Basic Option Pricing Drivers

Option prices reflect six fundamental inputs: underlying price, strike price, time to expiration, volatility, interest rates, and expected dividends. Understanding how each factor affects premiums helps you evaluate whether options are fairly priced and anticipate how values will change.

Definition and Key Concepts

The Six Pricing Inputs

Intrinsic vs. Extrinsic Value Review

Option premiums consist of:

• Intrinsic value: The in-the-money amount (immediate exercise value)
• Extrinsic value (time value): Everything above intrinsic value, determined by the other five inputs

Pricing models calculate the probability-weighted expected value of all possible outcomes, discounted appropriately, to determine fair extrinsic value.

How It Works in Practice

Underlying Price

As the underlying rises:

• Calls become more valuable (more likely to finish ITM, higher potential payoff)
• Puts become less valuable (less likely to finish ITM, lower potential payoff)

This relationship is captured by delta. A 0.50 delta call gains approximately $0.50 for each $1 increase in the underlying.

Strike Price

For a fixed underlying price:

• Lower strike calls are more valuable (closer to or further ITM)
• Higher strike calls are less valuable (further OTM)
• The reverse applies to puts

Strike selection involves balancing cost, probability, and leverage.

Time to Expiration

More time means more opportunity for favorable moves. Both calls and puts gain value with additional time to expiration. This relationship is captured by theta (time decay):

• Options lose extrinsic value daily as expiration approaches
• Time decay accelerates in the final weeks
• ATM options experience the highest theta in dollar terms

Time Value Decay Pattern:

The rate of decay increases as expiration nears.

Volatility

Volatility measures the magnitude of expected price swings. Higher volatility increases the probability of large moves in either direction, benefiting option holders (who have limited downside but unlimited or substantial upside).

• Higher implied volatility → higher option premiums
• This relationship is captured by vega
• A 1-percentage-point increase in IV might add $0.15 to a 30-day ATM option

Volatility is the most actively traded component of option prices. Many option strategies are volatility bets rather than directional bets.

Interest Rates

Interest rates affect option prices through the opportunity cost of capital:

• Call buyers defer paying the strike price; higher rates increase this benefit
• Put buyers defer receiving the strike price; higher rates decrease this benefit

In practice, interest rate sensitivity (rho) is usually small relative to other factors, especially for short-dated options.

Expected Dividends

Dividends reduce stock prices on ex-dividend dates:

• Call values decrease as expected dividends increase (stock drops reduce call value)
• Put values increase as expected dividends increase (stock drops increase put value)

Option prices incorporate expected dividends. Surprise dividend announcements can shift option values significantly.

Worked Example

Scenario: Analyzing option price sensitivity

XYZ stock trades at $100. Consider the $100 call with 30 days to expiration:

• Premium: $4.00
• Delta: 0.52
• Gamma: 0.03
• Theta: -$0.08 per day
• Vega: $0.15 per 1% IV change
• Current IV: 30%

Impact of Each Driver:

Combined Scenario: Stock rises $3, IV drops 5%, 7 days pass:

• Delta effect: +$3 × 0.52 = +$1.56
• Vega effect: -5% × $0.15 = -$0.75
• Theta effect: -7 × $0.08 = -$0.56
• Net change: +$1.56 - $0.75 - $0.56 = +$0.25
• New premium: $4.25

The $3 stock gain is partially offset by IV decline and time decay.

Greeks Summary Table:

Risks, Limitations, and Tradeoffs

Model Assumptions

Option pricing models assume:

• Continuous price movements (no gaps)
• Log-normal price distribution (limited accuracy for extreme moves)
• Constant volatility (in reality, volatility varies)
• No transaction costs

Real markets deviate from these assumptions, creating pricing anomalies and opportunities.

Implied vs. Realized Volatility

Implied volatility (IV) reflects market expectations. Realized volatility measures actual price swings. When IV exceeds realized volatility, option sellers profit. When realized exceeds IV, option buyers profit.

This gap between implied and realized is the foundation of many volatility strategies.

Non-Linear Relationships

Greeks are not constant:

• Delta changes as price moves (gamma)
• Vega changes with price and time
• Theta accelerates near expiration

Simple linear estimates work for small moves but break down for larger changes or longer periods.

Volatility Smile and Skew

Implied volatility varies across strikes:

• OTM puts often have higher IV than ATM options (skew)
• Far OTM calls and puts may have elevated IV (smile)

These patterns reflect demand for tail risk protection and don't match model assumptions of constant volatility.

Common Pitfalls

1. Ignoring volatility: Focusing only on direction while overpaying for inflated IV is a common error.

2. Underestimating theta: Time decay is certain; price movement is not.

3. Using static Greeks: Delta changes as price moves. Reassess after significant price changes.

4. Overlooking dividend adjustments: Surprise dividends can unexpectedly shift option prices.

5. Assuming Greeks are precise: They're estimates based on models with simplified assumptions.

Checklist for Evaluating Option Prices

• Identify the current underlying price and your directional view
• Compare implied volatility to historical volatility
• Calculate time decay (theta) over your expected holding period
• Assess delta for directional exposure and probability
• Check vega to understand volatility sensitivity
• Consider upcoming events that might change IV
• Factor in expected dividends before expiration
• Review whether the premium seems reasonable given all inputs

Next Steps

Before trading options, brokers require acknowledgment of risk disclosures. Learn what these documents contain and why they matter in Risk Disclosures Required Before Trading.

For background on how intrinsic and time value combine, see Intrinsic Value vs. Time Value.