Butterfly Spread Arbitrage 2
Given the NVIDIA (ticker: NVDA) options chain, all expiring at the end of the month with strike prices of $165, $170, $175, $180, and $185, suppose the put options respectively cost $9, $12, $14, $14.5, and $15, and the call options cost $15, $14, $13, $12, and $9. Is there an arbitrage opportunity if the underlying NVDA stock is selling at $175?
Answer
There are many butterfly spread arbitrages, one such is the following.
Consider a long call butterfly spread at strikes 175, 180, 185:
\[
+1\;\text{call}_{175},\quad -2\;\text{call}_{180},\quad +1\;\text{call}_{185}.
\]
Net premium received:
\[
-13 + 2\times12 - 9 = +2.
\]
In this case, the long butterfly’s payoff is always nonnegative (floor is \(2\)) and we lock in a (minimum) profit of $2.