Lesson 12: How Options Are Priced

🧮 The Two Components of an Option's Price

Every option premium can be broken down into exactly two parts. Understanding this split is the foundation of options pricing — and once you see it, you'll never look at an options chain the same way again.

graph LR A["💲 Option Premium
(what you pay)"] --> B["📐 Intrinsic Value
'Real' value
Would profit if exercised now"] A --> C["⏳ Extrinsic Value
'Time' value
Possibility of future profit"] B --> D["Only ITM options
have intrinsic value"] C --> E["ALL options have
extrinsic value
(until expiration)"] style A fill:#10b981,stroke:#059669,color:#fff style B fill:#3b82f6,stroke:#2563eb,color:#fff style C fill:#f59e0b,stroke:#d97706,color:#fff

📊 The Core Formula

Option Premium = Intrinsic Value + Extrinsic Value

This is the most important equation in options trading. Every pricing concept, every Greek, every strategy ultimately connects back to understanding these two components and what drives each one.

📐 Intrinsic Value: The "Real" Value

Intrinsic value is the amount of real, tangible profit an option would produce if you exercised it right now. It's the concrete, mathematical portion of the premium — no speculation, no hope, just cold hard math.

Calculating Intrinsic Value

Option Type	Formula	Condition
Call	Stock Price − Strike Price	Only if stock price > strike price (otherwise intrinsic = $0)
Put	Strike Price − Stock Price	Only if strike price > stock price (otherwise intrinsic = $0)

Intrinsic Value Examples

Scenario	Stock Price	Strike	Intrinsic Value	Status
Call option	$115	$100	$115 − $100 = $15.00	$15 in-the-money
Call option	$95	$100	$0.00 (stock is below strike)	$5 out-of-the-money
Put option	$85	$100	$100 − $85 = $15.00	$15 in-the-money
Put option	$110	$100	$0.00 (stock is above strike)	$10 out-of-the-money

💡 Key Insight: Intrinsic Value Can Never Be Negative

If the math gives you a negative number, intrinsic value is simply zero. An OTM option has zero intrinsic value — you'd never exercise an option that loses you money. This is why options are called "rights" not "obligations" for the buyer — you can always walk away. This floor at zero is what makes options fundamentally different from stocks: your maximum loss is limited to the premium you paid.

⏳ Extrinsic Value: The "Possibility" Value

Extrinsic value (also called time value) is everything in the premium above the intrinsic value. It represents the possibility that the option could become more valuable before expiration. It's the speculative component — what the market charges for uncertainty and time.

Calculating Extrinsic Value

📊 Extrinsic Value = Premium − Intrinsic Value

Example: A call option has a premium of $8.50. The stock is at $107 and the strike is $100.

Intrinsic value: $107 − $100 = $7.00

Extrinsic value: $8.50 − $7.00 = $1.50

You're paying $7.00 for real value and $1.50 for time and possibility. At expiration, that $1.50 will be gone — only the intrinsic value (if any) will remain.

What Drives Extrinsic Value?

Factor	Effect on Extrinsic Value	Why
Time to expiration	More time → higher extrinsic value	More time = more opportunities for the stock to move favorably. A 90-day option has far more extrinsic value than a 7-day option.
Implied volatility (IV)	Higher IV → higher extrinsic value	The market expects bigger moves, so the option is worth more. IV is the single biggest driver of extrinsic value changes day-to-day.
Moneyness	ATM options have the most extrinsic value	ATM options have the most uncertainty — could go either way. Deep ITM and deep OTM options have less uncertainty, so less extrinsic value.
Interest rates	Minor effect on extrinsic value	Higher rates slightly increase call premiums and decrease put premiums. For most retail traders, this effect is negligible.
Dividends	Upcoming dividends reduce call extrinsic value	Stock price drops by the dividend amount on ex-date, which hurts call holders. Put premiums may slightly increase.

