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Estimation of nifty spot price using put call parity (final)
1. Estimation of NIFTY Spot Price Using Put-Call Parity
Kushal Jain and Brajesh Kumar
Authors:
Kushal Jain
MBA-2, Jindal Global Business School,
O P Jindal Global University,Sonipat-Narela Road, Near Jagdishpur Village, Sonipat
Haryana-131001, NCR of Delhi
Mobile: +91-8053255859
Email: kushaljain@live.in
Brajesh Kumar (Fellow [PhD], IIM, Ahmedabad)
Assistant Professor and Assistant Dean Student Initiatives
Jindal Global Business School, O P Jindal Global University,Sonipat-Narela Road,
Near Jagdishpur Village, Sonipat
Haryana-131001, NCR of Delhi
Tel: +91-130-3057925
Mobile:+91-8930110773
Email: bkumar@jgu.edu.in
2. Estimation of NIFTY Spot Price Using Put-Call Parity
Abstract
Futures and options markets in India are relatively new. The National Stock Exchange (NSE)
introduced trading in Index Options (also based on Nifty) on June 4, 2001. The Futures and
Options on individual securities are available on only 223 securities. In developed markets,
derivatives play a very important role in price discovery and information dissemination.
However, in emerging markets where the derivatives markets are not very liquid, it is very
important to understand their role. This paper attempts to understand and estimates the
information content of Indian option market. Firstly, spot prices are calculated using Call-Put
Parity and then we compare estimated spot prices with the actual data. We also try to
understand the information superiority of Near month option and At–the–Money options. We use
4 months daily NIFTY options data of different strike prices ranging from 1 August, 2011 to 30
November 2011. NIFTY, a well-diversified 50 stock index accounting for 23 sectors of the
economy, is the leading index for large companies on the National Stock Exchange of India. It is
found that the Near month options and At–the–Money options is the most liquid option. Also, we
find very interesting result that Near month options and At–the–Money options have better
information content than other options. Our results have important implications for options
traders, hedgers and policy makers
1
3. Estimation of NIFTY Spot Price Using Put-Call Parity
1. Introduction
In the era of globalization, financial markets across the globe have become very volatile. Now
markets becoming more open and because of advancement in information technology, the
contagion effect of information dissemination is found in most of the financial markets. The
development of technology and financial engineering has also led to financial innovations and
many financial products including derivatives. Recently financial products have become
complex and volatile which makes it difficult to understand and analyze for inventors before
investing in these securities. Some of the crisis events like Asian Crisis [1997], Global Crisis
[2008], have raised issues about innovative derivatives products, regulations and their mis-
pricing. However, in developing countries, derivatives have also played an important role in
price discovery, hedging price risk and stabilizing spot market. Indian derivatives markets are
relatively new and facing lots of issues related to liquidity and participation of hedgers. In this
context, it is important to understand the characteristics of Indian options markets and their
information dissemination role.
1.1 Why derivatives markets?
Derivatives can be defined as a contract based on underlying asset. The asset can be a financial
asset like stock, currency and market index, a physical commodity or interest bearing security. In
developed and emerging markets, derivatives markets are used for speculation, investment and
hedging price risk. Generally, derivatives markets have low transaction cost as compared to spot
markets which led more participation and should play an important role in price dissemination
process The three important roles of derivatives products are as follows:
Investments – can be used for investments as well as for profit earing purposes.
Hedging – can be used to reduce spot price risk.
Price discovery – should lead the information dissemination process
2
4. 1.2. About Derivatives Markets
There are various types of derivatives products traded on exchanges across the world. They
range from the very simple to the most complex products. The following are the three basic
forms of derivatives:–
1.2.1 Forwards
A forwards contract is a contract between both buyer and seller of an asset which agrees to a
predetermined date and price on which the contract will be executed. The future date and price is
been agreed on the date on which the contract was made. The future decided date is called as
expiry date and the pre-decided price is called forward price. Forwards contracts are private
contracts which are only traded in Over the Counter (OTC) market. The terms of the contract is
been decided by the parties themselves or they can be tailor made as per traders requirement.
