Determine the limiting value of gamma as we approach maturity (i.e., find lim T0 ) for each

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Determine the limiting value of gamma as we approach maturity (i.e., find limT→0Γ) for each of the following options:

(a) A deep in-the-money European call option

(b) A deep out-of-the-money European call option

(c) An at-the-money European call option 

For each option, provide an intuitive explanation and a mathematical explanation.

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