, others swing wildly from week to week — and options become more expensive on the roads with more twists and turns.
Historical Volatility and Implied Volatility Are Different Things
There are actually two kinds of volatility, and confusing them is a common mistake. Historical volatility looks backward, asking, “How much has this stock actually moved over the past month or year?” — simply a measurement of history. Implied volatility looks forward, asking, “How much movement does today’s option market appear to be expecting?” Historical volatility is like looking through the rear-view mirror; implied volatility is like looking through the windshield.
Here’s why the difference matters: it’s how traders judge whether an option looks cheap or expensive. If implied volatility is running well above a stock’s historical volatility, options are pricing in more drama than the stock has actually shown recently, which may mean the market expects something — an earnings report, a court ruling, a Fed meeting — to shake things up. If implied volatility is running below historical volatility, options may be underpricing risk relative to how the stock has actually behaved. Comparing the two is one way to get a read on whether options are currently priced richly or cheaply.
One practical note: on a real option chain, implied volatility is displayed as an annualized percentage, something like “32% IV,” rather than a dollar figure. That percentage is a standardized way of expressing how much movement the market expects, so it can be compared across different stocks and expiration dates, and against a stock’s own historical volatility.
What Does That Percentage Actually Mean?
It’s worth pausing on that number, because “32% IV” doesn’t mean the market expects the stock to move exactly 32%. It’s a statistical measure, not a specific prediction.
Implied volatility is expressed as an annualized standard deviation of the stock’s expected returns. As a simplified approximation, a 32% IV means the options market is pricing in roughly a two-in-three chance—one standard deviation, under the model’s assumptions—that the stock will finish within approximately 32% above or below its current price one year from now. For a $50 stock, that produces a rough range of $34 to $66. There would still be approximately a one-in-three chance of the stock finishing outside that range.
This is only a convenient mental shortcut. Stock-price movements are not perfectly symmetrical: a stock cannot fall below zero, but there is no equivalent limit on how far it can rise. Option models therefore use a lognormal distribution—which recognizes that a stock cannot fall below zero but can rise without a fixed limit—rather than simply adding and subtracting the IV percentage. At moderate volatility levels, however, the simplified range provides traders with a useful approximation.
Another important detail is that IV is annualized, so it must be scaled when looking at shorter periods. A 32% IV doesn’t mean the stock is expected to move 32% by next week’s expiration. To estimate a shorter expected move, traders use the square root of time. For one month, a 32% annualized IV translates into a rough expected move of about 9%. For one week, it translates into approximately 4.4%. That’s why the same IV number implies very different price ranges depending on how much time remains before expiration.
One final clarification: although traders often speak of “a stock’s implied volatility,” implied volatility is technically a characteristic of an individual option contract, not of the stock itself. Every strike price and every expiration can have its own implied volatility because each option trades at its own market price. Those differences reflect variations in market expectations, supply and demand, and the amount of uncertainty investors assign to different strike prices and different expiration dates.
When traders casually refer to “the stock’s IV,” they’re usually using shorthand for the implied volatility of an at-the-money option or for an average derived from several actively traded options. This is a convenient shorthand, but technically every option has its own implied volatility.
So Is 32% High or Low?
There’s no universal cutoff, because normal IV varies considerably from one stock to another. For a large, stable company, IV in the teens or low 20s may be unremarkable. IV in the 40s, 50s, or higher generally signals considerably more uncertainty—perhaps because of an upcoming earnings report, a pending FDA decision, a lawsuit, or simply because the stock is unpredictable by nature, as is common with some small-cap or high-growth companies.
IV above 100% is unusual but not unheard of. It can appear around binary, high-stakes events, such as a biotechnology company awaiting a drug-trial result that could send its stock soaring or collapsing. At the other extreme, IV in the single digits is exceptionally low and suggests that the market is pricing in very little movement. That is more likely to occur in broad index funds during unusually calm periods than in individual stocks.
The number is generally more useful in relative terms than in absolute ones. An option with 35% IV might look expensive for a stock whose historical volatility is closer to 20%, but inexpensive for a different stock that routinely carries IV near 60%.
That’s why traders compare current IV with the stock’s own history, its recent implied volatility, and its historical volatility over a comparable period. Even then, the comparison is not a guarantee that an option is cheap or expensive. Historical volatility tells us what the stock did in the past; it cannot tell us how much the stock will move in the future.
Where Implied Volatility Comes From
Here’s one of the most important ideas in option pricing: the implied volatility displayed in an option chain is not measured directly. It is calculated backward from the option’s market price.
Buyers, sellers, and market makers establish market prices through competing bids, offers, and completed trades. A pricing system can then ask: “What volatility input would make our model produce approximately this option price?” The answer is implied volatility. The volatility is “implied” because it is inferred from the price at which the option is currently trading.
Once calculated, however, implied volatility can also be used as an input. Traders and pricing systems insert it into models to estimate theoretical values, calculate the Greeks, compare different options, and examine how prices might change if volatility rises or falls.
The relationship therefore works in both directions: the market price is used to derive implied volatility, and implied volatility is then used to analyze and model option prices.
