FUTURE VOLATILITY IN OPTIONS.1

8/7/2019 FUTURE VOLATILITY IN OPTIONS.1

1/22

FUTURE VOLATILITY IN OPTIONS

Presented by:SANJEEV KUMAR DUBEY

Faculty Guide

SURENDRA PODDAR

1


2/22

Name: SANJEEV KUMAR DUBEY

Course: PGPM(FINANCE & MARKETING)

Batch: 2009-11

Telephone: 9830259169

E-mail: [email protected]

Company Name: LOHIA SECURITIES LIMITED

Project Title: FUTURE VOLATILITY IN OPTIONS

Project Leader/ Supervisor: Mr. JITESH AGARWAL

Telephone: 9830591545

Start date for Internship: 05.04.2010

End date for Internship: 04.06.2010

Report date: 31.07.2010

2


3/22

CONTENTS

1. Abstract ......................................................................................................................3

2. About the Company.....................................................................................................4

3. History of Achievements..............................................................................................5

4. Introduction..................................................................................................................7

5. Options volatility..........................................................................................................8

Historical volatility........................................................................................8

Implied volatility...........................................................................................8

6. Collection of Data..........................................................................................................9

7. Calculation of Historical volatility..................................................................................9

8. Calculation of Implied volatility.....................................................................................9

9. Volatility trading Strategies..........................................................................................11

10. Pure Selling Volatility Strategies..................................................................................14

11. Analysis.........................................................................................................................18

12. Conclusions...................................................................................................................19

13. Bibliography & Webliography......................................................................................20

3


4/22

ABSTRACT

The internship was carried out in Lohia Securities Limited , a company which isheadquartered in Kolkata and it is the largest in eastern India in the F&O segment by

turnover.

The internship involved making a thorough research in the options market to develop

profitable trading strategies for the company. This required one to have a proper

understanding of the different factors which affect the option prices both in the short and the

long run. In order to achieve this, my first task was to understand the different forms of

volatility which influence the option prices. This was done by measuring the historical

volatility of various companies for a particular period. The volatilities thus calculated were

matched against the implied volatility calculated on the basis of Black-Scholes model for

option pricing, to develop the trading strategies. The volatility calculation for the abovepurpose was done by getting the data from NSE India website.

The key aspect of the internship would be the learning atmosphere which taught me the

intricacies of option pricing and a whole lot of other things which are dealt with while

valuing option prices. Since the model was to be prepared on excel spreadsheet, there were

other technical details which were acquired.

One another which is worth mentioning in the context would be the generous help from

my mentors. They had always been a source of inspiration to me with their valuable advices

during the course of my training.

4
http://www.investopedia.com/terms/b/blackscholes.asphttp://www.investopedia.com/terms/b/blackscholes.asp


5/22

ABOUT THE COMPANY

Lohia Securities Ltd. (LSL) is a Kolkata headquartered stock broking Company of 13 years

standing.

Shares are listed on Kolkata Stock Exchange Association Ltd and Bombay Stock

Exchange( In permitted category)

The Company has a presence in the Indian Capital Market with Trading and Clearing

Corporate Membership of :

National Stock Exchange

Capital Market Segment

Derivative Market Segment

Bombay Stock Exchange


Derivative Market Segment

Calcutta Stock Exchange Ltd,


Lohia Securities Ltd. is a Depository Participant of :

National Securities Depository Ltd. (NSDL)

Central Depository Services (India) Ltd. (CDSL).

5


6/22

LOHIA SECURITIES LIMITED - Brief History of Achievements

1977

Mr. Hari Kishan Lohia, the founder Chairman of LSL, has completed 30 years as a trader in

Capital market segment of CSE. Later on, he became a broker dealer of CSE in the year

1992.

1980

Mr. Mahesh Kumar Bajaj, the founder director of LSL joined the family run brokering

business in name and style M/s Satnarayan Bajaj, at the very early age of 21.

1985

Mr. Mahesh Bajaj acquired expertise in technical analysis and day trading.

1990

Mr. Bajaj became a common name in the trading circles of Calcutta Stock Exchange.

