Find a piecewise constant volatility function that is, Basic Computer Science

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Find a piecewise constant volatility function that is

A stock, S_t, follows geometric Brownian with time-dependent volatility. We have S_o =100, and r = 0%. Call options struck at 100 with maturities 0.5, 1 and 2 have implied volatilities of 10%, 15% and 20%. Find a piecewise constant volatility function that is consistent with these implied volatilities.

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Basic Computer Science: Find a piecewise constant volatility function that is

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