The Greeks Lab

The green curve is the option's value at every stock price; the white dashed line is the tangent at the current price — its slope is delta. Deep out of the money the curve is flat (delta ≈ 0: the stock moves, the option shrugs). Deep in the money it's a 45° line (delta ≈ 1: the option moves dollar-for-dollar). Delta is also a rough probability of expiring in the money — the proxy the wheel calculator uses for assignment odds.

This is delta plotted against the stock price — and gamma is the steepness of this curve. It peaks at the strike: that's where an option flips fastest between "probably worthless" and "probably stock". Watch what happens when you cut days-to-expiry above: the S-curve sharpens into a step, which is why the last week of an at-the-money option feels like a coin toss with a dial.

The option's value as the clock runs out, with the stock frozen at today's price. The dot is where you are now. Note the shape: decay is not linear — it accelerates toward expiry, especially at the money. This chart is the seller's whole business model and the buyer's rent bill; it's also why the payoff builder's time-machine slider melts fastest in its final days.

Option value against implied volatility, everything else frozen. The relationship is almost a straight line — and it never slopes down: more expected movement makes every option worth more, calls and puts alike. This is how you can be right about direction and still lose money after earnings: the stock moved your way, but implied volatility collapsed and vega took back more than delta paid you.

Option value against the risk-free rate. Higher rates nudge calls up and puts down — a call is partly a way to control stock while keeping your cash earning interest. Rho is the forgotten Greek for short-dated trades, but stretch days-to-expiry above to a year or two and watch it matter — the same carry logic that the box spread tool turns into an actual lending rate.