Put Arbitrage

If the Put option on the $50 strike is trading at $10, and the put option on the $30 strike is trading $6, is there an arbitrage opportunity?

What if the stock is also available to trade? Does it matter what the stock price currently is?

#QuantitativeFinance

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Comments

If you can pay 6$ to sell the share at 30$, it means that the price of the stock is probably lower than 30. If you can pay 10$ to sell the stock at 50$ while its currently trading for less than 30$, there is an opportunity: Buy the stock for less than 30$, buy the put with a strike price of $50 and sell the stock at 50$, the profit will be at least 50-30-10= 10$ ...right?

Thomas Derambure - 5 years, 9 months ago

Not true. Since the $50 put is only worth $10, this means that the intrinsic value is at most $10, and hence the price of the stock is at least $40. If the price was lower then $40, then we could buy the $50 put for $10 and buy the stock, and then on expiration exercise the put and sell the stock for $50.

Calvin Lin Staff - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$