Options fair value, also called theoretical value, is what an option should be worth based on mathematical pricing models. Understanding fair value helps you assess whether options are overpriced or underpriced relative to their theoretical value, potentially identifying trading opportunities.
What Is Options Fair Value?
Fair value is the calculated price of an option based on known inputs and a pricing model. It represents the theoretical worth of an option given current market conditions.
Key Concept: Fair value is a theoretical calculation. The actual market price can differ based on supply and demand, market sentiment, and factors not captured by models.
Inputs for Fair Value Calculation
Options pricing models require several inputs:
Known Inputs
- Stock price: Current price of the underlying
- Strike price: The exercise price of the option
- Time to expiration: Days or years until expiry
- Interest rate: Risk-free rate (typically Treasury rate)
- Dividends: Expected dividends during the option's life
Estimated Input
- Implied volatility: The market's expectation of future volatility
Implied volatility is the crucial variable because it must be estimated or derived from market prices.
The Black-Scholes Model
The most famous options pricing model is Black-Scholes:
Model Assumptions
- Log-normal distribution of stock prices
- Constant volatility over the option's life
- No dividends (basic model)
- European-style exercise only
- Efficient markets with no arbitrage
Model Limitations
- Assumes constant volatility (volatility actually changes)
- Does not account for early exercise (American options)
- Assumes continuous trading
- May misprice deep OTM and ITM options
Example: Black-Scholes Calculation
Inputs for a call option:
- Stock price: $100
- Strike price: $100
- Time to expiration: 30 days (0.082 years)
- Risk-free rate: 5%
- Implied volatility: 25%
Fair value: Approximately $2.89
Fair Value vs Market Price
The market price of an option can differ from its theoretical fair value:
When Market Price Exceeds Fair Value
- Option may be overpriced
- Could be opportunity to sell
- Or market anticipates something the model does not
When Market Price Is Below Fair Value
- Option may be underpriced
- Could be opportunity to buy
- Or there is a reason for the discount
Important: The market is often right. Before assuming an option is mispriced, consider what information the market might have that your model does not.
Components of Fair Value
Fair value can be broken into two components:
Intrinsic Value
- The in-the-money portion of an option
- Call intrinsic value: Max(Stock Price - Strike, 0)
- Put intrinsic value: Max(Strike - Stock Price, 0)
- Always positive or zero
Extrinsic Value (Time Value)
- Fair Value minus Intrinsic Value
- Represents time value and volatility premium
- Decays as expiration approaches
- Highest for ATM options
Example: Value Components
Stock at $105, $100 call trading at $7.50:
- Intrinsic value: $105 - $100 = $5.00
- Extrinsic value: $7.50 - $5.00 = $2.50
- Fair value: $5.00 + $2.50 = $7.50
Using Fair Value in Trading
Identifying Mispricing
Compare market prices to theoretical values:
- Calculate fair value using your volatility estimate
- Compare to current market price
- Look for significant deviations
- Investigate why the difference exists
Spread Pricing
Fair value helps evaluate spreads:
- Calculate fair value of each leg
- Sum the fair values for net spread value
- Compare to actual spread market price
Volatility Trading
Fair value is central to volatility trading:
- If you think volatility will be higher than implied, options are underpriced (buy)
- If you think volatility will be lower than implied, options are overpriced (sell)
Fair Value Across Strikes
Fair values vary predictably across strikes:
ITM Options
- High intrinsic value
- Lower extrinsic value relative to price
- Fair value mostly from intrinsic component
ATM Options
- Little or no intrinsic value
- Maximum extrinsic value
- Most sensitive to volatility changes
OTM Options
- No intrinsic value
- Entirely extrinsic value
- Fair value decays to zero at expiration if OTM
Advanced Pricing Models
Beyond Black-Scholes, other models address its limitations:
Binomial Model
- Handles American-style early exercise
- Models stock price moving in discrete steps
- More computationally intensive
Volatility Smile Models
- Account for different implied volatilities at different strikes
- Include SABR and local volatility models
- More realistic for real market pricing
Practical Considerations
Bid-Ask Spread Impact
Fair value falls somewhere between bid and ask:
- Market makers set prices around fair value
- Bid is below fair value
- Ask is above fair value
- The spread is the market maker's profit margin
Model Risk
All models have limitations:
- Models are simplifications of reality
- Input errors compound into pricing errors
- Markets can deviate from model assumptions
Analyze Options Fair Value
Pro Trader Dashboard provides theoretical pricing analysis to help you identify potentially mispriced options and make better trading decisions.
Summary
Options fair value is the theoretical price calculated using pricing models like Black-Scholes. It combines intrinsic value and extrinsic value based on inputs including stock price, strike, time, rates, and volatility. While fair value provides a benchmark for option pricing, market prices can differ due to supply and demand or information not captured by models. Understanding fair value helps you evaluate options prices, identify potential mispricings, and make more informed trading decisions.
Continue learning with our guides on intrinsic value and extrinsic value.