Dm Final Report V1.0.1

8/8/2019 Dm Final Report V1.0.1

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Option boundaries in indexoptions in India

By,

Rajeev Kumar (09FN088)

Rakesh Mathi (09FN089)


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Contents

1. Introduction..................................................................................................................................... 1

1.1 HistoryF&O Market in India............................................................................................... 1

1.2 Index options market in India ................................................................................................. 1

2. Literature review ............................................................................................................................. 3

3. Methodology ................................................................................................................................... 5

3.1 Price Calculation ..................................................................................................................... 5

3.2 Lower boundary condition for index options .......................................................................... 5

3.3 Data ......................................................................................................................................... 7

4. Future scope .................................................................................................................................... 7

5. References....................................................................................................................................... 8


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1. Introduction1.1 HistoryF&O Market in India

Derivatives trading commenced in India in June 2000 after SEBI granted the final

approval to this effect in May 2001. SEBI permitted the derivative segments of two stock

exchanges, NSE and BSE, and their clearing house/corporation to commence trading and

settlement in approved derivatives contracts. To begin with, SEBI approved trading in index

futures contracts based on S&P CNX Nifty and BSE30(Sensex) index. This was followed

by approval for trading in options based on these two indexes and options on individual

securities.

The trading in BSE Sensex options commenced on June 4, 2001 and the trading in options on

individual securities commenced in July 2001. Futures contracts on individual stocks were

launched in November 2001. The derivatives trading on NSE commenced with S&P CNX

Nifty Index futures on June 12, 2000. The trading in index options commenced on June 4,

2001 and trading in options on individual securities commenced on July 2, 2001.

The index futures and options contract on NSE are based on S&P CNX Trading and

settlement in derivative contracts is done in accordance with the rules, byelaws, and

regulations of the respective exchanges and their clearing house/corporation duly approved

by SEBI and notified in the official gazette. Foreign Institutional Investors (FIIs) are

permitted to trade in all Exchange traded derivative products.

1.2 Index options market in IndiaBSE and NSE are offering 5 index options products each. All the products are

European contracts. Although there have been products trading of index options never took

off big in BSE. At present the open interest in Index options in BSE is 2 whereas the no of

contracts traded in this financial year in NSE are 166066320. Figure 1 shows the products

available at NSE.

Underlying Index Product code

S&P CNX Nifty NIFTY

S&P CNX Nifty MINIFTY

CNX IT CNXIT

BANK Nifty BANKNIFTY

Nifty Midcap 50 NFTYMCAP50

Figure 1 - Index option products in NSE


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Figure 2 - Growth in derivative market in NSE

In the earlier years of the introduction of derivative trading in India, the investors

were trading more in futures than the options. According to figure 2, the data published by

NSE, stock futures were the most preferred product in NSE from 2002 to 2008. The share of

stock futures in F&O market is ranging from 5064% over those 7 years. But after 2008 the

dynamics of F&O market are changed and Index options started taking off. Share of index

options, as shown in figure 3, in F&O market is more than 50% now. This can be attributed

to the below two factors

1) Regulatory efforts by governmentIn March 2008 budget, government had said the STT (Securities transaction tax)

will be levied only on the option premium instead of the contract value. This has

helped the investors to invest more on index options.

2) Recession effect on the risk appetite of investorsOptions are less risky compared to that of futures. An investor will have the risk

of losing only the option premium and not the contract value in options whereas in

futures the risk will be on the total contract value. Recession had a great effect on

the risk appetite of the investors and made options more attractive to them than

futures.

As per the data released by NSE in June 2010, NIFTY is the 3rd

highest traded index

option product in the world after the Korean Index (KOSPI 200 options) and SPDR S&P 500

ETF options. NSE could achieve this only because of the above factors.


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Figure 3 - Share of index options in F&O market of NSE

2. Literature reviewIn this section, we provide brief review of literature dealing with efficiency of the

option market. In light of testing options market efficiency, Black and Scholes (1972, 1973)

tests the options valuation model using estimates of variance returns on the common stock for

US market and finds model as an accurate estimate of the variance, where, the high variance

stocks causing the model to overprice options and under-price options on low variance

stocks. Their later study empirically test the option valuation formula by deriving a

theoretical valuation formula with an assumption that efficiently priced options will not

provide definite profits in the market. The test proved to be the better working of the option

pricing model and suggested its applications for all corporate liabilities such as common

stock, corporate bonds and warrants. After the proposition of option pricing model by Blackand Scholes, Dan Galai (1977), examines the efficiency of CBOE using their option pricing

model and find consistency of the model with the trading strategies based on two hedging

tests; ex post and ex ante. Specifically, this model performs well on ex post hedge returns

(where the hedges are based on the model's evaluations of prices vs. the market prices).

Similarly, Mittnik and Rieken, (2000), investigate for German DAXoptions market by

simulating the trading strategies using ex-ante and ex-post tests, where the simulation tend to

be violated without showing any strong evidence on the market efficiency.

