As I mentioned previously, if all pricing parameters other than the underlying's price are equal, then a similar pecentage change in the UL will result in the same percentage price in the options. You can verify this for yourself with an option pricing formula.
True, you will be getting the same greeks and prices in the Black-Scholes world. However, in real world, do you think the liquidity profile, volatility risk premium, directional component of volatility and "jumpiness" of the asset would be different?
I've been trading the spx and the spy. They are priced at a 10 to 1 basis and they follow each other very closely. However I've noticed the options premiums don't follow each other on a 10 to 1 basis. Maybe 6 or 7 to 1. But the spx is safer to trade assignment wise so there is some trade off there. Not sure if anyone else can explain any other differences? Thanks.
I really don't know what any of that has to do with the OP's question. His question was that all if pricing parameters other than underlying price are equal (such as volatility, time to expiration, etc.), should there be any difference in the way the options perform. IOW, will the respective options appreciate in value by the same percents? I say yes. Do you believe otherwise, in the context of his specific question?
OP question was, as far as I read it: So, from the perspective of practical use ("implementation"), there definitely are differences. Does not mean you are wrong, it's just what I understood his question to be.
+1 for the question. esp today w/ hft, bots, whatever that is a ridic wide spread. if spx "only" went up by a factor of 9.9 that would still be a huge opp much less 6 or 7.
Thanks for all the responses so far. In the CBOE's rulebook there is a rule that relates to the permissible price deviation from the option's theoretical price, so that if an option trade is within that range the trade will usually not be considered an obvious price error for bust purposes. I noted that the range regarding options with high prices (such as above 20 points premium) is much lower, in percents, than the range regarding options with low prices (such as below 2 points premium). See the link: http://cchwallstreet.com/CBOETools/...nual-cboe_6.25&manual=/cboe/rules/cboe-rules/ I assume there is a reason that the exchange allows such different ranges in percents, and I want to understand how it can be relevant to my original question as to the difference between options with high premiums and low premiums. Do you have any idea?
I can see that interpretation if you ignore the OP's criteria that all other parameters except for the underlying price are equal. Obviously, implementation may be different based on different behavior of his $10 and $100 stocks but if all else is equal, option pricing is linear with respect to the UL's price.
If the two UL's track each other at an exact ratio of 10:1 and IV's are the same, the options should track pretty close to 10:1. IRL, they don't plus spread size varies. I assume there may be other small discrepancies as well. So I wouldn't expect an exact 10:1 correlation. But close. 6 or 7 to 1 is a bit extreme so like others have asked, got any examples?