In four iterations, the Newton Raphson method had done what Goal Seek couldn’t do in forty. It converged like a hawk diving on a mouse. The portfolio’s implied volatility: .
0.25 → 0.35 → 0.42 → 0.197 → 0.203 → 0.19999.
He saved his VBA module as "Module_Newton.bas" and placed the PDF in a new folder called “Weapons.”
He’d downloaded it six months ago and never read it. “Classic,” he sighed. How To Code the Newton Raphson Method in Excel VBA.pdf
But he did rename the file.
“You can’t solve for ‘x’ if it’s on both sides of the equation,” he muttered, sipping cold coffee.
Arjun’s eyes widened. He didn’t need calculus. He just needed two guesses. In four iterations, the Newton Raphson method had
He switched back to VBA and started typing. He didn’t copy-paste. He wanted to feel the logic. He declared his variables: x0 As Double , x1 As Double , tolerance As Double . He wrote a function called NewtonRaphson(FunctionName As String, guess As Double) .
“If you cannot calculate the analytic derivative, use the Secant approximation: f’(x) ≈ (f(x + δ) − f(x)) / δ.”
Do While Abs(x1 - x0) > tolerance fx0 = Application.Run(FunctionName, x0) fx0_plus_delta = Application.Run(FunctionName, x0 + delta) derivative = (fx0_plus_delta - fx0) / delta x1 = x0 - fx0 / derivative x0 = x1 Loop He linked it to his volatility model—a user-defined function named PriceError() that returned the difference between the market price and the model price. But he did rename the file
Arjun stared at the blinking cursor in the VBA editor. It was 11:47 PM. The spreadsheet, “Q3_Revenue_Forecast.xlsx,” was a mess of circular references and manual guesswork. His boss, Helena, needed the implied volatility of a client’s derivative portfolio by 8:00 AM, and the analytical solution was a ghost—impossible to isolate.
He double-clicked. The PDF was short—only seven pages—but it was beautiful. Page one had a diagram: a curved function, a tangent line kissing the x-axis, and an arrow labeled xₙ₊₁ = xₙ − f(xₙ)/f’(xₙ) .