I own some $16 puts which have gone ITM and I would like to roll them down but the exchange(s) haven't added 1/2 point strikes yet. Yes, I know that I can request that they add them and more often than not, they have complied. More than likely, they will add them tomorrow, on their own. But if not, with the stock at $14.50, can a combination of $15 and $14 puts be used to reasonably replicate the $14.50 puts which don't exist? Here's where I go off the reservation (g). Buying one $15 and one $14 puts would duplicate the delta of two $14.50 puts (if they existed). Makes sense so far... but if I were to model long 1 each and short the 2, it would look like a butterfly spread, so that's not the answer. Or is it? Meaning that the $14/$15 combo duplicates two $14.5's outside of the strikes ($14 and $15) but b/t the strikes, the non linear behavior of premium and delta results in a P&L difference and that is just the cost of doing business? Any other suggestions for a reasonable facsimile?
I'm responding before giving much thought, but for each 2 14.50 puts Desired, can't you merely do one 14 + one 15 put, as a rough replacement? Ie, roll 4 (of 8) 16 puts, to 14 strike, and the other 4 roll to the 15 strike, for a new position similar to a 14.50 strike?
What you described is what I suggested as a rough replacement. If price was somewhere other than the midpoint of the two strikes then the net delta could be simulated by doing more of one strike than the other or vice versa. Conveniently, it's right in the middle at $14.50 If one selected an arbitrary IV number, determined the theoretical value of each of the 3 strikes and modeled a position of long one $14p, long one $15 put and short two $14.5p then the P&L would flatline at zero if the replacement ($14 p plus $15 p) is equal to the desired leg ($14.5 p). It is outside of $14 and $15 but not in between. Overall, it would look like a butterfly. My guess is that's just the way it is, due to non linear characteristics and that's the rough replacement. I was just wondering if there was anything more accurate than that.
I am reasonably sure that there are all sorts of rather traditional techniques for that. One of the main purposes of various vol models out there is, among others, the sort of "arbtirage free" inter/extrapolation that you describe. Unfortunately, I don't know what the standard methodology is for equity options and not sure if there are "quick and dirty" ways of applying them.
FWIW, I E-mailed the CBOE at MARKETSERVICES@CBOE.COM and within 5 minutes they approved adding several expirations of the strike I wanted, to begin trading the next morning.