In order to avoid the problem of implied volatilities being different for different strike prices and maturities, a student of the Black Scholes theory suggests making the stock 's volatility a function of K and T, (K, T) What is wrong with this suggestion, at least from the theoretical modeling point of view (In practice, though, traders might use different volatilities for pricing options with different maturities and strike prices )

Question: In order to avoid the problem of implied volatilities being different for different strike prices and maturities, a student of the Black-Scholes theory suggests making

In order to avoid the problem of implied volatilities being different for different strike prices and maturities, a student of the Black-Scholes theory suggests making the stock's volatility σ a function of K and T, σ(K, T). What is wrong with this suggestion, at least from the theoretical/modeling point of view? (In practice, though, traders might use different volatilities for pricing options with different maturities and strike prices.)

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