0

10

20

30

40

50

60

2000-

01

2001-

02

2002-

03

2003-

04

2004-

05

2005-

06

2006-

07

2008-

09

2009-

10

2010-

11

No of contracts

Total Turnover


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The study of Cavallo and Mammola (2000), investigate the efficiency of Italian

index option market through putcall parity conditions. Additionally, find the validity of

Black and Scholes option pricing model using volatility hedging strategies. The result of put

call parity conditions seems to be a weak test for market efficiency. However, the test of

volatility hedging strategy does not provide any systematic abnormal returns, and areconsistent with the market efficiency.

There are few studies which examine the efficiency option markets internally and

with across markets through arbitrage pricing relationships using the box spread, call and put

spreads, and call and put convexity. This type of test is conducted by Ackert and Tian

(2000, 2001) on S&P 500 index options market for US. They find frequent mispricing in the

market and indicate that the market is inefficient because of arbitrage limitations. Their later

study in testing the efficiency of S&P 500 index options market and cross market effect of a

traded stock basket, Standard and Poor's Depository Receipts (SPDRs), on the link between

index and options markets finds the improvement of pricing efficiency within option market,

but does not support for enhancement of arbitrage across market by stock basket. Similar

tests for European market conducted by Capelle-Blancard and Chaudhury (2001) on CAC

40 index option for French market and Brunetti and Torricelli (2004) on MIB 30 index option

for Italian market. The former study verify the internal efficiency across S&P 500 index

options market and find violations in the market and coincides with brisk trading and exhibit

systematic patterns in contrast to US market. The later study verifies the cross market

efficiency with French market and finds a common pattern with the French market. The

overall result supports the efficiency of Italian market and shows the high level of

consistency between internal and cross market efficiency.

In India, the studies in this kind of subject are limited where the existing literature of

Varma (2002), examines the pricing efficiency of options market on NSE index options

using Breeden- Litzenberger formula on the basis of estimated implied volatility smiles and

finds the sever under-pricing of volatility. While his test of pricing efficiency using put-call

parity theorem finds the over- pricing of deep in the money call options and show

inconclusive evidence of violations of put- call parity. Misra and Sangeeta (2005) examine

existence of violation of put-call parity on the same NSE Nifty index options and exhibit the

put-call parity relationship violations in the market.

It has been found in the Indian market since price is not in line with the sound

principle of option pricing so a correct price-discovery mechanism is not prevalent in the

market (sanjay sehgal,2009).It is because option arent traded at efficient best delta hedging

capacity of the option is also quite low. In India even if the value of the option is calculated

by the weighted implied volatility measure the value obtained and the value at which it is

traded are found to be different( jayant varma ,2002); in the same analysis he used implied

volatility to prove that in the Indian context the put-call parity doesnt hold. In case of Indian

market it has also been established that NSE Nifty derivatives markets tend to lead the


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underlying stock index. The slightly over time (sathya swaroop Debashish,2009).After

reading those literature it has become important to analyse and compare the Indian market

with developed country market and see what is the real issue behind the price-mismatch and

market efficiency. One of the major reasons that has been supported by various researcher is

that it is because there does exist restriction on the short-sale in the Indian market, so itdoesnt allow traders to take advantage of the arbitrage opportunity that may arise if the

option are traded at less than their optimum value (Rakesh Gupta, 2010).

3. Methodology3.1 Price Calculation

NSE uses the Black-Scholes method to calculate the theoretical price of the options contract.

Base price of an option contract is calculated by NSE as follows

For a new contract,

The base price of the contract will be the theoretical price of the options contract

arrived at based on Black-Scholes model of calculation of options premiums.

For subsequent trading days,

If the contract is traded in the last half an hour, the closing price shall be the lasthalf an hour weighted average price.

If the contract is not traded in the last half an hour, but traded during any time ofthe day, then the closing price will be the last traded price (LTP) of the contract.

If the contract is not traded for the day, the base price of the contract for the nexttrading day shall be the theoretical price of the options contract arrived at based

on Black-Scholes model of calculation of options premiums.

Price Band:

Price band for the index options is contract specific. It is on the based on the

delta value of contract. Price band is computed and updated on a daily basis as per the delta

value of the contract. Orders placed at prices which are beyond the operating ranges would

reach the Exchange as a price freeze.

3.2 Lower boundary condition for index options

The LBC, first proposed by Merton and further extended by Galai assumes a major

role in assessing options market efficiency. To date, a number of research studies have been

carried out in different options markets using the LBC to assess the efficiency of the markets,


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including the first one by Galai. The LBC of option prices denotes the minimum price of the

option contract at a given point of time; its violation indicates arbitrage opportunities.

Therefore, the price for an option contract should necessarily be equal to or higher than that

suggested by the LBC. This is a necessary (although relatively weak) condition that needs to

be satisfied in order to uphold the no-arbitrage argument of option pricing to ensure thecorrect pricing.

In the literature, the LBC has been defined for both the European options as well as

American options. Because we are analysing the S&P CNX Nifty Index options and these are

European (which can be exercised only at maturity) in nature, the condition defined for

European options constitutes the basis of the study.

