Module – III Commodity Derivatives: Commodity Derivatives: Evolution of Commodity, Derivatives, Evolution of Commodity, Derivatives in India, Types of Derivatives, Other Classifications of Derivatives, Pricing Derivatives, Derivative Markets and Participants, Economic Importance of Commodity Derivatives Markets.

1. Chapter - 3
Commodity Market
Module – III
Commodity Derivatives: Commodity, Evolution of
Commodity, Derivatives in India, Types of Derivatives,
Other Classifications of Derivatives, Pricing Derivatives,
Derivative Markets and Participants, Economic
Importance of Commodity Derivatives Markets.

2. Understanding Risk: Risk is an essential part of doing any kind of
business. In general, it means any unanticipated variation in business
outcome variables, such as revenues, costs, profits, market share and
above all, firm value.
Firms are exposed to different sources of risk, which can broadly be
divided as:
1. Operational Risk: The risk of loss arising from inadequate or
failed internal processes, people and systems, or from external
events is operational risk.
2. Financial Risks: In addition to operational risks, unexpected
changes in financial variables – like interest rates, and exchange
rates – create financial risks for individual firms.
Derivatives for Managing Financial Risk: A firm faces several
kinds of risks. Its profitability fluctuates due to unanticipated changes
in demand, selling price, costs, taxes, interest rates, technology,
exchange rate and other factors.

3. Introduction to Commodity Derivatives Market:
Commodity derivatives markets have been in existence for centuries,
driven by the efforts of commodities producers, users and investors to
manage their business and financial risks. Producers want to manage
their exposure to changes in the prices they receive for their
commodities. End-users want and need to hedge the prices at which
they can purchase commodities.
At the same time, investors and financial intermediaries can either
buy or sell commodities through the use of derivatives.
Today, the commodity derivatives market is global, and includes both
exchange-traded and over-the-counter (OTC) derivatives contracts. It
consists of a wide range of segments: agriculture, base metals, coal,
commodity index products, crude oil, emissions, freight, gas, oil
products, plastics products, power, precious metals and weather.

4. Meaning of Derivatives: A derivative is an instrument whose value is
derived from the value of underlying asset, which may be
commodities, foreign exchange, bonds, stocks, stock indices, etc. for
ex: in case of a wheat derivative, say ‘wheat futures’ the underlying
asset is wheat, which is a commodity. The value of the ‘wheat futures’
will be derived from the current price of wheat. Similarly, in the case
of ‘index future’, say BSE Index Futures, the BSE index (the Sensex)
is the underlying asset.
Definition of Derivative: In the Indian context the Securities
Contracts (Regulation) Act, 1956 (SCRA) defines “Derivative” as
follows: - “A security derived from a debt instrument, share, loan
whether secured or unsecured, risk instrument or contract for
differences or any other form of security”. Trading of securities is
governed by the regulatory framework under the SCRA.
Derivative Contracts include Forwards, Futures (Financial & Commodity),
Options (Call & Put) and Swaps (Interest & Currency) broadly.

5. Evolution of Commodity:
Historically, dating from ancient Sumerian use of sheep or goats,
other peoples using pigs, rare seashells, or other items as commodity
money, people have sought ways to standardize and trade contracts in
the delivery of such items, to render trade itself more smooth and
predictable.
Classical civilizations built complex global markets trading gold or
silver for spices, cloth, wood and weapons, most of which had
standards of quality and timeliness. Considering the many hazards of
climate, piracy, theft and abuse of military fiat by rulers of kingdoms
along the trade routes, it was a major focus of these civilizations to
keep markets open and trading in these scarce commodities.
Reputation and clearing became central concerns, and the states
which could handle them most effectively became very powerful
empires, trusted by many peoples to manage and mediate trade and
commerce.

6. Sumerian: 5000 years ago

7. Sea Shells

8. Clay Vessels

9. Small Clay Tokens

10. Baked Clay Token

11. Token

12. Flat Tablet

13. Sealed Tablet

14. Major Events that shaped Derivative Markets:
 Rice futures in China 6000 years ago
 Forward agreement related to rice markets in 17th century in Japan.
 The first exchange for trading in derivatives appeared to be the Royal
Exchange in London, which permitted forward contracting.
 The first “future” contracts are generally traced to the Yodoya rice market in
Osaka, Japan around 1650.
 The history of futures markets are concerned was the creation of the Chicago
Board of Trade in 1848.
 A group of traders created the “to-arrive” contract, which permitted farmers to
lock in the price and deliver the grain later.
 These contracts were eventually standardized around 1865, and in 1925 the
first futures clearing house was formed.

15.  The early 20th century was a dark period of derivatives trading as BUCKET
SHOPS WERE RAMPANT.
 In 1922 the federal government made its effort to regulate the futures market
with the Grain Futures Act.
 In 1936 options on futures were banned in the US.
 The year 1973 marked the creation of both the Chicago Board Options
Exchange and the publication of perhaps the most famous formula in finance,
the option pricing model of Fischer Black and Myron Scholes.
 The 1980’s marked the beginning of the era of Swaps and other over-the-
counter derivatives.
 In 1983, the Chicago Board Options Exchange decided to create an option on
an index of stocks.
 While some minor changes occurred in the way in which derivatives were sold,
most firmed simply instituted tighter controls and continued to use derivatives.