1.2.2 Future
A future contract is similar to a forward contract in which both buyer and seller agrees to execute
the contract on a predetermined date and price. The predetermined date and price is been agreed
on the date on which the contract is been made. The future contracts are traded in recognized
stock exchanges unlike the forwards contracts which were traded in OTC markets. Generally all
the future contracts are standardized in nature i.e. the expiry date is same for all the buyers and
sellers. The terms of the contracts are been decided by the stock exchanges which was not the
case in forwards contracts. The counter party risk in the case of futures contracts is protected by
clearing corporations.
1.2.3 Options
As futures and forwards contracts, options contracts also provide the opportunity to both buyer
and seller to buy and sell and underlying asset on a future date. In options the two parties to
contract are buyer of the option and seller of the options. In options the buyer of the option buys
the right to buy/sell the underlying asset from the seller (he may or may not use that right as it is
not an obligation for the buyer) at an agreed price of underlying asset (strike price of the option)
3
5. and before a specific date, on the other hand seller sells his right over the underlying asset to the
buyer after charging premium (price of option) from the buyer at the pre-decided price. If buyer
is using his right then seller had to sell/buy underlying asset from/to the buyer.There are two
types of options — Call Options and Put Options — which are explained below:
1.2.3.1 Vanilla Call Option
Call option is a right for the buyer of the option (not obligation) to buy a particular underlying
asset before a specific date and a predetermined price. The price of the underlying which is been
decided is called call option’s strike price, and the money which is been charged by the seller of
the option over the underlying asset price is call the premium (price of the call option). For e.g. a
call option buyer will only exercise his right when the price of the underlying asset is more than
the strike price of the option before the expiry date of the option contract, if the price is less than
the strike price of the call option then buyer will not exercise his right as he doesn’t have any
obligation to buy the underlying.
1.2.3.2 Vanilla Put Option
Put Option is a right to the buyer of the option (not obligation) to sell a particular underlying
asset at a pre-decided price and before a specific date. The person who has the right to sell the
option is called the “buyer of the put option”. The price of the underlying asset which is been
pre-decided is called the put option’s strike price of the, and the money which is been charged by
the seller is called the “premium” (price of the put option). For e.g. if a put option buyer will
only exercise his right when the price of underlying asset is less than the strike price and before
the expiry date of the option. As if the price goes up than the strike price then the buyer of the
put option will not exercise the option as he doesn’t have any obligation to buy the underlying.
1.2.3.3 Exotic Options
Exotic options are more complex in nature and are non-standard in nature. These options are
special conditions options; they are more flexible and better suited to individual investors. These
options are generally not found in any stock exchange, these option are been made by using
combinations of option as per the invertors risk appetite and return demand
4
6. 1.3 Types of Traders
In today’s scenario derivatives can be traded for variety of reasons. As derivatives markets are no
different to any other financial market therefore there are three different types of participants
who take active participation in this market. They are:
1.3.1 Hedger
These types of trader are expected to have some exposure to the underlying asset. The trader
wants to reduce its spot price risk (of the underlying asset) by taking a position in the derivatives
market. These traders mainly participate in derivatives market just to reduce price risk
management of assets and portfolio.
1.3.2 Speculators
These are the traders who are believed to have some information about the future price of the
stock. These traders buy and sell future and options accordingly in respect to make future profits
from the price movement of the underlying assets. In real life it is very difficult to bifurcate
between speculators and hedgers. But an active market requires both hedgers and speculators to
participate for market to be efficient.
1.3.3 Arbitrageurs
These are the traders who participate in the market to earn riskless profit from the discrepancies
in the spot and derivatives market’s prices. These types of trader help in keeping the market
efficient and work in sync.
