Theoretical Price
What a pricing model says an option should be worth, versus what it trades for.
Definition
Theoretical price is the fair value of an option calculated by a pricing model, most commonly Black-Scholes, from five inputs: the spot price, the strike, time to expiry, the risk-free interest rate, and volatility. It is the model's estimate of what the option ought to cost.
Formula
Theoretical price = f(Spot, Strike, Time, Rate, Volatility)
For a Black-Scholes call: C = S×N(d1) − K×e-rt×N(d2), where N() is the cumulative normal distribution.
Why it matters
Comparing the theoretical price to the live market price tells you whether the market is pricing more or less volatility than you assume. It is also the basis for the option Greeks, since each Greek is a sensitivity of this fair value to one input. Traders use it to judge relative value, build hedges, and reverse-engineer implied volatility.
Example
You feed a model spot 1,000, strike 1,000, 7 days to expiry, and 20% volatility, and it returns a theoretical call price of 18. If the market is quoting 24, the market is implying higher volatility than your 20% assumption.
See it live
TradePulse's Greeks calculator computes theoretical prices and Greeks so you can compare model value to live quotes.