Estimation of nifty spot price using put call parity (final)

Estimation of NIFTY Spot Price Using Put-Call Parity Kushal Jain and Brajesh KumarAuthors:Kushal JainMBA-2, Jindal Global Business School,O P Jindal Global University,Sonipat-Narela Road, Near Jagdishpur Village, SonipatHaryana-131001, NCR of DelhiMobile: +91-8053255859Email: kushaljain@live.inBrajesh Kumar (Fellow [PhD], IIM, Ahmedabad)Assistant Professor and Assistant Dean Student InitiativesJindal Global Business School, O P Jindal Global University,Sonipat-Narela Road,Near Jagdishpur Village, SonipatHaryana-131001, NCR of DelhiTel: +91-130-3057925Mobile:+91-8930110773Email: bkumar@jgu.edu.in

Estimation of NIFTY Spot Price Using Put-Call Parity AbstractFutures 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 andOptions 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 veryimportant to understand their role. This paper attempts to understand and estimates theinformation content of Indian option market. Firstly, spot prices are calculated using Call-PutParity and then we compare estimated spot prices with the actual data. We also try tounderstand the information superiority of Near month option and At–the–Money options. We use4 months daily NIFTY options data of different strike prices ranging from 1 August, 2011 to 30November 2011. NIFTY, a well-diversified 50 stock index accounting for 23 sectors of theeconomy, is the leading index for large companies on the National Stock Exchange of India. It isfound that the Near month options and At–the–Money options is the most liquid option. Also, wefind very interesting result that Near month options and At–the–Money options have betterinformation content than other options. Our results have important implications for optionstraders, hedgers and policy makers 1

Estimation of NIFTY Spot Price Using Put-Call Parity1. IntroductionIn the era of globalization, financial markets across the globe have become very volatile. Nowmarkets becoming more open and because of advancement in information technology, thecontagion effect of information dissemination is found in most of the financial markets. Thedevelopment of technology and financial engineering has also led to financial innovations andmany financial products including derivatives. Recently financial products have becomecomplex and volatile which makes it difficult to understand and analyze for inventors beforeinvesting 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 inprice discovery, hedging price risk and stabilizing spot market. Indian derivatives markets arerelatively new and facing lots of issues related to liquidity and participation of hedgers. In thiscontext, it is important to understand the characteristics of Indian options markets and theirinformation dissemination role.1.1 Why derivatives markets?Derivatives can be defined as a contract based on underlying asset. The asset can be a financialasset like stock, currency and market index, a physical commodity or interest bearing security. Indeveloped and emerging markets, derivatives markets are used for speculation, investment andhedging price risk. Generally, derivatives markets have low transaction cost as compared to spotmarkets which led more participation and should play an important role in price disseminationprocess 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

1.2. About Derivatives MarketsThere are various types of derivatives products traded on exchanges across the world. Theyrange from the very simple to the most complex products. The following are the three basicforms of derivatives:–1.2.1 ForwardsA forwards contract is a contract between both buyer and seller of an asset which agrees to apredetermined date and price on which the contract will be executed. The future date and price isbeen agreed on the date on which the contract was made. The future decided date is called asexpiry date and the pre-decided price is called forward price. Forwards contracts are privatecontracts which are only traded in Over the Counter (OTC) market. The terms of the contract isbeen decided by the parties themselves or they can be tailor made as per traders requirement.1.2.2 FutureA future contract is similar to a forward contract in which both buyer and seller agrees to executethe contract on a predetermined date and price. The predetermined date and price is been agreedon the date on which the contract is been made. The future contracts are traded in recognizedstock exchanges unlike the forwards contracts which were traded in OTC markets. Generally allthe future contracts are standardized in nature i.e. the expiry date is same for all the buyers andsellers. The terms of the contracts are been decided by the stock exchanges which was not thecase in forwards contracts. The counter party risk in the case of futures contracts is protected byclearing corporations.1.2.3 OptionsAs futures and forwards contracts, options contracts also provide the opportunity to both buyerand seller to buy and sell and underlying asset on a future date. In options the two parties tocontract are buyer of the option and seller of the options. In options the buyer of the option buysthe right to buy/sell the underlying asset from the seller (he may or may not use that right as it isnot an obligation for the buyer) at an agreed price of underlying asset (strike price of the option) 3