1.4 Types of Contracts
There are mainly two types of markets which are in which shares and derivatives are been traded
across the world:
5
7. 1.4.1 Over the Counter (OTC) Contracts
These contracts are generally private in nature. As the negotiation in these types of contracts are
been done by both buyer and seller individually. The terms under these contracts are very
flexible and very often are been settled as per the requirements of the buyer’s and seller’s. OTC
contracts are not regulated by government or any institution so the credit risks under these
contracts are equivalent to the counter party credit risk. Generally forwards contracts are been
traded under these contracts.
1.4.2 Exchange Traded Contracts
Contracts like futures contracts which have a standardized format and which is been regulated by
institutions i.e. size of the contract, underlining asset to be delivered and all the logistics of the
delivery. The trade under these contracts are been done in organized exchanges, in which the
credit risk is minimal as it is the onus of the clearing house1 which is been set up/taken care by
exchanges. Daily margin requirement evaluation and daily marking-to-market of the contracts
helps to reduce the credit risk which is not there in the OTC contracts.
1.5 Development of Indian Derivatives Market
The derivatives markets in India are relatively new as compared to developed markets. However,
they are showing tremendous growth potential especially Index derivatives (NIFTY). The
exchange traded derivatives were introduced in India in June 2000 on the National Stock
Exchange (NSE). The NSE is the largest exchange in India in derivatives trading including stock
futures & options, Index futures and Options. The first contract launched on NSE was the Nifty
50 index futures contract. After the introduction of index futures, index options, stock options
and stock futures were also introduced. Recently, Currency and Interest Rate Futures contracts
are also launched on NSE.
The Standard & Poor's CRISIL NSE Index 50 (Appendix 1) or S&P CNX Nifty nicknamed
Nifty 50, is the leading index in India other than SENSEX traded on BSE. The Nifty is a well
diversified 50 stock index accounting for 23 sectors of the economy. It is used for a variety of
1
A clearing house becomes a buyer to sellers and seller to buyers to assure the performance of the contract.
6
8. purposes such as benchmarking fund portfolios, index based derivatives and index funds. Nifty is
owned and managed by India Index Services and Products Ltd. (IISL), which is a joint venture
between NSE and CRISIL. The S&P CNX Nifty stocks represent about 60% of the total market
capitalization of the National Stock Exchange (NSE).
The base period for the S&P CNX Nifty index is November 3, 1995, which marked the
completion of one year of operations of NSE's Capital Market Segment. The base value of the
index has been set at 1000, and a base capital of Rs 2.06 trillion. From June 26, 2009, the index
is computed based on free float methodology.
2 Objectives of the Study
In this paper, we intend to investigate the important characteristics of Indian options markets
(call and put contracts) and their role in price dissemination process. The specific objectives are
outlined below:
To understand the trading activity (trading volume and open interest) of call and put
contracts at different strike prices
To understand the impact of the strike price (In – the – Money (ITM), At – the – Money
(ATM), Out – the – money (OTM)) on information dissemination process
To understand the role of trading activity on information dissemination process. Whether
highly traded contracts are playing an important role in processing information?
3 Research Methodology
Put-call parity is an important principle in options pricing first identified by Hans Stoll in his
paper, The Relation Between Put and Call Prices, in 1969. It states that the premium of a call
option implies a certain fair price for the corresponding put option having the same strike price
and expiration date, and vice versa. Support for this pricing relationship is based upon the
argument that arbitrage opportunities would materialize if there is a divergence between the
value of calls and puts. Arbitrageurs would come in to make profitable, riskless trades until the
put-call parity is restored.
7
9. Since American style options allow early exercise, put-call parity will not hold for American
options unless they are held to expiration. Early exercise will result in a departure in the present
values. The put-call parity provides a simple test of option pricing models. Any pricing model
that produces option prices which violate the put-call parity is considered flawed.
The NIFTY stock price is estimated using Put-Call parity as explained below:
C = Call Premium,
P = Put Premium,
K = Strike Price of Call and Put,
r = Annual Interest Rate,
t = Time in Years,
So = Initial Price of Underlying
In this research we have taken the equation of Put – Call parity as the base and then we have
conducted all the calculation on these bases itself.
