Here's what a "Senior Specialist in Derivatives Trading" at Schwab wrote me, after they checked in real time during our phone call that the SPX ITM puts I referenced had significant negative extrinsic value (aka time value):

From: Schwab Client Service
Dear NAME DELETED

After further researching the pricing of in the money long term puts on SPX, I did find a couple reasons for the intrinsic value not being fully priced into the current Ask price.

The main reason will be because index options are European style which means they can not be exercised until expiration. This means the option must be held full term which will tie up some buying power whereas with stock options arbitrage could be captured by instantly exercising the option to take on the share position. This does allow for index options to sometimes be priced below the intrinsic value to consider the time factor involved.

> Above seems related to the point I made: SPX doesn't have 'shares', so you can't arbitrage SPX options with shares like you can arbitrage SPY options with shares. The share arbitrage mechanism for SPY keeps SPY option's extrinsic value non-negative. The extrinsic value of SPX options can be significantly negative, as per my examples.

Interest rates will also effect options pricing which is expressed through the option greek Rho. Calls have positive Rho while Puts have negative Rho so as interest rates increase the value of puts will be lowered while premium on calls will be raised. If you look at option prices when interest rates are lower you will see how pricing was different during these times of lower rates.

> Not sure I understand the above because Rho is an *instaneous* measure and interest rates didn't jump at the time of my examples. BWDIK?

If you have any additional questions please feel free to contact us back at the trade desk at 877-870-7271.

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Sincerely,

NAME DELETED
Sr Specialist | Derivatives Trading
Tel 877-870-7271
500 Maryville Center Dr, St. Louis, MO 63141