and before a specific date, on the other hand seller sells his right over the underlying asset to thebuyer after charging premium (price of option) from the buyer at the pre-decided price. If buyeris using his right then seller had to sell/buy underlying asset from/to the buyer.There are twotypes of options — Call Options and Put Options — which are explained below:1.2.3.1 Vanilla Call OptionCall option is a right for the buyer of the option (not obligation) to buy a particular underlyingasset before a specific date and a predetermined price. The price of the underlying which is beendecided is called call option’s strike price, and the money which is been charged by the seller ofthe option over the underlying asset price is call the premium (price of the call option). For e.g. acall option buyer will only exercise his right when the price of the underlying asset is more thanthe strike price of the option before the expiry date of the option contract, if the price is less thanthe strike price of the call option then buyer will not exercise his right as he doesn’t have anyobligation to buy the underlying.1.2.3.2 Vanilla Put OptionPut Option is a right to the buyer of the option (not obligation) to sell a particular underlyingasset at a pre-decided price and before a specific date. The person who has the right to sell theoption is called the “buyer of the put option”. The price of the underlying asset which is beenpre-decided is called the put option’s strike price of the, and the money which is been charged bythe seller is called the “premium” (price of the put option). For e.g. if a put option buyer willonly exercise his right when the price of underlying asset is less than the strike price and beforethe expiry date of the option. As if the price goes up than the strike price then the buyer of theput option will not exercise the option as he doesn’t have any obligation to buy the underlying.1.2.3.3 Exotic OptionsExotic options are more complex in nature and are non-standard in nature. These options arespecial conditions options; they are more flexible and better suited to individual investors. Theseoptions are generally not found in any stock exchange, these option are been made by usingcombinations of option as per the invertors risk appetite and return demand 4

1.3 Types of TradersIn today’s scenario derivatives can be traded for variety of reasons. As derivatives markets are nodifferent to any other financial market therefore there are three different types of participantswho take active participation in this market. They are:1.3.1 HedgerThese types of trader are expected to have some exposure to the underlying asset. The traderwants to reduce its spot price risk (of the underlying asset) by taking a position in the derivativesmarket. These traders mainly participate in derivatives market just to reduce price riskmanagement of assets and portfolio.1.3.2 SpeculatorsThese are the traders who are believed to have some information about the future price of thestock. These traders buy and sell future and options accordingly in respect to make future profitsfrom the price movement of the underlying assets. In real life it is very difficult to bifurcatebetween speculators and hedgers. But an active market requires both hedgers and speculators toparticipate for market to be efficient.1.3.3 ArbitrageursThese are the traders who participate in the market to earn riskless profit from the discrepanciesin the spot and derivatives market’s prices. These types of trader help in keeping the marketefficient and work in sync.1.4 Types of ContractsThere are mainly two types of markets which are in which shares and derivatives are been tradedacross the world: 5

1.4.1 Over the Counter (OTC) ContractsThese contracts are generally private in nature. As the negotiation in these types of contracts arebeen done by both buyer and seller individually. The terms under these contracts are veryflexible and very often are been settled as per the requirements of the buyer’s and seller’s. OTCcontracts are not regulated by government or any institution so the credit risks under thesecontracts are equivalent to the counter party credit risk. Generally forwards contracts are beentraded under these contracts.1.4.2 Exchange Traded ContractsContracts like futures contracts which have a standardized format and which is been regulated byinstitutions i.e. size of the contract, underlining asset to be delivered and all the logistics of thedelivery. The trade under these contracts are been done in organized exchanges, in which thecredit risk is minimal as it is the onus of the clearing house1 which is been set up/taken care byexchanges. Daily margin requirement evaluation and daily marking-to-market of the contractshelps to reduce the credit risk which is not there in the OTC contracts.1.5 Development of Indian Derivatives MarketThe derivatives markets in India are relatively new as compared to developed markets. However,they are showing tremendous growth potential especially Index derivatives (NIFTY). Theexchange traded derivatives were introduced in India in June 2000 on the National StockExchange (NSE). The NSE is the largest exchange in India in derivatives trading including stockfutures & options, Index futures and Options. The first contract launched on NSE was the Nifty50 index futures contract. After the introduction of index futures, index options, stock optionsand stock futures were also introduced. Recently, Currency and Interest Rate Futures contractsare also launched on NSE.The Standard & Poors CRISIL NSE Index 50 (Appendix 1) or S&P CNX Nifty nicknamedNifty 50, is the leading index in India other than SENSEX traded on BSE. The Nifty is a welldiversified 50 stock index accounting for 23 sectors of the economy. It is used for a variety of1 A clearing house becomes a buyer to sellers and seller to buyers to assure the performance of the contract. 6

