The buyer of an at$-$the$-$money forward$-$start call option, with forward$-$start date T$1$

and exercise date T$2>$ T$1,$ receives at date T$1$ a standard European call option struck

at K $=$ ST$1$ and expiring at date T$2.$ Suppose the Black$-$Scholes assumptions hold.

a$.$ What is the price of the forward$-$start option at date T$1?$

b$.$ What is the price of the forward$-$start option at date $0?$ Relate this to the price

of a standard option at date $0.$