OTM Options Are ALL Extrinsic Value

Option	Premium	Intrinsic	Extrinsic	Implication
OTM call (stock $95, strike $100)	$2.00	$0.00	$2.00 (100%)	You're paying entirely for possibility. If the stock doesn't move above $100 by expiration, this option is worthless.
Deep ITM call (stock $120, strike $100)	$21.50	$20.00	$1.50 (7%)	Almost all real value. This option behaves like owning the stock. Very little extrinsic "overhead."
ATM call (stock $100, strike $100)	$5.00	$0.00	$5.00 (100%)	Maximum extrinsic value. Maximum uncertainty. The market is pricing in the widest range of possible outcomes.

⚠️ The Extrinsic Value Countdown

Here's the critical fact about extrinsic value: it goes to zero at expiration. Always. No exceptions. When you buy an option, the extrinsic value portion of your premium is a wasting asset — it's guaranteed to disappear by expiration day. This is why time is the option buyer's enemy and the option seller's friend. Every day that passes, a small piece of extrinsic value evaporates. Understanding this is what separates successful options traders from those who wonder why their options keep losing value.

🔧 The Five Inputs That Drive Option Prices

Options pricing models use five inputs to calculate the "theoretical" fair value of an option. Four of them are known quantities — only one is uncertain, which is why it gets the most attention.

#	Input	Known or Unknown?	Effect on Calls	Effect on Puts
1	Current stock price	Known (changes constantly)	Stock ↑ → Call ↑	Stock ↑ → Put ↓
2	Strike price	Known (fixed for the contract)	Lower strike → More expensive call	Higher strike → More expensive put
3	Time to expiration	Known (decreases every day)	More time → More expensive	More time → More expensive
4	Risk-free interest rate	Known (changes slowly)	Higher rate → Slightly higher	Higher rate → Slightly lower
5	Implied volatility (IV)	❓ Unknown — estimated by the market	Higher IV → More expensive	Higher IV → More expensive

💡 Why Implied Volatility Is the "X-Factor"

Four of the five inputs are objective facts. But implied volatility is the market's opinion about how much the stock will move in the future — and opinions change. When the market gets nervous (earnings, geopolitical events, economic data), IV spikes and all options become more expensive. When calm returns, IV drops and premiums shrink. This is why two options on the same stock with the same strike and expiration can have very different premiums on different days — the IV has changed. Understanding this is the key to avoiding overpaying for options.

🎓 The Black-Scholes Model (Conceptual)

In 1973, Fischer Black, Myron Scholes, and Robert Merton published a formula that revolutionized finance and earned a Nobel Prize. The Black-Scholes model provides a mathematical framework for pricing European-style options. You don't need to memorize the formula — but understanding what it does and its limitations will make you a better trader.

What Black-Scholes Does

Aspect	Details
Purpose	Takes the five inputs (stock price, strike, time, interest rate, volatility) and outputs a theoretical "fair value" for the option.
Core assumption	Stock prices follow a log-normal distribution — they can go up infinitely but can only go down to zero. Price movements are random and normally distributed around a mean.
What it calculates	The probability-weighted expected payoff of the option, discounted back to today's dollars. In plain English: "Given how much this stock typically moves, what's this option worth right now?"
How traders use it	Brokerages use it (or variants) to calculate the Greeks, theoretical values, and implied volatility. When you see Greeks on your screen, they come from this model or a similar one.

Key Limitations

Limitation	Reality	Impact
Assumes constant volatility	Volatility changes minute-by-minute	The model can under- or over-estimate option values during volatile periods. This is partly why volatility skew exists (more on this below).
European-style only	Most stock options are American-style (can be exercised early)	Slightly underprices American options. The binomial model handles this better and is what most platforms actually use for American options.
No dividends in original model	Dividends affect option prices	Modified versions (Merton's adjustment) account for dividends. All modern platforms include this.
Assumes normal distribution	"Fat tail" events (crashes, squeezes) happen more often than the model predicts	Extreme moves are more likely than Black-Scholes suggests. This is why far OTM puts often cost more than the model's "fair value" — traders pay extra for crash protection.

📊 You Don't Need the Formula

The actual Black-Scholes formula involves calculus and probability distributions that are beyond what any trader needs to memorize. What matters is understanding the concept: the model takes knowable inputs plus an estimate of future volatility, and spits out a fair price. Your brokerage calculates this for you automatically. Your job is to understand why the price is what it is and whether the market's IV estimate seems reasonable given what you know about the stock.