By using this equation we want to understand the normal impact of different the strike prices and
in different durations of the contract and to find out that which strike price and which contract
period gives the best result for the estimation of the Nifty prices by using Put – Call parity.
4 Properties of Data
In this paper, firstly we analyze the characteristics of NIFTY option and then estimate the spot
price using put-call parity. The option prices (call and put), NIFTY spot prices, trading volume
and open interest data is collected from National Stock Exchange (www.nseindia.com ). In our
analysis, we are intentionally incorporating different strike prices and different maturity (Near
Month, Next to Near Month and Far Month series) contracts to understand the effect of strike
prices and different maturity contracts on price discovery.
The data is collected from 1 August, 2011 to 30 November 2011. We intended to extend the data
for a year but it requires more strike prices to be analyzed and hence, complicate the study and
interpretation. In this paper, 11 strike prices ranging from `4500 – `5500 are considered. As the
8
10. stock price for this whole span is at an average of `5038.27 (figure 1) therefore we consider
`5000 as At – the – Money contract. The NIFTY call and put premium at strike price of 5000 is
presented in figure 2.
Nifty
5600
5400
5200
5000
4800
4600
05-Dec-11
01-Aug-11
08-Aug-11
15-Aug-11
22-Aug-11
29-Aug-11
19-Sep-11
03-Oct-11
10-Oct-11
17-Oct-11
24-Oct-11
31-Oct-11
07-Nov-11
14-Nov-11
21-Nov-11
28-Nov-11
05-Sep-11
12-Sep-11
26-Sep-11
Closing Price Average
Figure 1: Nifty Spot Price Movement
The data period consists of 7 contracts ranging from 1st August, 2011 to at December. We prepare near
month, next to near month and far month series from the 7 contracts (June to December Contracts). In
case of near month series, data from current month maturity contract is considered and rolled over for 5
months. Similarly, for next to near month series the data from contract maturing in next month is
considered and rolled over of the entire period. The NIFTY option has maturity period of three months so
only three different maturity series are possible.
Call and Put Preview @ 5000 Strike Price
₹400
₹500
₹400 ₹300
₹300 ₹200
₹200
₹100
₹100
₹- ₹0
29-Jul-11 28-Aug-11 27-Sep-11 27-Oct-11 26-Nov-11
Call Put
Figure 2: NIFTY Call and Put Premium at Strike Price of 5000.
9
11. The preparation of these series is demonstrated as follows. The 3 month contract starting in June matures
in August. Similarly, July contract matures in September; August contract matures in October and so on.
In case of near month series (August to December), the June contract is considered in August (as this is
the maturing contract), the July contract is considered in September, the August contract is considered in
October and so on. In case of next to near month series (August to December), the July contract is
considered in August (as this is the maturing in next month), the August contract is considered in
September, the September contract is considered in October and so on. In case of far month contract
(August to December), the August contract is considered in August (as this is the maturing in next to next
month), the September contract is considered in September, the October contract is considered in October
and so on. As we will see in our analysis, these series have different characteristics (trading activity), they
may have different role in price discovery process, which we intend to examine in this paper.
4.2 Analysis of the different Contract
o take any further analysis, first of all we want to understand the characteristics the different maturity
(Near month, next to near and far month) contracts. First, we compare the trading volume of Near Month,
Next to Near Month and Far month contracts. The near month options contact volume (turnover) for the
entire period is much higher than the next to near month and far month contacts. This is true for both put
as well as call volume. It seems that in Indian options markets, near month contacts are most liquid
contacts and it should play an important role in price discovery process. We separately analyze each
contract and find similar results. The comparisons of near month futures volume with next to near month
and far month contacts for the entire period and contract-wise is presented in figure-3 to figure 8.