1995

LSL came into existence as a corporate entity with a vision to make it a professionally runbroking house and acquired membership of NSE Capital Market.

1998

First branch office was opened near Bombay Stock Exchange.

1999

Institutional Dealing business started, major Clients till date are LIC,GIC,EXIM

2000

First to provide Bloomberg online service to its clients.

In the month of February, NSE Future segment business started.

In the month of July, NSE Option segment business started.

2001

Became Depository participants of NSDL, CDSL.

2002

Developed the team for recruiting and training freshers for strategy based trading in futures

6


7/22

& option segment.

2003

Soon LSL became one of the leading firms in Eastern India doing Strategy based trading.

2004

By the time we had developed around 50 dealer in F&O Segment.

2005

Acquired BSE Capital market membership.

2006

Acquired BSE Future & Option Market Membership.

2007

Presently we operate with more than 250 dealers in F&O segment, being largest in Eastern

India by Turnover.

The Growth Story Continues...

7


8/22

INTRODUCTION

As has been said earlier, Lohia Securities is a stock broking cum investment banking outfit,the internship project assigned to me was directed towards the same. In this respect I wouldthink myself quite lucky to have landed up with a project like this. I say this because I havealways been enamoured by the functioning of the stock markets. Hence it had a greatrelevance for me as far as my interests were concerned.

The assignment was concerned with options in the Indian market. It would be worthmentioning that options in India are available only on four basic underlying assets. They are:

1) stocks ;

2) indices ;

3) commodities ; and

4) exchange rates.

My area of operation was confined to only the first two types of underlying assets.

An option is a contract that gives the buyer the right, but not the obligation, to buy or sell anunderlying asset at a specific price on or before a certain date. An option, just like a stock orbond, is asecurity. It is also a binding contract with strictly defined terms and properties .Hence the underlying asset here would be stocks or indices. There are two types of options,call and put. Call options give the purchaser the right to buy any stock at any predeterminedprice and volume. Similarly, put options give the purchaser the right to sell a stock at apredetermined price and volume.

8
http://www.investopedia.com/terms/u/underlying.asphttp://www.investopedia.com/terms/s/security.asphttp://www.investopedia.com/terms/s/security.asphttp://www.investopedia.com/terms/u/underlying.asphttp://www.investopedia.com/terms/s/security.asp


9/22

OPTIONS VOLATILITY

An essential element determining the level of option prices, volatility is a measure of therate and magnitude of the change of prices (up or down) of the underlying. If volatility ishigh, the premium on the option will be relatively high, and vice versa. Once you have ameasure of statistical volatility (SV) for any underlying, you can plug the value into astandard options pricing model and calculate the fair market value of an option.

A model's fair market value, however, is often out of line with the actual market value forthat same option. This is known as option mispricing.

What good is a model of option pricing when an option's price often deviates from themodel's price (that is, its theoretical value)? The answer can be found in the amount ofexpected volatility (implied volatility) the market is pricing into the option. Option modelscalculate IV using SV and current market prices. For instance, if the price of an option should

be three points in premium price and the option price today is at four, the additional premiumis attributed to IV pricing. IV is determined after plugging in current market prices of options,usually an average of the two nearest just out-of-the-money option strike prices.

HISTORICAL VOLATILITY

The realized volatility of a financial instrument over a given time period. Generally, thismeasure is calculated by determining the average deviation from the average price of afinancial instrument in the given time period. Standard deviation is the most common but notthe only way to calculate historical volatility.

Also known as "statistical volatility".

IMPLIED VOLATILITY

The estimated volatility of a security's price. In general, implied volatility increases whenthe market is bearish and decreases when the market is bullish. This is due to the commonbelief that bearish markets are more risky than bullish markets.

Implied volatility is sometimes referred to as "vols."

9
http://www.investopedia.com/terms/v/volatility.asphttp://www.investopedia.com/terms/o/outofthemoney.aspasphttp://www.investopedia.com/terms/v/volatility.asphttp://www.investopedia.com/terms/o/outofthemoney.aspasp


10/22

COLLECTION OF DATA

The data for the purpose of the project was collected fromwww.nseindia.com. Whilecollecting the data due care was taken with regards to the expiry date and the type of options(implied volatility is different in case of both call and put options). Again, the expiry dateselected needed to be a current one because not much volume of trade is done on options withexpiry date of more than two months. If such expiry date is selected the volatility calculationwould have been futile. Options prices are affected by time decay i.e. more the time left toexpiry the more options value and vice-versa.