⏰ The Time Decay Curve

Time decay (theta) doesn't happen at a constant rate. It follows a curve that accelerates dramatically as expiration approaches. Understanding this curve is crucial for choosing when to buy, when to sell, and when to close positions.

How Time Decay Accelerates

Days to Expiration	Approximate Extrinsic Value Remaining (ATM option)	Daily Decay Rate	Behavior
90 days	~100%	Slow (~0.5% per day)	Gentle erosion. You barely notice it day-to-day.
60 days	~82%	Moderate (~0.7% per day)	Starting to matter. Noticeable over a week.
45 days	~71%	Increasing (~0.9% per day)	The curve is bending. Many sellers enter positions here.
30 days	~58%	Fast (~1.3% per day)	⚠️ Danger zone for buyers. Decay is now very noticeable daily.
14 days	~39%	Very fast (~2.2% per day)	Options are melting. Buyers should strongly consider exiting.
7 days	~27%	Rapid (~3.5% per day)	Weekend decay becomes significant. Holding over weekends is costly.
1 day	~5%	Extreme	Almost all extrinsic value is gone. Only intrinsic value (if any) remains.
Expiration	0%	Complete	Extrinsic value = $0. Option is worth only its intrinsic value.

graph LR A["90 DTE
💚 Slow decay
~$0.03/day"] --> B["60 DTE
💛 Moderate
~$0.05/day"] B --> C["30 DTE
🟠 Accelerating
~$0.08/day"] C --> D["14 DTE
🔴 Fast
~$0.14/day"] D --> E["7 DTE
🔴 Rapid
~$0.22/day"] E --> F["Exp Day
⬛ Gone
Extrinsic = $0"] style A fill:#10b981,stroke:#059669,color:#fff style B fill:#f59e0b,stroke:#d97706,color:#fff style C fill:#ef4444,stroke:#dc2626,color:#fff style D fill:#ef4444,stroke:#dc2626,color:#fff style E fill:#ef4444,stroke:#dc2626,color:#fff style F fill:#1f2937,stroke:#111827,color:#fff

💡 The Square Root Rule

Time decay follows approximately a square root relationship. An option with 4x the time doesn't cost 4x as much — it costs about 2x as much (because √4 = 2). This means the first half of an option's life consumes far less extrinsic value than the second half. It also means that buying 60-day options instead of 30-day options doesn't cost double — you get significantly more time per dollar spent. This is one of the mathematical reasons the 45–60 DTE range is the "sweet spot" for buyers.

🌊 Volatility's Effect on Price

If time decay is the slow bleed, volatility is the earthquake. Changes in implied volatility can move an option's price more in a single day than weeks of time decay. Understanding this relationship is what separates knowledgeable options traders from everyone else.

Historical vs. Implied Volatility

Type	What It Measures	Looking At	Use
Historical Volatility (HV)	How much the stock actually moved in the past	Backward-looking (past data)	Benchmark. "Is IV currently higher or lower than what the stock has historically done?"
Implied Volatility (IV)	How much the market expects the stock to move in the future	Forward-looking (embedded in option prices)	Pricing. IV is the input the market uses to set option premiums. Higher IV = more expensive options.

How IV Changes Affect Your Position

Your Position	IV Increases	IV Decreases
Long call or long put (buyer)	✅ Your option gains value (positive vega)	❌ Your option loses value — even if the stock moves your way
Short call or short put (seller)	❌ The option you sold becomes more expensive to buy back	✅ The option you sold becomes cheaper to buy back — profit

Volatility Scenario: Same Stock Move, Different IV

📊 Why IV Matters More Than You Think

Scenario A: You buy a call for $5.00 when IV = 25%. Stock goes up $3. IV stays at 25%. Your option is now worth ~$6.80. Profit: $1.80.

Scenario B: You buy the same call for $5.00 when IV = 25%. Stock goes up $3. But IV drops to 18%. Your option is now worth ~$5.40. Profit: $0.40.

Scenario C: You buy the same call for $5.00 when IV = 25%. Stock goes up $3. IV rises to 32%. Your option is now worth ~$8.20. Profit: $3.20.

Same stock. Same $3 move. Profits range from $0.40 to $3.20 depending on IV. Volatility is not a sideshow — it's the main event.