Total Call Distribution
400000000
350000000
300000000
Turnover (in Lacs)
250000000
200000000
150000000
100000000
50000000
0
Near Month Next to Near 3 Month
Month
Turnover (Lacs) 359416720 35309109 1884687
Percentage 90.62% 8.90% 0.48%
Figure 3: Call Trading Volume for Near Month, Next to Near Month and Far Month Contracts
10
12. Total Put Distribution
₹400,000,000
₹350,000,000
Turnover (in lacs)
₹300,000,000
₹250,000,000
₹200,000,000
₹150,000,000
₹100,000,000
₹50,000,000
₹-
Near Month Next to Near 3 Month
Month
Turnover (Lacs) 356530010 38498790 2191629
Percentage 89.89% 9.71% 0.55%
Figure 4: Put Trading Volume for Near Month, Next to Near Month and Far Month Contracts
Put Expiry - October 2011
₹80,000,000
₹70,000,000
₹60,000,000
₹50,000,000
Turnover
₹40,000,000
₹30,000,000
₹20,000,000
₹10,000,000
₹-
3 Months Next to Near Near Month
Month
Turnover 598850 9271157 71469565
Percentage of Trade 0.73623451 11.3980892 87.8656763
Figure 5: Put Trading Volume for Near Month, Next to near Month and Far Month Series of
October Contract
11
13. Call Expiry - October 2011
₹70,000,000
₹60,000,000
₹50,000,000
Turnover
₹40,000,000
₹30,000,000
₹20,000,000
₹10,000,000
₹0
3 Months Next to Near
Near Month
Month
Turnover 591943 7816248 68345657
Percentage of Trade 0.77122257 10.1835259 89.0452515
Figure 6: Call Trading volume for Near Month, Next to near Month and Far Month Series of
October Contract
Put Expiry - November 2011
₹80,000,000
₹70,000,000
₹60,000,000
₹50,000,000
Turnover
₹40,000,000
₹30,000,000
₹20,000,000
₹10,000,000
₹0
3 Months Next to Near
Near Month Month
Turnover 411688.9 6566827 78811985
Percentage of Trade 0.48% 7.65% 91.86%
Figure 7: Put Trading Volume for Near Month, Next to Near Month and Far Month Series of
November Contract
12
14. Call Expiry - November 2011
₹90,000,000
₹80,000,000
₹70,000,000
₹60,000,000
Turnover
₹50,000,000
₹40,000,000
₹30,000,000
₹20,000,000
₹10,000,000
₹0
3 Months Next to Near Near Month
Month
Turnover 413238.3 6304508 86397156
Percentage of Trade 0.44% 6.77% 92.78%
Figure 8: Call Trading volume for Near Month, Next to Near Month and Far Month Series of
November Contract
4.3 Comparison between Call and Put Trade Volume
It is important to understand the liquidity of call and put contracts before using call-put parity to estimate
stock price. The trade volume of call and put options are estimated and analyzed. The comparison is
performed for near month, next to near month and far month contracts as well as for different month
contacts as presented in Figure 9 and Figure 10.
Comparision of Call & Put by Contract
₹350,000,000
₹300,000,000
Turnover (in lacs)
₹250,000,000
₹200,000,000
₹150,000,000
₹100,000,000
₹50,000,000
₹-
Near Month Next to Near Month 3 Month
Call 359416720 35309109.39 1884686.75
Put 356530010 38498790.09 2191628.68
13
15. Figure 9: Call and Put Trading Volume of Near Month Next to Near Month and Far Month
Series
Comparison Of Call and Put Trade Values
₹120,000,000
₹100,000,000
₹80,000,000
Turnover
₹60,000,000
₹40,000,000
₹20,000,000
₹0
August September October November December
Call 92150660 109640732 77155135 93114902 26098000
Put 84444872 106377921 81762522 85790501 24227576
Figure 10: Call and Put Trading Volume of August, September, October, November and
December Contracts
It is found that the call and put trading volume is almost equal for all strike prices and in all the three
(Near Month, Next to Near Month and Far Month) contracts. As discusses in the section 4.1, it is again
reinforced that the near month trading volume is very high as compared to next to near month and far
month contracts.