CALCULATION OF HISTORICAL VOLATILITY

Short term or more active traders tend to use the shorter time period for measuringhistorical volatility, the most common being 5-day, 10-day, 20-day, and 30-day. Intermediateterm and long term investors tend to use longer time periods, most commonly 60-day, 180-day, and 360-day. In my project I used the 60-day time period to calculate the volatility. Thefollowing steps are undertaken to calculate:

1. Measure the day-to-day price changes in the market: Calculate the natural log ofthe ratio (Rt) of a stock price (S) from the current day (t) to the previous day(t-1).

This corresponds closely to percentage price change of the stock.

2. Calculate the average day-to-day changes over a certain period: Add together allthe changes for the given period (n) and calculate an average for them (Rm).

3. Find out how far prices vary from the average calculated in step-2: The Historicalvolatility is the average variance from the mean (the standard deviation) and isestimated .

4. Express volatility as an annual percentage : To annualize the historical volatility,theabove result is multiplied by the square root of 252 (the average number of tradingdays in a year).

10
http://www.nseindia.com/http://www.nseindia.com/http://www.nseindia.com/http://www.nseindia.com/


11/22

IMPLIED VOLATILITY AND ITS CALCULATION

In financial mathematics, the implied volatility of anoptioncontract is thevolatilityimplied by the market price of the option based on anoption pricingmodel. In other words, itis the volatility that, when used in a particular pricing model, yields a theoretical value for theoption equal to the current market price of that option. Non-option financial instruments thathave embeddedoptionality, such as aninterest rate cap, can also have an implied volatility.Implied volatility, a forward-looking measure, differs from historical volatility because thelatter is calculated from known past returns of a security.

An ordinary option pricing model, such as Black-Scholes, uses a variety of inputs to derive

a theoretical value for an option. Inputs to pricing models vary depending on the type of

option being priced and the pricing model used. However, in general, the value of an option

depends on an estimate of the future realized volatility, , of theunderlying. Or,

mathematically:

where Cis the theoretical value of an option, and fis a pricing model that depends on ,

along with other inputs.

The function fis monotonically increasing in , meaning that a higher value for volatility

results in a higher theoretical value of the option. Conversely, by the inverse function

theorem, there can be at most one value for that, when applied as an input to , will

result in a particular value forC.

Put in other terms, assume that there is some inverse function g() = f1(), such that

where is the market price for an option. The value is the volatility implied by the

market price , or the implied volatility.

In general, a pricing model function, f(), does not have a closed-form solution for itsinverse, g(). Instead, a root finding technique is used to solve the equation:

While there are many techniques for finding roots, two of the most commonly used areNewton's method and Brent's method. Because options prices can move very quickly, it is

often important to use the most efficient method when calculating implied volatilities.

Newton's method provides rapid convergence, however it requires the first partial derivative

of the option's theoretical value with respect to volatility, i.e. , which is also known as

vega (see The Greeks). If the pricing model function yields a closed-form solution forvega,

which is the case forBlack-Scholes model, then Newton's method can be more efficient.

However, for most practical pricing models, such as abinomial model, this is not the case

and vega must be derived numerically. When forced to solve vega numerically, it usuallyturns out that Brent's method is more efficient as a root-finding technique.

