I would like to understand why the Black and Scholes greek letter theta for european call option behave in the following way:
as time to maturity is far away (right part of the x-axis in the the graph) theta is small for all the call options (ATM, ITM e OTM). Therefore this means that the call value decrease by a small amount as time passes when time to maturity is far away.
as time to maturity approach zero, i.e. close to the expiry, (left part of the x-axis in the graph) ITM and OTM call option theta get close to zero (i.e. theta decrease in absolute value) while ATM call option theta get bigger and bigger in absolute value. Therefore, when we are close to maturity, ATM call option decrease in value much more than ITM and OTM call option due to passage of time.