💥 IV Crush: When Premiums Collapse

IV crush is the sudden, sharp decline in implied volatility that occurs after an anticipated event — most commonly an earnings announcement. It's responsible for more beginner losses than almost any other single concept in options trading.

How IV Crush Works

graph LR A["📅 2+ Weeks Before
IV: 30%
Normal levels"] --> B["📅 1 Week Before
IV: 40%
Rising as earnings approach"] B --> C["📅 Day Before Earnings
IV: 55%
Peak uncertainty"] C --> D["📢 Earnings Announced
Uncertainty resolved"] D --> E["📅 Day After Earnings
IV: 25%
💥 IV CRUSH"] style C fill:#ef4444,stroke:#dc2626,color:#fff style E fill:#10b981,stroke:#059669,color:#fff

Phase	What Happens to IV	What Happens to Premiums
Before the event	IV rises steadily as uncertainty builds	All options become more expensive. You're paying an "event premium."
At the event	IV peaks. Maximum uncertainty priced in.	Premiums are at their highest. This is the worst time to buy options.
After the event	IV collapses back to normal (or below). The uncertainty is resolved.	Premiums plummet — even if the stock moved in your direction. The vega loss can overwhelm the delta gain.

IV Crush Example: Earnings Play Gone Wrong

Detail	Before Earnings	After Earnings
Stock price	$100	$105 (+5%)
IV	55%	28% (crushed)
ATM call premium	$6.50	$5.80
Your P/L	—	−$0.70 per share (−$70 per contract)
What went wrong?	The stock moved up 5% — a great move! But IV dropped from 55% to 28%, destroying $2.70 of extrinsic value. The $5 stock gain only added ~$2.00 via delta. Net result: a loss despite being right about direction.

⚠️ How to Protect Against IV Crush

Option 1: Don't buy options right before earnings. Wait until after the event when IV has settled.

Option 2: Use spread strategies (like vertical spreads — covered in Lesson 17). When you buy one option and sell another, the IV crush affects both legs, partially canceling out the impact.

Option 3: Be the seller. Selling options before earnings lets you collect the inflated premium. When IV crushes, you profit. But this carries its own risks — the stock can still move more than expected.

Option 4: Check the expected move. The options market prices in a specific expected move around earnings. If the stock moves more than expected, the buyer wins despite IV crush. If less, the seller wins. Most platforms show this expected move — compare it to your thesis.

📈 Volatility Skew & the Smile

If Black-Scholes were perfectly accurate, all options on the same stock and expiration would have the same implied volatility. But they don't. In the real market, IV varies across strike prices — and this pattern tells you something important about how the market perceives risk.

What Is Volatility Skew?

Pattern	What It Looks Like	Why It Exists
Put skew (most common for stocks)	OTM puts have higher IV than OTM calls. IV increases as you go to lower strikes.	Investors pay more for downside protection (crash insurance). After the 1987 crash, the market permanently priced in the risk of extreme drops. This is sometimes called the "fear premium."
Volatility smile	Both OTM puts and OTM calls have higher IV than ATM. The IV curve looks like a "U" shape.	Common in currencies and commodities where extreme moves in either direction are feared. Also seen in meme stocks or biotech where huge moves up or down are possible.
Flat skew	IV is similar across all strikes.	Rare. Usually only seen in very calm markets or highly liquid index options during low-volatility periods.

What Skew Means for Your Trades

Situation	Practical Impact
Buying OTM puts	You're paying a higher IV than ATM options — puts are expensive relative to calls. This is the "crash insurance premium." It's a real cost that cuts into protective put strategies.
Selling OTM puts	You're collecting a higher premium because of skew. This is one reason selling puts (cash-secured puts, part of the Wheel strategy in Lesson 19) is a popular income strategy.
Comparing calls and puts at the same distance OTM	Don't assume symmetry. A put that's $10 OTM will typically cost more than a call that's $10 OTM due to skew. Factor this into spread strategies.

