Pricing Long-term Options on the NIFTY (Part II)

In my last post,   I ended up looking at long-term call options on the NIFTY mainly in terms of liquidity.  This one looks at their prices in greater detail.   my motivation is to come up with a decent, intuitively grasp-able, model for pricing these instruments.  That Black-Scholes fails badly here is quite appearent from the base priecs that one sees set by the NSE when these contracts are listed.  These computed base prices show up as the closing price on the F&O Bhav sheets until the first trade takes place.  In all cases that I've looked at the first actual trade happened at anywhere between 20-70% of NSE's base price.  Here's the evidence from the 6 contracts that we're tracking from the previous post:

Contract	Last base Price	First Trade	Ratio
24-Jun-10 5000	2001.95	880	44%
30-Jun-11 4000	2353.9	1585	67%
30-Jun-11 4500	2489.55	1470	59%
30-Jun-11 5000	2407.7	950	39%
30-Jun-11 5500	2236.75	600	27%
30-Jun-11 5700	2172.7	519	24%

As a first exercise, I made scatter plots of "Price" vs. "Underlying"  (no time order).  My feeling was that, since the expiries are way out in time, it really donesn't matter when the trade took place over the last 6 months.  All that really counts is that a trade took place on that day.  So I used close price as a proxy for "Price" and NIFTY's closing as a proxy for "Underlying" on all days when any trades took place.  The results appear below.

The biggest suprise for me was the fact that the data seems to fit a nice linear regression like some textbook physics experiment.   And the more trades a contract had (see JUN-2011 call @ 5000, for example), the better the fit appeared to be.

I used excel to do the fit and here are the equations it threw up (Price = A*NIFTY + B):

Contract	A	B
24-Jun-10 5000	0.4074	-1190
30-Jun-11 4000	0.6523	-1768.6
30-Jun-11 4500	0.652	-1965.3
30-Jun-11 5000	0.5677	-1788
30-Jun-11 5500	0.3034	-788.47
30-Jun-11 5700	0.3857	-1196.6

We're now closer we were than at the end of the last post to answer my original question: what is the delta on these things?  But we're nowehere near done yet.

(To be continued...)