Model and input conventions
The search interval runs from zero to 500% annualized volatility. Positive time to expiry is required, and the call must lie between its discounted zero-volatility payoff and the discounted underlying-price limit. A premium at the upper limit has no finite-volatility solution. A premium requiring more than 500% is rejected explicitly. Inside the bracket, bisection repeatedly narrows the interval using the model’s increasing price relationship.
Worked numerical example
For spot 100, strike 100, one year to expiry, a 5% continuously compounded rate and zero yield, entering a call premium near 10.450584 returns approximately 20% volatility. Re-entering the model premium produced at 75% should recover approximately 75%. Changing the rate while keeping the observed premium fixed generally changes the solved volatility, which is why all valuation conventions must remain consistent.
Read the scenario table
The comparison table shows model premiums at the solution and several alternative volatility assumptions, including bracket endpoints. The residual column subtracts the entered premium from each repriced value. It helps distinguish a well-matched numerical solution from a mistaken quote currency or expiry input. A small residual verifies the equation being solved; it does not verify the source quote or a profitable trade.
Where the model stops
Implied volatility is a parameter fitted to a price, not a direct measurement of future realized volatility. Deep intrinsic options and very short maturities can make the inversion sensitive to tiny quote changes. Quotes within the numerical price tolerance of the zero-volatility bound return zero rather than spurious precision. American exercise, inverse settlement, stale premiums and a different yield convention require separate treatment.