We assume no arbitrage hypothesis. We assume that the interest rate of the money market account is equal to r. We denote by C(t,St,T,K) (resp. P(t,St,T,K)) the price at time t of the call (resp. of put) with maturity T and strike K. We are interested to price an option, called Chooser, that gives the right to chose at time T0 if this option is a call with maturity T>T0 and strike K or a put with same maturity and strike 1. Justify why the value of the option at time T0 is equal to Chooser(T0,ST0,T,K)=max[C(T0,ST0,T,K),P(T0,ST0,T,K)] 2. Give the final payoff of this option at time T. 3. Using call-put parity, show that the chooser payoff can be written as Chooser(T0,ST0,T,K)=C(T0,ST0,T,K)+V(T0,ST0,T,K) where V(T0,ST0,T,K) is a function to be calculate. 4. Give the price of this option for t[0,T0] and give a static hedging thanks to vanilla option for t[0,T0]