Organization Profile
Elind Computers Pvt. Ltd. – Bangalore.
•
Best
for India.
• 10 year old company.
• Offices in 5 Cities
•
Clients
• Major Stock Exchanges
• NSE, BSE, NASDAQ etc.
•
Products & Partners
•
•
•
•
OM Technologies,Intel, Microsoft.
Equity Exchanges - STRIDE suite.
DSTRIDE, IPO-STRIDE, OrderXpress & InvestorNet.
NeatXS & NeatIxs –first Internet trading in India.
System Configuration
• HARDWARE
COMPAQ Deskpro
Pentium III with 500 MHz
128 MB RAM
• SOFTWARE
OS : Windows 2000
Developed in : JAVA v3.1
System Overview
OPTIONS CALCULATOR DESCRIPTION
The options calculator is a service for individuals
investors, professional money managers, corporate accounting
departments and pension fund managers involved in pricing,
performance measurement or risk management of derivative
securities. The options calculator performs fast, accurate
pricing of a wide variety of European or American style call
and put options.
This options calculator computes the value of an
option using common formulas. The resulting premium values
are based on your inputs and the applicable formula.
WORKING OF THE OPTIONS CALCULATOR
LIBRARY OF FUNCTIONS
OPTIONS
CALCULATOR
Inputs to the calculator
Stock Price
Risk-free rate
Volatility
Time to maturity
Exercise price
Steps
Dividends
Time to dividend payment
OUTPUTS THE:
OPTION PRICE
ALONG WITH THE
DELTA, GAMMA,
THETA,VEGA &
RHO VALUES
WHAT IS AN OPTION?
• An option gives the holder the right to do do something.
• The holder does not have to exercise this right.
• The purchase of an option requires an up-front payment,
unlike forward or futures contracts.
TYPES OF OPTIONS
THERE ARE TWO BASIC TYPES OF OPTIONS:
 Call Option
 Put Option
CALL OPTION
 A call option gives the holder the right to
buy an asset by a certain date for a certain
price.
PUT OPTION
 A put option gives the holder the right to
sell an asset by a certain date for a certain
price.
EXAMPLE OF A CALL OPTION
An investor buys a call option to purchase 100 IBM shares
Strike price: $40
Current stock price: $38
Price of an option to buy one share = $5
Initial investment is 100 x $5 = $500
The outcome:
At the expiration of the option, IBM’s stock price is
$55. At this time, the option is exercised for a gain of
($55 - $40) x 100 = $1,500
When the initial cost of the option is taken into
account, the net gain is
$1,500 - $500 = $1,000
If the stock price is less than $40 the holder will not
exercise the right to buy. In this circumstance the
investor loses the whole initial investment of $500.
EXAMPLE OF A PUT OPTION
An investor buys a put option to sell 100 Exxon shares
Strike price: $70
Current stock price: $65
Price of an option to buy one share = $7
Initial investment is 100 x $7 = $700
The outcome:
At the expiration of the option, Exxon’s stock price
is $55. At this time the, the investor buys 100 Exxon shares
and, under the terms of the put option, sells them for $70 per
share to realize a gain of $15 per share or $1500 in total.
When the initial cost of the option is taken into
account, the net gain is
$1500 - $700 = $800
There’s no guarantee that the investor will make a
gain. If the final stock price is above $70, the put
option expires worthless and the investor loses
$700.
OPTIONS CAN BE EITHER
 American
 European
American options: are options that can be exercised at any
time up to expiration date.
European options: are options that can only be exercised on
the expiration date itself.
EXCHANGE –TRADED OPTIONS
Options trade on many different exchanges throughout
the world. Options can be written on many kinds of
assets. The asset upon which an option is based is called
underlying asset. The underlying assets include:
 Stocks (Equity) Options
 Foreign Currency Options
 Index Options
 Futures Options
EQUITY
One contact gives gives the holder the right to buy or sell 100
shares at a specified strike price.
FOREIGN CURRENCY
It is specific to the currency of the area. For example, in
Britain one contract gives the holder the right to buy or sell
31,250 pounds. Or in Japan one contract enables 6.25 million
yen.