Why Market Makers Care About Implied Volatility
Now let’s return to the market maker. Imagine you work for a large trading firm and a customer wants to buy an option. How much should you charge?
If you expect the stock to move only a dollar over the next month, you’ll quote one price. If you believe it could move twenty dollars, you’ll quote a much higher one. Greater expected movement creates more opportunity for the option to become valuable and more risk for the market maker taking the other side of the trade.
That’s why volatility becomes a common language of the options market. Instead of saying, “I think this stock will probably move about twelve dollars before expiration,” professionals can express that uncertainty as a volatility estimate. Pricing models then translate that estimate, together with the stock price, strike price, time remaining, interest rates, and dividends, into a theoretical option value.
Do Market Makers Use Black-Scholes?
Yes and no. The original Black-Scholes equation changed finance forever, but today’s market makers use more sophisticated descendants that incorporate decades of additional research and can account more fully for features such as changing volatility, early exercise, dividend schedules, and sudden price jumps.
Different firms use different models and pricing systems, many of which are proprietary and closely guarded. However, they all begin with the same basic idea: estimate future uncertainty, then use mathematics to estimate what the option should be worth.
The models themselves don’t create the market price—they estimate a theoretical value. The actual trading price still depends on the bids and offers submitted by buyers, sellers, and market makers.
If Everyone Has a Pricing Model, Why Don’t All Options Trade at Exactly the Same Price?
Suppose several market makers estimate that an option’s theoretical value is about $3.50. Will it necessarily trade at exactly $3.50? No.
Imagine a rare vintage guitar heading to auction. Several instrument experts estimate that it is worth approximately $40,000, but two collectors who have wanted that exact model for decades show up to bid, and the auction closes at $58,000. Were the experts wrong? Not necessarily. Their appraisals reflected what the guitar might ordinarily be worth, while the final price reflected what actual buyers were willing to pay that day.
Options work in a similar way. A theoretical value depends on the assumptions entered into a particular model, while the market price comes from actual bids, offers, and trades. Different firms may use different volatility estimates or other assumptions and therefore arrive at somewhat different theoretical values.
In liquid option markets, many market makers and investors compete with one another continuously. That competition generally produces narrow bid-ask spreads and prevents prices from drifting far enough to create obvious arbitrage opportunities. In thinly traded options, spreads can be much wider because fewer participants are competing to buy and sell. A displayed market price may therefore sit farther from one platform’s theoretical estimate without necessarily indicating that the option is incorrectly priced.
The Foundation for Everything That Follows
By now, we’ve covered a lot of ground. Pricing models estimate an option’s theoretical value. Every option’s price splits into intrinsic value and time value, with time value being the part most directly affected by uncertainty. Market prices reveal how much uncertainty investors are pricing into individual options through implied volatility. Actual trading prices are still established by buyers, sellers, and market makers—not by a mathematical equation alone.
These ideas form the foundation for understanding every option chain you’ll ever see.
In Part 3, we’ll examine a real option chain from a relatively quiet stock. We’ll see how market makers use these ideas to quote prices when there are relatively few buyers and sellers, why bid-ask spreads become much wider, and why call and put prices can differ even when trading activity is minimal.
After examining that quieter market, we’ll turn to one of the busiest option markets in the world—NVIDIA—and see how thousands of competing buyers and sellers can influence prices in ways that simply don’t occur in less active stocks.
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A Beginner’s Guide to Option Pricing: Complete Series Index
1. A Beginner’s Guide to Option Pricing – Part 1 (Theoretical Value)
https://www.philstockworld.com/2026/07/11/who-decides-what-an-option-is-worth/
2. A Beginner’s Guide to Option Pricing – Part 2 (Implied Volatility)
https://www.philstockworld.com/2026/07/12/who-decides-what-an-option-is-worth-part-2/
3. A Beginner’s Guide to Option Pricing – Part 3 (Thinly Traded Options)
https://www.philstockworld.com/2026/07/12/a-beginners-guide-to-option-pricing-part-3/
4. A Beginner’s Guide to Option Pricing – Part 4 (Liquid Options)
https://www.philstockworld.com/2026/07/13/a-beginners-guide-to-option-pricing-part-4/
5. A Beginner’s Guide to Option Pricing – Part 5 (Put-Call Parity)
https://www.philstockworld.com/2026/07/14/a-beginners-guide-to-option-pricing-part-5/
6. A Beginner’s Guide to Option Pricing – Part 6 (Delta)
https://www.philstockworld.com/2026/07/15/a-beginners-guide-to-option-pricing-part-6-delta/
7. A Beginner’s Guide to Option Pricing – Part 7 (Gamma)
https://www.philstockworld.com/2026/07/15/a-beginners-guide-to-option-pricing-part-7-gamma/
8. A Beginner’s Guide to Option Pricing – Part 8 (Theta)
https://www.philstockworld.com/2026/07/16/a-beginners-guide-to-option-pricing-part-8-theta/
9. A Beginner’s Guide to Option Pricing – Part 9 (Vega)
https://www.philstockworld.com/2026/07/17/a-beginners-guide-to-option-pricing-part-9-vega/
