Straddle = Call + Put?

[CGiuliano]

In the European case does it always hold that the value (V_0,) of a straddle (|S_n - K|,) has

(V_0 = C_0 + P_0,)

Where (C_0) and (P_0) are the values for a call and put respectively.

This question seems almost trivially true.... But how to prove?

 

[ktang]

It is really trivial. Using the fact that |S-K|=(S-K)+ + (K-S)+ where (x)+=max(0,x) you will get the solution.