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

question 21

Multiple Choice

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.

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Definitions:

Alimentary Canal

The digestive tube extending from the mouth to the anus, through which food is ingested, digested, absorbed, and waste material expelled.

Amylase

An enzyme that catalyzes the hydrolysis of starch into sugars, found in the saliva and pancreatic fluid of humans.

Starch

A carbohydrate consisting of a large number of glucose units, serving as a major energy source from food.

Gallbladder

A small organ located under the liver, which stores and concentrates bile, a digestive enzyme produced by the liver.