No-arbitrage cap on a 20/24 put spread

Consider a put spread built by buying a put with strike $24$ and selling a put with strike $20$, both expiring at $T$. The stock is at $S_0 = 23$, and a zero-coupon bond paying $1$ at $T$ costs $0.9$ today.

What is the tightest upper bound on the spread's price at time $0$?

$3.6$. The spread pays $\max(24-S_T,0)-\max(20-S_T,0)$, which is never more than $24-20 = 4$. Four bonds therefore dominate it, so by no-arbitrage its price is at most $4 \times 0.9 = 3.6$. More generally, for strikes $a<b$ the put spread is worth at most $(b-a)$ discounted bonds.