INDEX
One contract gives the holder the right to buy or sell 100 times
the index at the specified strike price. For example one share
has strike price of $280, if it is exercised when the value of the
index is 292 the writer of the contract pays the holder
(292-280)x100=$1200
This cash payment is based on the index at the end of the day.
FUTURES
When the holder of a call option exercises, he or she will get the
amount in the futures option plus a cash amount equal to the
excess of the futures price over the strike price.
When the holder of a put option exercises, he or she will get the
amount in the futures option plus a cash amount equal to the
excess of the strike price over the futures price.
PRICING MODELS
A pricing model is used to find out whether the market
price of a option is valid or not, so as to be able to make a
decision as to buy or sell options.
There are two kinds of Pricing Models:
Discrete Models
Analytical Models
Analytical Pricing Models
 Analytical American (Bjerksund Strensland 1993)
 American call options with dividends (Roll-Geske Whaley)
 American Barone-Adesi-Whaley (1987)
Discrete Pricing Models
 Binomial American (Cox-Ross Rubinstein 1979)
 Binomial American with Discrete Dividends
 American Trinomial
THE INPUTS
• Stock Price
• Exercise Price
• Time to Exercise
• Risk-free rate
• Dividends
• Volatility
• Time to Dividends
• Steps
THE INPUTS
• Foreign Risk Free Rate
• Dividend Yield
THE OUTPUTS
• Option Price
• Implied Volatility
• Delta
• Gamma
• Theta
• Vega
• Rho
ANALYTICAL PRICING MODELS
Analytical American Approximation (Bjerksund &
Strensland -1993 )
 The Bjerksund Strensland (1993) approximation can be
used to price American options on stocks, futures,
currencies and index.
 The code consists of three functions. The first one
checks if the option is a call or put. If the option is a put,
the function uses the American put-call transformation.
The function then calls the main function
BSAmericanCallApprox which calculates the option
value.
 The main function uses the GBlackScholes() function.
Analytical American Approximation (Roll, Geske &
Whaley-1981)
This model is applicable to the valuation of
American calls on assets paying dividends and was
developed in a series of independent papers by Roll (1977),
Geske (1979), and Whaley (1981).
Analytical American Approximation (Barone – Adesi &
Whaley – 1987)
In 1987 Giovanni Barone-Adesi and Robert
Whaley published an article in the Journal of Finance
describing quadratic approximation method of valuing
American options. Their goal was to develop an accurate,
quick calculation closed-form solution to valuing in
American call and put options. The quadratic
approximation they developed has become one of the
most popular pricing algorithms used by the institutional
investors in North America.
DISCRETE PRICING MODELS
Binomial American (Cox, Ross & Rubinstein – 1979)
The Cox, Ross and Rubinstein model was developed
using a similar approach to the Black Scholes model, but
assumes the underlying instrument follows a binomial
distribution. The benefit of the binomial model is that it can
be used to evaluate options with an American style exercise.
BINOMIAL TREES
 A useful and very popular technique for pricing an option
or other derivative involves constructing what is known as
binomial tree. This is a tree that represents possible paths
that might be followed by the underlying asset’s price over
the life of the derivative.
 American options can be valued using a binomial tree,
the procedure is to work back through the tree from the end
to the beginning, testing at each node to see whether early
exercise is optimal.
ONE-STEP BINOMIAL MODEL
Stock price =$22
Option price = $1
Stock price
=$20
Stock price =$18
Option price = $0
TWO-STEP BINOMIAL MODEL
Su
Su2
Fu2
fu
Sud
S
f
Fud
Sd
fd
Sd2
Fd2
Binomial American with Discrete Dividends
The binomial model is widely used for valuing
such options, despite the greater computational
expense involved. The attraction of this model is that
it is more intuitively appealing than the alternatives;
therefore it is more easily understood. It also lends
itself to easy derivation of the sensitivities of the
option such as Delta, Gamma, etc. Moreover it can be
used for both puts and calls on indices that are
characterized as paying dividends. Thus it is a versatile
model.
Trinomial American
A useful and popular technique for pricing an
option or other derivative involves constructing what
is known as a trinomial tree. This is a tree that
represents possible paths that might be followed by
the underlying asset’s price over the life of the
derivative. This model is very much similar to the
binomial model, but for the fact that the option
sensitivities are not computed.
