First define a Black-Scholes process with constant parameters.
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You can compute the expected payoff of a European call option with strike 100 maturing in 1 year.
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You can then compare the result to the theoretical price.
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This is incorporating local volatility term structure.
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Again, you can compute the expected payoff of a European call option with strike 100 maturing in 1 year.
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Then you can compute the implied volatility.
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In this example we implied volatility surface obtained using a piecewise interpolation of known prices.
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