11
http://en.wikipedia.org/wiki/Financial_mathematicshttp://en.wikipedia.org/wiki/Option_(finance)http://en.wikipedia.org/wiki/Option_(finance)http://en.wikipedia.org/wiki/Option_(finance)http://en.wikipedia.org/wiki/Volatility_(finance)http://en.wikipedia.org/wiki/Volatility_(finance)http://en.wikipedia.org/wiki/Market_pricehttp://en.wikipedia.org/wiki/Valuation_of_optionshttp://en.wikipedia.org/wiki/Valuation_of_optionshttp://en.wikipedia.org/wiki/Valuation_of_optionshttp://en.wikipedia.org/wiki/Interest_rate_caphttp://en.wikipedia.org/wiki/Interest_rate_caphttp://en.wikipedia.org/wiki/Black-Scholeshttp://en.wikipedia.org/wiki/Black-Scholeshttp://en.wikipedia.org/wiki/Underlyinghttp://en.wikipedia.org/wiki/Underlyinghttp://en.wikipedia.org/wiki/Inverse_function_theoremhttp://en.wikipedia.org/wiki/Inverse_function_theoremhttp://en.wikipedia.org/wiki/Inverse_function_theoremhttp://en.wikipedia.org/wiki/Root_findinghttp://en.wikipedia.org/wiki/Newton's_methodhttp://en.wikipedia.org/wiki/Brent's_methodhttp://en.wikipedia.org/wiki/The_Greekshttp://en.wikipedia.org/wiki/Black-Scholeshttp://en.wikipedia.org/wiki/Binomial_options_pricing_modelhttp://en.wikipedia.org/wiki/Binomial_options_pricing_modelhttp://en.wikipedia.org/wiki/Binomial_options_pricing_modelhttp://en.wikipedia.org/wiki/Financial_mathematicshttp://en.wikipedia.org/wiki/Option_(finance)http://en.wikipedia.org/wiki/Volatility_(finance)http://en.wikipedia.org/wiki/Market_pricehttp://en.wikipedia.org/wiki/Valuation_of_optionshttp://en.wikipedia.org/wiki/Interest_rate_caphttp://en.wikipedia.org/wiki/Black-Scholeshttp://en.wikipedia.org/wiki/Underlyinghttp://en.wikipedia.org/wiki/Inverse_function_theoremhttp://en.wikipedia.org/wiki/Inverse_function_theoremhttp://en.wikipedia.org/wiki/Root_findinghttp://en.wikipedia.org/wiki/Newton's_methodhttp://en.wikipedia.org/wiki/Brent's_methodhttp://en.wikipedia.org/wiki/The_Greekshttp://en.wikipedia.org/wiki/Black-Scholeshttp://en.wikipedia.org/wiki/Binomial_options_pricing_model


12/22

VOLATILITY TRADING STRATEGIES

Volatility is essentially the risk aspect of the market. It is the perception of risk that is

securitized in the time value component of an option premium. The volatility can be implied

in the options price(which includes traders expectations of future price movements) or bebased upon the actual fluctuations in the price of the asset which underlies the option. Traders

buy or sell volatility as their perception of risk in the future changes.

The ideal way to trade volatility is to maximize the exposure to both kinds of volatility

(actual and implied) and minimize the exposure to the other factors which influence option

prices, such as small movements in the underlying market and if possible time decay. This is

done by using the Greeks to assess the exposure the trading strategy has to all the variables

which drive option prices. To benefit from a change in actual volatility of the market, the

trader will want to establish a gamma positive or negative position. To benefit from a change

in implied volatility, the trader will focus on her kappa (vega) exposures. For the other

derivatives such as delta, theta, and rho, she will try to minimize her exposure to these

.Greeks by driving their level to zero. By doing so, the trader can focus her viewpoint onvolatility alone. When one is completely neutral to the underlying market and is just trading

volatility, it is termed pure volatility trading. In addition to pure volatility trading one can

establish trading strategies that are initially neutral to the underlying market but can become

an equivalent long or short position as the underlying market price moves to a particular

level. These trades are usually called leaning volatility trades. Below we examine some of the

pure volatility strategies.

1. Pure Buying Volatility Strategies

Suppose one purchased a call option which is an equivalent long position. If volatility

increases one will profit. If the same person also bought a put option, which is an equivalentshort position, in combination with the long call what would we have? The put option has an

12


13/22

opposite exposure to the underlying market, but will also benefit if volatility increases. These

two trades can be combined in such a way that they will be neutral to the underlying market

but they will still have a long volatility bias. That is how you go .long volatility; by buying

options. If one buys both a call and a put and adjusts carefully for the delta exposure of each,

then the position can be neutralized to the underlying asset and will then be purely a volatility

trade. Depending on which strike prices you choose, this combination trade is called either astraddle or a strangle.