TRINOMIAL MODEL
 The Trinomial trees can be used as an alternative to
binomial trees.
 The probability of the stock price can move up, down
or remain the same.
Su2
Su
Su
S
Sd
S
Sd
Sd2
FEATURES OF THE OPTIONS CALCULATOR
GRAPHS
The Options Calculator enables the user to view how the
various input parameters vary against the output parameters with the
help of 2D graphs. Over 1,300 graphs have been designed with all
possible combinations.
SCREEN SHOT FOR GRAPHS – EQUITY, AMERICAN CALL,(BARONE,
ADESI & WHALEY – 1987)- ASSET PRICE VS. OPTION PRICE.
COMPARATIVE OUTPUTS
The Calculator provides the user with the facility to
compare the outputs of the other models which fall under the
same underlying type and option type.
SCREEN SHOT FOR COMPARATIVE OUTPUTS
HELP MENU
The Help Menu is designed to aide the user to understand
the functionality of the Calculator and how to make use of its
various features.
SCREEN SHOT FOR HELP MENU
SCREEN SHOT FOR HELP MENU – QUICK START
SCREEN SHOT FOR HELP MENU – USING OPTIONS
CALCULATOR
SCREEN SHOT FOR HELP MENU – MODEL DESCRIPTIONS
SCREEN SHOT FOR HELP MENU – ABOUT OPTIONS
CALCULATOR
SCREEN SHOT FOR UNDERLYING TYPE
SCREEN SHOT FOR OPTION TYPE – AMERICAN CALL
SCREEN SHOT FOR PRICING MODELS – EQUITY
SCREEN SHOT FOR UNDERLYING TYPE EQUITY,
AMERICAN CALL, ANALYTICAL AMERICAN
APPROXIMATION (BARONE, ADESI & WHALEY –
1987)
SCREEN SHOT FOR UNDERLYING TYPE EQUITY,
AMERICAN PUT, ANALYTICAL AMERICAN
APPROXIMATION (BJERKSUND & STENSLAND – 1993)
SCREEN SHOT FOR UNDERLYING TYPE EQUITY,
AMERICAN CALL, ANALYTICAL AMERICAN
APPROXIMATION (ROLL, GESKE & WHALEY – 1981)
SCREEN SHOT FOR UNDERLYING TYPE
FUTURES, AMERICAN PUT, BINOMIAL
AMERICAN (COX, ROSS & RUBINSTEIN –
1979)
SCREEN SHOT FOR UNDERLYING TYPE EQUITY,
AMERICAN PUT, BINOMIAL AMERICAN WITH DISCRETE
DIVIDENDS
SCREEN SHOT FOR UNDERLYING TYPE CURRENCY,
AMERICAN PUT, AMERICAN TRINOMIAL
CONCLUSION
The Options Calculator application was designed
under the requirements of the Security Industry catered by
Elind Computers Pvt.,Ltd.
The application is developed in Java. It is a product
expected to be launched on the Internet in due course.
The Calculator can be extended to add more facilities
and modified to meet the demands of the user.
BIBLIOGRAPHY
1. Patrick Naughton, Herbert Schildt, Java 2-The Complete Reference,
Tata McGraw-Hill, 1999.
2. Cay S. Horstmann, Gray Cornell, Core Java Volume II, The Sun
Microsystems Press, 2000.
3. Robert W Kolb, Ricardo J Rodriguez, Financial Markets, BlackWell
Publishers, Inc., 1996.
4. Jonathan Kundsen, JAVA 2D Graphics, O’Reilly & Associates,
Inc.1999.
5. Dr. Satyaraj Pantham, Pure JFC Swing, McMillan Computer
Publishing, 1999.
6.
Terry J Watsham, Futures and Options in Risk
Management, Thomson Business Press, 1998.
7.
John Cox and Mark Rubinstein, Options Markets,
Prentice-Hall, 1985.
8.
John Hull, Options, Futures and other Derivatives,
Prentice-Hall, Third Edition, 1998.
9.
Paul Wilmott, Jeff Dewynne, and Sam Howison, Option
Pricing, Mathematical Models and Computation, Oxford
Financial Press, 1994.
10.
Milton Abramowiz and Irene A Stegun, Handbook of
Mathematical Functions,
National Bureau of Standards, 1964.