purposes such as benchmarking fund portfolios, index based derivatives and index funds. Nifty isowned and managed by India Index Services and Products Ltd. (IISL), which is a joint venturebetween NSE and CRISIL. The S&P CNX Nifty stocks represent about 60% of the total marketcapitalization of the National Stock Exchange (NSE).The base period for the S&P CNX Nifty index is November 3, 1995, which marked thecompletion of one year of operations of NSEs Capital Market Segment. The base value of theindex has been set at 1000, and a base capital of Rs 2.06 trillion. From June 26, 2009, the indexis computed based on free float methodology.2 Objectives of the StudyIn 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 areoutlined 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 MethodologyPut-call parity is an important principle in options pricing first identified by Hans Stoll in hispaper, The Relation Between Put and Call Prices, in 1969. It states that the premium of a calloption implies a certain fair price for the corresponding put option having the same strike priceand expiration date, and vice versa. Support for this pricing relationship is based upon theargument that arbitrage opportunities would materialize if there is a divergence between thevalue of calls and puts. Arbitrageurs would come in to make profitable, riskless trades until theput-call parity is restored. 7

Since American style options allow early exercise, put-call parity will not hold for Americanoptions unless they are held to expiration. Early exercise will result in a departure in the presentvalues. The put-call parity provides a simple test of option pricing models. Any pricing modelthat 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 UnderlyingIn this research we have taken the equation of Put – Call parity as the base and then we haveconducted all the calculation on these bases itself.By using this equation we want to understand the normal impact of different the strike prices andin different durations of the contract and to find out that which strike price and which contractperiod gives the best result for the estimation of the Nifty prices by using Put – Call parity.4 Properties of DataIn this paper, firstly we analyze the characteristics of NIFTY option and then estimate the spotprice using put-call parity. The option prices (call and put), NIFTY spot prices, trading volumeand open interest data is collected from National Stock Exchange (www.nseindia.com ). In ouranalysis, we are intentionally incorporating different strike prices and different maturity (NearMonth, Next to Near Month and Far Month series) contracts to understand the effect of strikeprices and different maturity contracts on price discovery.The data is collected from 1 August, 2011 to 30 November 2011. We intended to extend the datafor a year but it requires more strike prices to be analyzed and hence, complicate the study andinterpretation. In this paper, 11 strike prices ranging from `4500 – `5500 are considered. As the 8

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 ispresented in figure 2. Nifty560054005200500048004600 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 MovementThe data period consists of 7 contracts ranging from 1st August, 2011 to at December. We prepare nearmonth, next to near month and far month series from the 7 contracts (June to December Contracts). Incase of near month series, data from current month maturity contract is considered and rolled over for 5months. Similarly, for next to near month series the data from contract maturing in next month isconsidered and rolled over of the entire period. The NIFTY option has maturity period of three months soonly 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

The preparation of these series is demonstrated as follows. The 3 month contract starting in June maturesin 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 isthe maturing contract), the July contract is considered in September, the August contract is considered inOctober and so on. In case of next to near month series (August to December), the July contract isconsidered in August (as this is the maturing in next month), the August contract is considered inSeptember, 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 nextmonth), the September contract is considered in September, the October contract is considered in Octoberand so on. As we will see in our analysis, these series have different characteristics (trading activity), theymay have different role in price discovery process, which we intend to examine in this paper. 4.2 Analysis of the different Contracto 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 theentire period is much higher than the next to near month and far month contacts. This is true for both putas well as call volume. It seems that in Indian options markets, near month contacts are most liquidcontacts and it should play an important role in price discovery process. We separately analyze eachcontract and find similar results. The comparisons of near month futures volume with next to near monthand 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

