A chooser option is a derivative that allows the holder to choose, at a pre-specified future time, whether it is a call or a put option. To be precise, let 0

H=max{cT1,pT1}

where cT1 is the time T1 price of a call option that was initiated at time 0 and expires at time T2, and pT2 is the price of a similar put option. Both these options are assumed to have the same strike price K and are based on the same asset S. Find the time 0 price of H if S evolves according to the Black-Scholes model.