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.
At 7:55 AM, he emailed Helena the results. He attached a clean sheet with one button: “Calculate Vol.” He didn’t tell her about the PDF. He didn’t mention the cold coffee or the 11:47 PM panic.
Then he turned to Page 4.
He ran it.
Arjun’s eyes widened. He didn’t need calculus. He just needed two guesses.
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) .
He saved his VBA module as "Module_Newton.bas" and placed the PDF in a new folder called “Weapons.” How To Code the Newton Raphson Method in Excel VBA.pdf
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: .
He minimized Excel and opened his downloads folder. Scrolling past a dozen forgotten files, he found it: How To Code the Newton Raphson Method in Excel VBA.pdf .
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. Do While Abs(x1 - x0) > tolerance fx0 = Application
Because next time the equation was impossible, he wouldn't be searching his downloads. He'd be ready.
“The derivative is the problem,” Arjun whispered. He didn’t have a symbolic derivative. He had a messy Monte Carlo simulation in column G.