📊 Viewing Skew on Your Platform

Some platforms (like Thinkorswim, tastytrade, and Interactive Brokers) have a volatility skew chart that plots IV across all strikes for a given expiration. This visual instantly shows you whether puts are expensive relative to calls. Even without a dedicated chart, you can see skew in the options chain by comparing the IV column for equidistant OTM calls and puts. The difference tells you how much the market fears a drop versus a rally.

🔍 Is This Option Fairly Priced?

Now that you understand all the components of pricing, you can start asking the most important question in options trading: "Am I paying too much for this option?"

A Checklist for Evaluating Option Price

Check	What to Evaluate	Where to Look
1. IV Rank / IV Percentile	Is IV high or low relative to this stock's history?	Your platform's options analytics, tastytrade, or Barchart. High IVR = expensive premiums.
2. Compare IV to HV	Is the market expecting more or less movement than the stock has historically shown?	If IV > HV, options are priced for more movement than usual. If IV < HV, options might be underpriced.
3. Extrinsic value percentage	What percentage of the premium is extrinsic (time/hope) value?	Calculate: (Premium − Intrinsic) ÷ Premium. If you're paying 80%+ in extrinsic value, the stock needs to move a lot for you to profit.
4. Breakeven distance	How far does the stock need to move for you to break even at expiration?	For a call: Strike + Premium = Breakeven. Compare this to the stock's typical move over the option's timeframe.
5. Upcoming events	Is IV inflated because of earnings, FDA decisions, or other catalysts?	Check the earnings calendar. If the event is within the option's expiration, you're paying event premium that will crush after.

💡 The Expected Move

Many platforms display the expected move — how far the stock is expected to move (up or down) by a given expiration, based on current IV. The formula is approximately: Stock Price × IV × √(DTE/365). If a $100 stock has 30% IV and 30 days to expiration, the expected move is: $100 × 0.30 × √(30/365) ≈ $8.60. This means the market expects the stock to be between roughly $91.40 and $108.60 at expiration. If your trade requires the stock to move beyond this range, you're betting against the market's consensus — which can work, but you should know you're doing it.

🎯 Key Takeaways

Concept	What to Remember
Premium = Intrinsic + Extrinsic	Intrinsic is real profit if exercised now. Extrinsic is time and possibility — it goes to zero at expiration.
Intrinsic value	Call: Stock − Strike (if positive). Put: Strike − Stock (if positive). OTM options have zero intrinsic value.
Extrinsic value	Driven by time (more time = more extrinsic) and IV (higher IV = more extrinsic). ATM options have the most.
Five pricing inputs	Stock price, strike, time, interest rate, and IV. Only IV is unknown/estimated — it's the X-factor.
Time decay curve	Accelerates as expiration approaches. ~50% of extrinsic value lost in the last 30 days. Buy 45–60 DTE; sell 30–45 DTE.
IV crush	IV spikes before events and collapses after. Buying options before earnings is risky — even a correct directional move can lose money. Use spreads or sell premium to mitigate.
Volatility skew	OTM puts are typically more expensive than equidistant OTM calls (fear premium). Know this when comparing strategies.
Fair value assessment	Check IV Rank, compare IV to HV, calculate breakeven, and know the expected move before entering any trade.

📝 Knowledge Check

Test your understanding of options pricing mechanics.

Question 1: A call option has a premium of $9.00. The stock is at $108 and the strike is $100. What is the extrinsic value?

$8.00 $1.00 $9.00 $0.00

Question 2: An out-of-the-money option's premium is made up of:

100% intrinsic value 50% intrinsic, 50% extrinsic Mostly intrinsic value with a small extrinsic component 100% extrinsic value — it has zero intrinsic value

Question 3: Which of the five pricing inputs is the only one that is unknown/estimated?

Current stock price Time to expiration Implied volatility Strike price

Question 4: Time decay is fastest when:

In the final 30 days before expiration — the curve accelerates sharply In the first 30 days after purchasing — options lose value immediately Time decay is constant and linear throughout the option's life When implied volatility is low

Question 5: You buy a call before earnings. The stock jumps 6%, but your option barely breaks even. The most likely cause is:

The strike price changed after earnings IV crush — implied volatility collapsed after the event, destroying extrinsic value The option expired before earnings The bid-ask spread widened to absorb your profit

⚠️ Important Disclaimer

📋 In This Lesson