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

NSE notified long term contracts on the NIFTY on Feb 27, 2008. In addition to the near, next and far month expiries, we now had 3 quaterly expiries and 5 half-yearly expiries. In effect, these contracts allow one to take a view on the NIFTY upto 3 years into the future. Trading started on Mar 3, 2008.

When these contracts were introduced, there was much doubt raised to their viability. It was pointed out that the volumes on far (and even next) month options were quite thin for the most part. In a ominous sign a month or two following its launch, ICICIdirect, India's largest brokerage by some measures, suddenly and inexplicably dropped support for these contracts from their trading platform. Press coverage was muted (see here). That NSE's most recent attempt at broadening the derivatives market, the so-called Mini-NIFTY contracts, had been an utter failure didn't help either.

Today, 6 months later, we may safely conclude that these contracts are here to stay. The volumes, while not spectacular, are very respectable. There is a good mix of trading and investment activity from the looks of the order books. Most importantly, investment companies such a KMIL are introducing hedge-fund style products that are built on top of these contracts. The table below gives the open interest position as on Sep 5, 2008 across all expiries.

Series	Expiry	Open calls (Rs. Cr.)	Open puts (Rs. Cr.)	Total O.I. (Rs. Cr.)
Near, next and far month	25-Sep-2008	8650.31	9688.93	18339.25
	29-Oct-2008	441.89	1121.86	1563.75
	27-Nov-2008	96.02	139.05	235.07
3 quarterly expiries	25-Dec-2008	2037.88	3200.97	5238.85
	26-Mar-2009	62.30	226.47	288.77
	25-Jun-2009	494.62	340.37	834.98
5 half-yearly expiries	31-Dec-2009	326.64	289.38	616.01
	24-Jun-2010	98.73	66.62	165.35
	30-Dec-2010	318.56	320.85	639.41
	30-Jun-2011	1272.46	893.19	2165.65
	29-Dec-2011	3.05	0.63	3.68

I am interested in these contracts as a means of taking leveraged bets on the NIFTY. As a firm believer in the NIFTY's long term growth potential, my options before Mar 2008 were between buying an index linked exchange traded fund, such as the NIFTY BeES, or buying and constantly rolling over NIFTY futures contracts. The former offers no leverage at all, the latter is quite painful to do without a large corpus and full-time staff. Long-term options provide leverage (high-delta) and require no maintenance. But what is the delta on these things? This is the question that I shall attempt to answer in subsequent articles.

For my study, I needed to pick a sub-set of contracts whose pricing could be meaningfully studied. As a long-only investor, I'm naturally only interested in calls. As a long term investor, only the half-yearly expiries interest me. But even after filterting for those two, I'm left with a total of 114 contracts across the 5 expiries. Of these only 44 have ever been traded. A glance down this list of 44, revealed that the action seems to be bunched up around a few contracts. I set the somewhat atrbitrary criteria that I'll picks only those contracts that have seen trades on at least a fourth of the days on which they have been listed and ended up with just six. The table below lists the 44. The ones I picked are in red.

Expiry	Strike	Listed Since	Days Listed	Days Traded	Max O.I	O.I
24-Jun-2010	4300	10-Mar-2008	121	3	100	50
24-Jun-2010	4400	05-Mar-2008	123	1	50	50
24-Jun-2010	4500	04-Mar-2008	124	1	50	50
24-Jun-2010	4900	03-Mar-2008	125	7	7800	7800
24-Jun-2010	5000	03-Mar-2008	125	42	185750	185700
24-Jun-2010	5100	03-Mar-2008	125	5	3750	3750
24-Jun-2010	5200	03-Mar-2008	125	2	100	100
24-Jun-2010	5400	03-Mar-2008	125	1	50	50
30-Jun-2011	3500	01-Jul-2008	47	2	1150	1150
30-Jun-2011	4000	18-Mar-2008	115	50	342200	342200
30-Jun-2011	4100	14-Mar-2008	117	1	40750	40750
30-Jun-2011	4200	14-Mar-2008	117	2	9350	9350
30-Jun-2011	4300	10-Mar-2008	121	2	115050	115050
30-Jun-2011	4500	04-Mar-2008	124	56	561550	561150
30-Jun-2011	4600	04-Mar-2008	124	1	58750	58750
30-Jun-2011	4700	03-Mar-2008	125	1	50	50
30-Jun-2011	4900	03-Mar-2008	125	1	5250	5250
30-Jun-2011	5000	03-Mar-2008	125	102	773400	773400
30-Jun-2011	5100	03-Mar-2008	125	2	25050	25050
30-Jun-2011	5200	03-Mar-2008	125	1	9250	9250
30-Jun-2011	5300	03-Mar-2008	125	1	100000	100000
30-Jun-2011	5500	03-Mar-2008	125	62	112000	105150
30-Jun-2011	5700	03-Mar-2008	125	58	487750	469850
31-Dec-2009	4000	18-Mar-2008	115	3	50000	50000
31-Dec-2009	4100	14-Mar-2008	117	2	50	0
31-Dec-2009	4300	10-Mar-2008	121	3	50	50
31-Dec-2009	4400	05-Mar-2008	123	1	50	50
31-Dec-2009	4500	04-Mar-2008	124	10	200150	200150
31-Dec-2009	4600	04-Mar-2008	124	4	50	50
31-Dec-2009	4700	03-Mar-2008	125	1	125000	125000
31-Dec-2009	4800	03-Mar-2008	125	3	250050	250050
31-Dec-2009	4900	03-Mar-2008	125	2	75000	50000
31-Dec-2009	5000	03-Mar-2008	125	8	400	400
31-Dec-2009	5200	03-Mar-2008	125	1	25000	25000
31-Dec-2009	5500	03-Mar-2008	125	1	50	50
30-Dec-2010	4300	10-Mar-2008	121	3	401500	401500
30-Dec-2010	4500	04-Mar-2008	124	1	50000	50000
30-Dec-2010	4600	04-Mar-2008	124	2	50200	50200
30-Dec-2010	4800	03-Mar-2008	125	2	250	250
30-Dec-2010	5000	03-Mar-2008	125	15	200400	200400
29-Dec-2011	3600	30-Jun-2008	48	1	50	50
29-Dec-2011	4000	27-Jun-2008	49	1	150	150
29-Dec-2011	4500	27-Jun-2008	49	3	600	600
29-Dec-2011	5000	24-Jul-2008	30	6	5400	5400

My arbitrary critera does leave out some contracts with very large open interest on account their not having been traded on many days. I've indicated some of these (those with O.I. greater than 1,00,000) in green. My problem with these is that since Iwont have price discovery on most days, any attempt to back calculate delta from these is likely to badly misfire. Much better to use my short-list and come back to these to see if the theory fits.

(To be continued...)