Option Pricing Curve

An option pricing curve is a plotted line showing what an option's theoretical price would be across a range of possible underlying stock prices, at a given moment in time. Picture a chart with the stock price along the bottom axis and the option's price up the side; the curve traces out the option's value at every point along that range, holding time and volatility fixed.

The curve is not drawn from market trades — it is generated by a pricing model (commonly a variant of Black-Scholes or a binomial model) that takes inputs like the stock price, strike price, time remaining until expiration, volatility, and interest rates, and outputs a theoretical option price. Feed the model a range of hypothetical stock prices instead of just one, and you get the whole curve rather than a single point.

The shape of the curve tells you two things at once: intrinsic value (what the option would be worth if exercised right now) and time value, or extrinsic value (the extra premium buyers pay for the chance the option becomes more valuable before expiration). Far from the strike price, the curve tends to flatten toward zero or hug the intrinsic value line; near the strike, it bulges upward because uncertainty about the outcome is highest there, and that bulge is time value.

The detail that trips beginners up is that the curve is a snapshot, not a fixed object. Every input to the model — days to expiration, implied volatility, interest rates — shifts the curve. As expiration approaches, the curve flattens and hugs intrinsic value more tightly (time value shrinks toward zero). Delta, the number that tells you how much an option's price moves per one-dollar move in the stock, is simply the steepness (slope) of the curve at the point matching today's stock price — so delta itself changes as the stock price moves along the curve, or as the curve reshapes over time.