Convert implied volatility to local volatility using the Dupire formula. Calculates the instantaneous local volatility at a specific (strike, expiry) point from an implied volatility surface. Uses finite differences to approximate derivatives. Essential for building local volatility surfaces for exotic option pricing and Monte Carlo simulations.
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Current spot price of the underlying
x >= 0100
Risk-free interest rate (continuously compounded)
-0.1 <= x <= 10.05
Strike price for local vol calculation
x >= 0105
Time to expiry in years
x >= 01
Implied volatility at (strike, expiry). For full surface conversion, use a volatility surface function
0 <= x <= 50.25
Strike increment for finite difference (as fraction of strike)
0.0001 <= x <= 0.10.01
Time increment for finite difference (in years)
0.0001 <= x <= 0.10.01