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 ₹50,000,000Turnover ₹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 87.8656763Figure 5: Put Trading Volume for Near Month, Next to near Month and Far Month Series of October Contract 11

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 89.0452515Figure 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

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 Contract4.3 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

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 ContractsIt 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 againreinforced that the near month trading volume is very high as compared to next to near month and farmonth contracts.4.4 Speculation RatioWe 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 nearmonth and far month contracts. We find similar results when different month contacts are analyzed. Itseems that information dissemination in the Indian options markets is happening through speculation andnear month contract is leading this process. It is also interesting to note that as strike price is going awayfrom spot price speculation ratio decreases. 14

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 DecFigure 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 ratiobetween 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 inAugust was very high and was gone down, therefore, speculation ratio of both Call and Put options werehigh but call was higher than put. In coming months the market fell down and the speculation ratios alsowent down and the highest speculation ratio was .078 of call option in the month of August only. 15

0.09 0.05 Call `5500 Near Put `5500 Near0.08 Month 0.045 Month0.07 0.04 Next to Next to Near 0.035 Near0.06 Month Month0.05 0.03 0.0250.04 0.020.03 0.0150.02 0.010.01 0.005 0 0 Aug Sep Oct Nov Dec Aug Sep Oct Nov DecFigure 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 0.120.15 0.1 0.08 0.1 0.060.05 0.04 0.02 0 0 Aug Sep Oct Nov Dec Aug Sep Oct Nov DecFigure 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 isAt–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 (Figure13).After combining the results of trading volume and speculation ratio, it can be interpreted that near monthcontract is most liquid contracts where both speculators and hedgers are participating and playing an 16

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

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-11Figure 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-11Figure 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

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-11Figure 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-11Figure 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

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-11Figure 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-11Figure 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

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-11Figure 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-11Figure 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

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-11Figure 22: Comparison between NIFTY Spot prices Estimated from Call and Put Prices of Far Month Contract at Strike Price of 5500 and Observed Spot PriceOur analysis reveals very important characteristics of Indian Options markets in informationdissemination process. Near month contacts where trading activity including trading volume and openinterest is high as compared to next to near month and far month, play a leading role in informationdissemination process. For all strike prices, the root mean square error of the near month future isminimum. The root mean square error is maximum for the far month contracts. Also, At-the-Moneyoptions are highly liquid contract and they play an important role in price dissemination. It can beconcluded from our analysis that near month and At-the-Money contracts are highly liquid contracts andthey are leading the information dissemination process.5 ConclusionIn India, derivatives markets especially options markets are relatively new and facing lots of issuesincluding less volume of trade and lower participation of hedgers. In this paper we are trying tounderstand the characteristics of Indian options markets and their role in price dissemination process. Theinformation dissemination role is examined through estimating spot price using Put – Call parity andcomparing with observed spot price. The comparison is based on the root men square error. The analysisis performed on the data for 6 contracts (June to October) with 11 strike prices (`4500 to `5500) which 22

covers In-the- Money, At-the-Money and Out-of the-money contracts. We prepare three series namelyNear month, Next to near month and Far month series based on time to maturity of contacts. We find veryinteresting results which reveals important information about the Indian options markets. Near monthcontracts and At-the-Money options are liquid contracts as compared to Next to near month and far monthcontracts. These contacts are leading the information dissemination in the options market. 23

6. References  http://en.wikipedia.org/wiki/S%26P_CNX_Nifty  http://www.nseindia.com/content/ncfm/EDBM_workbook.pdf  http://www.theoptionsguide.com/understanding-put-call-parity.aspx  http://www.nseindia.com/content/ncfm/DMDM_rev.pdf  http://www.newyorkfed.org/research/economists/sarkar/derivatives_in_india.pdf  www.nseindia.com 24