4.4 Speculation Ratio
We estimate the speculation ratio which is defined as the ratio of volume to open interest for near month,
next to near month and far month contacts of call and put contacts at different strike prices.
It is important to note that speculation ratio is higher for near month contract as compared to next to near
month and far month contracts. We find similar results when different month contacts are analyzed. It
seems that information dissemination in the Indian options markets is happening through speculation and
near month contract is leading this process. It is also interesting to note that as strike price is going away
from spot price speculation ratio decreases.
14
16. 0.04 0.06
Call `4500 Put `4500 Near Month
0.035 Next to Near
Near Month 0.05 Month
0.03 3 Month
Next to
Near Month 0.04
0.025 3 Month
0.02 0.03
0.015
0.02
0.01
0.005 0.01
0 0
Aug Sep Oct Nov Dec Aug Sep Oct Nov Dec
Figure 11: Speculation Ratio of Near Month, Next to Near Month and Far Month Contacts
of Call and Put at Strike price of 4500.
As shown in figure 11, the speculation ratio of Put is higher than the Call options at the strike price of
`4500. As the average spot price was 5000 for the entire period for call option the Strike Price is In – the
– Money but in case of Put the Strike Price is Out – the – Money. The market fell in August, September,
October therefore the Call option has less speculation ratio than Put Options. The Maximum ratio
between these above Graphs is .047 that is in Put Option.
We also analyze another case Call option is Out – the – Money and Put Option is In – the – Money. Here,
we can see that the Call Option had more speculation ratio than Put Option (figure 12). The spot price in
August was very high and was gone down, therefore, speculation ratio of both Call and Put options were
high but call was higher than put. In coming months the market fell down and the speculation ratios also
went down and the highest speculation ratio was .078 of call option in the month of August only.
15
17. 0.09 0.05
Call `5500 Near Put `5500 Near
0.08 Month 0.045 Month
0.07 0.04 Next to
Next to
Near 0.035 Near
0.06 Month
Month
0.05 0.03
0.025
0.04
0.02
0.03
0.015
0.02
0.01
0.01 0.005
0 0
Aug Sep Oct Nov Dec Aug Sep Oct Nov Dec
Figure 12: Speculation Ratio of Near Month, Next to Near Month and Far Month Contacts
of Call and Put at Strike price of 5500.
0.25 0.18
Call `5000 Near Month Put `5000 Near Month
0.16
0.2 Next to Near 0.14
Next to Near
Month Month
0.12
0.15
0.1
0.08
0.1
0.06
0.05 0.04
0.02
0 0
Aug Sep Oct Nov Dec Aug Sep Oct Nov Dec
Figure 13: Speculation Ratio of Near Month, Next to Near Month and Far Month Contacts
of Call and Put at Strike price of 5000.
Now let us consider the speculation ratio of both call and put contracts at the strike prices of 5000. This is
At–the–Money for both Call and Put options. It is worth mentioning that for both Call and Put contracts,
speculation ratios are very high as compared to speculation ratio at strike prices of 4500 and 5500 (Figure
13).
After combining the results of trading volume and speculation ratio, it can be interpreted that near month
contract is most liquid contracts where both speculators and hedgers are participating and playing an
16
18. active role is information dissemination process. On the other hand far month futures contacts are illiquid
and mostly dominated by speculators in the market. Also, when the strike price is near the current spot
price, liquidity and speculation ratio in the option market increases and the contract becomes most active
contract for both speculators and hedgers. It raises an important question about the contract design and
use of options market in Indian options market.
4.5 Estimation of NIFTY spot Price using Put-Call Parity.
One of the important objectives of the paper is to estimate the spot price using put-call parity and to
compare with observed spot price. We also want to investigate and compare the role of near month, next
to near month and far month futures in information dissemination process. It is also important to analyze
the information dissemination role of At-the-Money, In-the-Money and Out-the- Money options contacts.
