Exercise: Extracting implied forward from market quotes

For the 1-year options on SPY, you observe the following market mid-quotes:

Assume $r = 5\%$, no short-sale constraints.

Tasks

1. For each strike, compute $C - P$, then extract the "implied forward price" $F_K = K + e^{rT}(C - P)$.

2. If the market is arbitrage-free, $F_K$ should be the same across all strikes. Do the four values agree?

3. If you observed $F_K$ with noticeable variation, what would it tell you about the market?

4. The SPY spot price is $S_0 = 440$. The "implied dividend yield" satisfies $F = S_0 e^{(r - q)T}$. Extract $q$.

Hint

$e^{rT} = e^{0.05} \approx 1.05127$.