Appendix 1 LIST OF COMPANIES IN CALCULATION OF NIFTY Issued Free Float ImpactSl. Weightage Symbol Capital Market Beta R2 costNo. Percent (` cr.) Capitalization (Percent) (` cr.)1 ACC 18.8 10,449 0.60 0.60 0.41 0.062 AMBUJACEM 306.0 12,122 0.69 0.90 0.47 0.083 AXISBANK 410.1 36,070 2.05 1.32 0.74 0.064 BAJAJ-AUTO 289.4 19,790 1.13 0.68 0.45 0.065 BHEL 489.5 32,592 1.86 0.82 0.63 0.056 BPCL 361.5 7,906 0.45 0.63 0.32 0.077 BHARTIARTL 1,898.80 43,164 2.46 0.75 0.41 0.078 CAIRN 1,901.60 15,240 0.87 0.80 0.53 0.059 CIPLA 160.6 16,322 0.93 0.47 0.34 0.0710 DLF 339.5 9,741 0.55 1.50 0.71 0.0711 DRREDDY 84.6 20,622 1.17 0.51 0.37 0.0812 GAIL 1,268.50 20,842 1.19 0.59 0.44 0.0613 GRASIM 91.7 15,603 0.89 0.49 0.28 0.0614 HCLTECH 137.0 11,518 0.66 0.95 0.57 0.0815 HDFCBANK 464.7 83,513 4.76 1.00 0.72 0.0516 HEROHONDA 39.9 15,168 0.86 0.50 0.26 0.0517 HINDALCO 191.4 26,876 1.53 1.57 0.72 0.0618 HINDUNILVR 217.2 29,925 1.70 0.53 0.41 0.0519 HDFC 293.1 91,043 5.19 1.13 0.70 0.0720 ITC 772.2 96,580 5.50 0.74 0.54 0.0621 ICICIBANK 1,151.40 128,521 7.32 1.50 0.80 0.0622 INFOSYSTCH 287.1 156,245 8.90 0.79 0.63 0.0523 IDFC 1,460.90 16,430 0.94 1.35 0.69 0.0724 JPASSOCIAT 425.3 10,663 0.61 1.68 0.70 0.0725 JINDALSTEL 93.4 27,085 1.54 1.07 0.69 0.0726 KOTAKBANK 368.2 16,173 0.92 1.15 0.66 0.0827 LT 121.8 88,264 5.03 1.10 0.71 0.0628 M&M 307.0 33,210 1.89 1.14 0.62 0.0629 MARUTI 144.5 16,697 0.95 0.78 0.50 0.0630 NTPC 8,245.50 24,680 1.41 0.66 0.56 0.0731 ONGC 4,277.70 39,296 2.24 0.66 0.45 0.0732 POWERGRID 4,629.70 14,426 0.82 0.47 0.42 0.0533 PNB 315.3 16,136 0.92 0.85 0.61 0.08 25

34 RANBAXY 210.6 6,791 0.39 0.87 0.54 0.0635 RELCAPITAL 245.6 6,569 0.37 1.30 0.60 0.0736 RCOM 1,032.0 7,140 0.41 1.21 0.47 0.0837 RELIANCE 3,289.70 177,723 10.12 1.01 0.71 0.0638 RELINFRA 267.4 9,645 0.55 1.25 0.50 0.0739 RPOWER 2,805.10 7,161 0.41 1.05 0.51 0.0840 SESAGOA 86.0 11,088 0.63 1.29 0.56 0.0641 SIEMENS 67.4 13,314 0.76 0.54 0.35 0.0442 SBIN 635.0 71,287 4.06 1.15 0.67 0.0443 SAIL 4,130.40 9,934 0.57 1.20 0.65 0.0644 STER 336.2 24,688 1.41 1.50 0.68 0.0745 SUNPHARMA 103.6 16,627 0.95 0.57 0.39 0.0746 TCS 195.7 60,122 3.42 0.86 0.56 0.0647 TATAMOTORS 537.3 43,641 2.49 1.47 0.68 0.0648 TATAPOWER 237.3 21,606 1.23 0.62 0.52 0.0749 TATASTEEL 959.4 40,914 2.33 1.32 0.72 0.0450 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 (final)

by Kushal Jain on Jul 06, 2012

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Estimation of nifty spot price using put call parity (final) Document Transcript