The NIFTY spot price is calculated using put-call parity and compared among 33 series (11 strike prices
and 3 different maturity contracts). The comparison is performed using root mean square error. The
results are given in TABLE 1 and Figure-14 to Figure 22.
Table 1: Comparison of Root Mean Square Error
Strike Prices (K) Near Month Next to Near Month 3 Months
4500 20.504 63.77 188.10
4600 24.25 218.10 283.07
4700 20.78 123.00 220.33
4800 22.17 64.43 215.53
4900 21.83 97.00 138.29
5000 23.30 67.23 109.56
5100 24.74 69.09 120.72
5200 26.35 72.28 119.40
5300 27.77 75.20 125.43
5400 28.74 85.50 137.67
5500 29.48 78.73 138.86
17
19. 5650 Near Month (K = 4500) Estimated Price 5650
5550 Underlying Value 5550
5450 5450
5350 5350
5250 5250
5150 5150
5050 5050
4950 4950
4850 4850
4750 4750
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 14: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Near Month Contract at Strike Price of 4500 and Observed Spot Price
5650 Next to Near Month (K = 4500) Underlying Value 5650
5550 Estimated Price 5550
5450 5450
5350 5350
5250 5250
5150 5150
5050 5050
4950 4950
4850 4850
4750 4750
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 15: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Next to Near Month Contract at Strike Price of 4500 and Observed Spot Price
18
20. 3 Month (K = 4500) Estimated Price
5650 Underlying Value 5650
5450 5450
5250 5250
5050 5050
4850 4850
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 16: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Far Month Contract at Strike Price of 4500 and Observed Spot Price
5650 Near Month (K = 5000) Estimated Price 5650
5550 Underlying Value 5550
5450 5450
5350 5350
5250 5250
5150 5150
5050 5050
4950 4950
4850 4850
4750 4750
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 17: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Near Month Contract at Strike Price of 5000 and Observed Spot Price
19
21. 5650 Next to Near Month (K = 5000) 5650
Estimated Price
5550 5550
Underlying Value
5450 5450
5350 5350
5250 5250
5150 5150
5050 5050
4950 4950
4850 4850
4750 4750
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 18: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Next to Near Month Contract at Strike Price of 5000 and Observed Spot Price
3 Months (K = 5000) Underlying Value
5650 Estimated Price 5650
5450 5450
5250 5250
5050 5050
4850 4850
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 19: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Far Month Contract at Strike Price of 5000 and Observed Spot Price
20
22. 5650 Near Month (K = 5500) 5650
Estimated Price
5550 5550
Underlying Value
5450 5450
5350 5350
5250 5250
5150 5150
5050 5050
4950 4950
4850 4850
4750 4750
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 20: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Near Month Contract at Strike Price of 5000 and Observed Spot Price
5650 Next to Near Month (K = 5500) 5650
Estimated Price
5550 5550
Underlying Value
5450 5450
5350 5350
5250 5250
5150 5150
5050 5050
4950 4950
4850 4850
4750 4750
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 21: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Next to Near Month Contract at Strike Price of 5500 and Observed Spot Price
21
23. 3 Months(K = 5500) Estimated Price
5650
5650 Underlying Value
5450
5450
5250 5250
5050 5050
4850 4850
4650 4650
29-Jul-11 29-Aug-11 29-Sep-11 29-Oct-11
Figure 22: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of
Far Month Contract at Strike Price of 5500 and Observed Spot Price
Our analysis reveals very important characteristics of Indian Options markets in information
dissemination process. Near month contacts where trading activity including trading volume and open
interest is high as compared to next to near month and far month, play a leading role in information
dissemination process. For all strike prices, the root mean square error of the near month future is
minimum. The root mean square error is maximum for the far month contracts. Also, At-the-Money
options are highly liquid contract and they play an important role in price dissemination. It can be
concluded from our analysis that near month and At-the-Money contracts are highly liquid contracts and
they are leading the information dissemination process.