The LBCs defined for the call and put options are given in equations (1) and (2) respectively;

these conditions need to be satisfied in an efficient market.

------(1)

------(2)

In the above equations, Ct is the market price of a call option at time t, Pt is the market price

of a put option at time t, It is the level of underlying index (S&P CNX Nifty) at time t, K is

the strike price of the option contract, T is the expiration time of the option at the time when

it was floated, r is the continuously compounded annual risk-free rate of return and (T-t) is

the time-to-maturity of the option at time t (measured in years).

Equations (1) and (2) describe the LBCs where the underlying asset is not expected to pay

any dividends during the life of the option. Because, in general, almost all the financial assets

pay dividends, equations (1) and (2) need to be modified by incorporating dividends. The

treatment of dividends in the test varies based on the assumption made about the payment of

dividends. Some of the studies treated it as a discrete payment and others as a continuous

yield. In this study, since S&P CNX Nifty Index (which includes 50 scrips) based options are

being analysed, it would be difficult to test the LBC, assuming discrete dividends.

Therefore, following Chance, it has been assumed that dividends are paid as continuouslycompounded yield. The LBC equations for call and put options, assuming that the index is

paying continuously compounded annual dividend yield (d), are given in equations (3) and

(4) respectively.

----(3)

----(4)

)}(emax{0,Ct)()( tTr

t

tT

keI

)}e(,0max{)()(

t

tTtTr

tIkeP

)}(max{0,Ct)( tTr

tkeI

)}(,0max{)(

t

tTr

tIkeP


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3.3 DataThe data to be considered for the analysis can be broadly classified into three categories,

namely, data related to option contracts, data related to the underlying asset (that is, the main

index of the NSE, formally known as the S&P CNX Nifty Index) and data on the risk-free

rate of return. The data on the options consist of daily closing prices of options, strike prices,

deal dates, maturity dates and number of contracts of call and put options respectively. In

order to minimise the bias associated with non synchronous trading, only liquid option

quotations (that is, contracts that have at least one contract traded) will be considered for the

analysis. The second data set pertains to the underlying asset, which includes the daily

closing value of S&P CNX Nifty Index and the dividend yield on it. The third data set

consists of monthly average yield on 91-day Treasury-bills. The data on T-bills have been

converted into a continuously compounded annual rate of return.

The data for these three categories will be collected between 4 June 2001 (the starting date

for index options in the Indian securities market) and 30 July 2010. The first and second data

sets will be collected from the website of NSE and CMIE (Centre for Monitoring Indian

Economy) database Prowess, and the third data set will be collected from the website of

Reserve Bank of India.

4. Future scopeDerivatives are considerably young in India. As explained earlier, Index option has become

most traded derivative instrument now. One in every 2 derivatives traded in Indian market is

an index option. Many earlier studies suggest that option pricing was not efficient in India till

2008. But after 2008 there has been a quantum leap in the number of market participants

trading the index options. Thus, it becomes imperative to establish that whether the

inefficient pricing is still prevalent. We would be making assessment on the number of

boundary violation on NIFTY and on CBOE to check the inefficient pricing. This would help

us establish a relationship between a developed market and a developing market on the basis

of the number and degree of the boundary violation. Second objective of our research would

be to learn and analyse difference between put option and call option boundary violation.

This would help in determining which of the two types of option are more price-efficient and

thus has less probability of sub-optimal pricing.


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5. References1. An econometric analysis of the lead- lag relationship between Indias NSE Nifty and its

derivative contracts by Sathya Swaroop Debasish, Journal of Risk Finance, 2009.2. Mispricing of Volatility in the Indian Index Options Market by Jayanth R Varma, April 2002.3. S&P 500 Index option tests of Jarrow and Rudd approximate Option valuation formula by

Charles J. Corrado, 1996.

4. Short-sales Restrictions and Efficiency of Emerging Option Market: A Study of Indian StockIndex Optionsby Rakesh Gupta,2010

5. Testing of pricing efficiency of the Indian index options marketby Sanjay Sehgal,International Journal Business and Society ,2009

6. Ackert, L.F., and Tian, Y.S. (1998). The introduction of Toronto index participation units andArbitrage opportunities in the Toronto 35 index options markets. Journal of Derivatives,

7.

Ackert, L.F., and Tian, Y.S. (2000). Evidence on the efficiency of index options markets,Federal Reserve Bank of Atlanta Economic Review, First Quarter.

8. Black, F., and Scholes, M. (1972). The valuation of option contracts and a test of marketefficiency. Journal of Finance, 27, 399-418.

9. Brunetti. M., and Torricelli, C. (2003). The put-call parity in the index options markets: furtherresults for the Italian mib30 options market. Materiali di Discussione, Dipartimento di

Economia Politica, Universit di Modena e Reggio Emilia, N. 436.

10. Capelle-Blancard G., and Chaudhury, M. (2001). Efficiency tests of the French index (CAC

40) Options market. Working paper, McGill Finance Research Center, SSRN

11. Cavallo, L., and Mammola, P. (2000). Empirical tests of efficiency of the Italian index options

market.

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