I'm currently stuck on trying to prove the following:
use a 1-step binomial model, we have two otherwise identical call options with expiration $T_1$ and $T_2$. Prove that $c_1 ≤ c_2$.
Here's the notations I've used:
$S_0$ = spot price
$u$ is when price moves up, S0 becomes $S_0\times u$; similar for $d$ but when price moves down
$S_u = S_0 \times u$
$S_d = S_0\times d$
$K$ = strike price for the option
$C_1$ & $C_2$ indicates the option price for the corresponding call
I've successfully proved the cases where $S_d < k < S_u$ and where $K > S_u > S_d$.
However, I'm stuck to prove for the case where $K < S_d < S_u$.