1.1 Buying a Straddle

A long (or buying or bottom) straddle is achieved when you buy a call option and a

put option both at the same strike price and expiration date (generally both at-the-

money).

The call option you purchase is a long position relative to the underlying market and the put

option is a short position relative to the underlying. The total exposure of these two in

combination will cancel out relative to the underlying position. This is because the positions

bought are at-the-money options with delta exposures that approximately offset (recall thatthe deltas of at-the-money calls and puts are approximately 0.5 and0:5; respectively).

While you have no exposure to the underlying market, this trade will be extremely

sensitive to volatility.

Purchasing at-the-money options, which have the greatest time value, gives you the

greatest absolute volatility sensitivity. Unfortunately, these options are also extremely

sensitive to time decay. This is the reason very few traders can afford to maintain these

strategies for long periods or until expiration. Most dealers rarely buy straddles for more

than a few days. They use them as a short term trade expecting an immediate increase in

volatility to occur. If this occurs, they close out the straddle, take their profits and run.1

Straddles essentially double the exposure to volatility compared to the purchase of a single

option. This means a doubling in the straddle value for the same increase in the rate of

volatility.

The profit pattern (at expiration) of a long straddle is shown in Figure 1a. (The profit and

loss profile of a long straddle over time is presented in Figure 1b.) The strike price of the call

and put options is denoted by X: If the stock price is close to the strike price at expiration of

the options, the straddle leads to a loss. However, if there is a sufficiently large movement in

either direction, a significant profit will result. The payout from a straddle is calculated below

(to calculate the profit you need to subtract from the payout the call and put premiums):

PAYOFF FROM A LONG STRADDLESTOCK PRICERANGE

PAYOFF FROM ALONG CALL OPTION

PAYOFF FROM ALONG PUT OPTION

TOTALPAYOFF

ST X O X ST

X- ST

ST X ST - X O

ST- X

1.2 Buying a Strangle

A variation on the above theme is the strangle which costs less than the straddle toestablish.

13


14/22

With the long strangle you are buying a call and a put on the same underlying asset

for the same maturity, but at different strike prices. A long strangle is sometimes

called a bottom vertical combination.Like the straddle, the equivalent longposition and the equivalent short

position will offset each other relative to the underlying market. Generally, strangles areestablished with out-of-the-money options. If they are established with in-the-money options

they are often referred to as guts positions.

The only way to quantify the differences between a straddle and a strangle is to examine the

.Greek derivatives for each strategy. Throughout the life of the options, the straddle will

always have a higher gamma than the strangle and will therefore be more appropriate for

those traders who are betting on an increase in the actual volatility of the market.

Since with the strangle you are buying out-of-the-money options, you are paying a

smaller premium compared to the straddle and you are not going to have the same

amount of money exposed to time decay, because you have purchased less time

value.2 With the strangle, youare no longer maximizing your exposure to time value or to volatility. But you do have a

position that does not cost as much to establish and therefore has a smaller loss potential.

These trades can be established for perhaps a longer time period than the straddle, you still

will want to take them off within 7 to 10 days if market volatility has failed to change.

The other major benefit of the strangle is that it is constructed using out-of-the-

money options which experience a greater percentage increase in their value from

a change in volatility.

When an option is at-the-money, it will experience the greatest absolute increase in price

from a change in implied volatility but the out-of-the-money options will have the greatest

percentage impact. So the strangle is preferred by those traders who wish to bet on increases

of the implied volatility while the straddle traders are betting on both an increase in the actual

volatility (gamma effect) and the absolute impact of the implied volatility (kappa or

vega effect).

The payoff function of a long strangle is given in the following table. The call strike price

(X2) is higher that the put strike price (X1) :

PAYOFF FROM ALONG STRANGLE

STOCK PRICERANGE

PAYOFF FROM ALONG CALL OPTION

PAYOFF FROM ALONG PUT OPTION

TOTALPAYOFF

ST

X1 O X1 ST

X1

- STX1

FUTURE VOLATILITY IN OPTIONS.1

Documents

Transcript of FUTURE VOLATILITY IN OPTIONS.1