What does it mean when put option is undervalued and overvalued?

[oouu5703]

I am studying p1, t1, Stulz's governance chapter and I really do not understand the part below. What is put option's undervalue and overvalue have to do with NPV? I appreciate your help. Thank you!

"A trading desk’s writing of underpriced, deep-out-of-the-money puts based on traders’ expectation that if the puts are not exercised and the desk ends up booking the premiums as income, the traders will receive higher bonuses. For the traders themselves, this seems like a can’t-lose proposition. If the puts do end up being exercised, the traders would have been unlikely to receive a bonus anyway because
asset values would have had to have fallen by a lot. But for the bank’s shareholders, such a trading strategy is a negative NPV project as a stand-alone project since the bank is selling an asset for less than it is worth."

 

[Sixcarbs]

There is a price at which selling way out of the money puts is a good risk/reward and positive NPV. Since a lot of models do not account for fat tails of the probability distribution, out of the money puts can easily be priced too low. (Although by today I hope most market makers have figured this out.)

If your model is not adjusting for the tail risk and it tells you some way out of the money put is worth 25 cents, even selling it for 35 cents might not be a sale that has any edge or NPV. Maybe the fair value if priced correctly is 45 cents and selling at 35 cents has negative NPV.

To make money you need to sell options above their model value, buy options below their model value, and continuously hedge over the life of the option. The most important input into the model is volatility. But if you are just using a single volatility for all of your options you need to manually boost the out of the money options (The cheap ones), especially on the downside.

Way out of the money puts are not easy to hedge with the underlying stock, you usually need to bid up some similar out of the money puts.

So back to the traders selling out of the money puts because they look like free money. They may be, until they are not. The price they sell them for does not change the return profile, but it does change the risk/reward or here they call it NPV. Think of it as selling cheap flood insurance in an area that is prone to flooding. It's ok to sell that insurance, but it needs to be priced appropriately.

We used to say that selling cheap puts are like picking up nickels in front of a steam roller.

Finally the term, "deep-out-of-the-money puts" is not a good way to refer to them. "Deep" always implies way in the money, whether they are calls or puts.