The Black-Scholes model is time-inconsistent in the way it is applied in practice. This is because the model assumes that volatility is constant, even though the trader changes it every day to obtain a new price. Using this definition of time-inconsistency, which of the following statements is valid?
A) The stochastic volatility model is time-consistent because the volatility of volatility is allowed to change in the model.
B) The GARCH model is time-consistent because traders who use GARCH do not change their inputs to the model frequently.
C) Implied binomial trees are time-consistent even though the implied volatility smile used to calibrate it changes over time.
D) The stochastic volatility model is time-inconsistent.

Question

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The Answer of The Black-Scholes model is time-inconsistent in the way it is applied in practice. This is because the model assumes that volatility is constant, even though the trader changes it every day to obtain a new price. Using this definition of time-inconsistency, which of the following statements is valid?
A) The stochastic volatility model is time-consistent because the volatility of volatility is allowed to change in the model.
B) The GARCH model is time-consistent because traders who use GARCH do not change their inputs to the model frequently.
C) Implied binomial trees are time-consistent even though the implied volatility smile used to calibrate it changes over time.
D) The stochastic volatility model is time-inconsistent.

The Black-Scholes Model Is Time-Inconsistent in the Way It Is