5 Conclusion
In India, derivatives markets especially options markets are relatively new and facing lots of issues
including less volume of trade and lower participation of hedgers. In this paper we are trying to
understand the characteristics of Indian options markets and their role in price dissemination process. The
information dissemination role is examined through estimating spot price using Put – Call parity and
comparing with observed spot price. The comparison is based on the root men square error. The analysis
is performed on the data for 6 contracts (June to October) with 11 strike prices (`4500 to `5500) which
22
24. covers In-the- Money, At-the-Money and Out-of the-money contracts. We prepare three series namely
Near month, Next to near month and Far month series based on time to maturity of contacts. We find very
interesting results which reveals important information about the Indian options markets. Near month
contracts and At-the-Money options are liquid contracts as compared to Next to near month and far month
contracts. These contacts are leading the information dissemination in the options market.
23
27. 34 RANBAXY 210.6 6,791 0.39 0.87 0.54 0.06
35 RELCAPITAL 245.6 6,569 0.37 1.30 0.60 0.07
36 RCOM 1,032.0 7,140 0.41 1.21 0.47 0.08
37 RELIANCE 3,289.70 177,723 10.12 1.01 0.71 0.06
38 RELINFRA 267.4 9,645 0.55 1.25 0.50 0.07
39 RPOWER 2,805.10 7,161 0.41 1.05 0.51 0.08
40 SESAGOA 86.0 11,088 0.63 1.29 0.56 0.06
41 SIEMENS 67.4 13,314 0.76 0.54 0.35 0.04
42 SBIN 635.0 71,287 4.06 1.15 0.67 0.04
43 SAIL 4,130.40 9,934 0.57 1.20 0.65 0.06
44 STER 336.2 24,688 1.41 1.50 0.68 0.07
45 SUNPHARMA 103.6 16,627 0.95 0.57 0.39 0.07
46 TCS 195.7 60,122 3.42 0.86 0.56 0.06
47 TATAMOTORS 537.3 43,641 2.49 1.47 0.68 0.06
48 TATAPOWER 237.3 21,606 1.23 0.62 0.52 0.07
49 TATASTEEL 959.4 40,914 2.33 1.32 0.72 0.04
50 WIPRO 490.8 24,303 1.38 0.80 0.54 0.07
Source: NSE Factbook 2011
Beta & R2 are calculated for the period 01-Apr-2010 to 31-Mar-2011
Beta measures the degree to which any portfolio of stocks is affected as compared to the effect on
the market as a whole.
The coefficient of determination (R2) measures the strength of relationship between two variables
the return on a security versus that of the market.
Volatility is the Std. deviation of the daily returns for the period 01-Mar-2011 to 31-Mar-2011
Last day of trading was 31-Mar-2011
Impact Cost for S&P CNX Nifty is for a portfolio of ` 50 Lakhs
Impact Cost for S&P CNX Nifty is the weightage average impact cost
26
![Estimation of NIFTY Spot Price Using Put-Call Parity
Kushal Jain and Brajesh Kumar
Authors:
Kushal Jain
MBA-2, Jindal Global Business School,
O P Jindal Global University,Sonipat-Narela Road, Near Jagdishpur Village, Sonipat
Haryana-131001, NCR of Delhi
Mobile: +91-8053255859
Email: kushaljain@live.in
Brajesh Kumar (Fellow [PhD], IIM, Ahmedabad)
Assistant Professor and Assistant Dean Student Initiatives
Jindal Global Business School, O P Jindal Global University,Sonipat-Narela Road,
Near Jagdishpur Village, Sonipat
Haryana-131001, NCR of Delhi
Tel: +91-130-3057925
Mobile:+91-8930110773
Email: bkumar@jgu.edu.in](https://image.slidesharecdn.com/estimationofniftyspotpriceusingput-callparityfinal-120706095749-phpapp01/85/Estimation-of-nifty-spot-price-using-put-call-parity-final-1-320.jpg)