16. Bucket Shops: A fraudulent brokerage firm that uses aggressive telephone
sales tactics to sell securities that the brokerage owns and wants to get rid of.
The securities they sell are typically poor investment opportunities, and almost
always penny stocks. A brokerage that makes trades on a client's behalf and
promises a certain price. The brokerage, however, waits until a different price
arises and then makes the trade, keeping the difference as profit.

17. History of Derivatives in India:
 The history of organized commodity derivatives in India goes back to the
nineteenth century.
 Organized trading in commodity derivatives was initiated in India with the
setup of Bombay Cotton Trade Association Ltd in 1875.
 Gujarati Vyapari Mandali was set up in 1900 to carryout futures trading in
groundnut, castor seed and cotton.
 wheat in Hapur (1913), raw jute and jute goods in Calcutta (1919) and oilseeds
in Bombay (1900) and Bullion in (1920).
 Speculation - With a view to restricting speculative activity in cotton market,
the Government of Bombay prohibited options business in cotton in 1939.
 Later in 1943, forward trading was prohibited in oilseeds and some other
commodities including food-grains, spices, vegetable oils, sugar and cloth.
 Parliament passed Forward Contracts (Regulation) Act, 1952 - The Act applies
to goods, which are defined as any movable property other than security,
currency and actionable claims.

18.  The already shaken commodity derivatives market got a crushing blow when in
1960s – Severe drought in country lead to default by farmers for contract.
 The Government set up a Committee in 1993 to examine the role of futures
trading. The Committee (headed by Prof. K.N. Kabra) recommended allowing
futures trading in 17 commodity groups.
 The first step towards introduction of derivatives trading in India was the
promulgation (new law or idea) of the securities laws (Amendment) ordinances,
1995, which withdrew the prohibition on options in securities.
 SEBI set up a 24- member committee under the chairmanship of Dr. L. C.
Gupta on Nov 18, 1996 to develop appropriate regulatory framework for
derivatives trading in India.
 The committee recommended that derivatives should be declared as
“securities” to govern trading of derivatives.
 Derivatives trading commenced in India in June 2000. SEBI permitted the
derivatives segments of two stock exchanges BSE & NSE and their clearing
house / corporation to commence trading and settlement in approved
derivatives.

19.  SEBI approved trading in index futures contracts based on S&P CNX Nifty
and BSE- 30 Index (Sensex) this was followed by approval for trading in
options which commenced in June 2001 and trading in options on individual
securities commenced on July 2001.
 Future contracts on individual stocks were launched in Nov 2001; futures and
options contracts on individual securities are available on more than 200
securities. – Controlled by SEBI.
 The Exchange – FMC – Department of Consumer Affairs, Food and Public
Distribution is the ultimate regulatory authority. – 3 tier authority for
derivatives.
The Forward Markets Commission (FMC) is the chief regulator of
commodity futures markets in India. As of July 2014, it regulated Rs 17
trillion worth of commodity trades in India. It is headquartered in
Mumbai and this financial regulatory agency is overseen by the Ministry
of Finance. The Commission allows commodity trading in 22 exchanges
in India, of which 6 are national. On 28 September 2015 the FMC was
merged with the Securities and Exchange Board of India (SEBI).

20. FEATURES OF DERIVATIVE MARKETS:
Derivatives are traded globally having strong popularity in
financial markets.
Derivatives maintain a close relationship between their values
and the values of underlying assets; the change in values of underlying
assets will have effect on values of derivatives based on them.
Derivatives traded on exchanges are liquid and involves the
lowest possible transaction costs.
Derivatives can be closely matched with specific portfolio
requirements.
The margin requirements for exchange traded derivatives are
relatively low, reflecting the relatively low level of credit risk
associated with the derivatives.
It is comfortable to take a short position in derivatives than in
other assets. An investor is said to have a short position in a derivatives
product, if he is obliged to deliver the underlying asset in specified future
date.

21. FUNCTIONS OF DERIVATIVE MARKETS:
(ECONOMIC IMPORTANCE)
 It performs the price discovery function.
 Derivatives market helps to transfers the risks.
 Higher trading volumes. (Spot to Future market)
 Speculative trades shift to a more controlled environment of
the derivatives market.
 Derivative act as a catalyst for new entrepreneurial activity.
 Derivatives markets help increase savings and investment in
the long run.

22. RISK ASSOCIATED WITH DERIVATIVES:
Market Risk: Price sensitivity to fluctuations in interest rates and
foreign exchange rates.
Liquidity Risk: Most derivatives are customized instruments, hence
may exhibit substantial liquidity risk.
Credit Risk: Derivatives trades not traded on the exchange are traded
in the Over the Counter exchange (OTC) markets. OTC contracts are
subject to counter party defaults.
Hedging Risk: Derivatives are used as hedges to reduce specific
risks. If the anticipated risks do not develop, the hedge may limit the
funds total return.
Regulatory Risk: Owing to the high characteristic inherent in the
derivatives market, the regulatory controls are sometimes too
oppressive for market participants.

23. 1. Using these products can help you to reduce the cost of an
underlying asset.
2. Earn money on shares that are lying idle.
3. Benefit from arbitrage (Buying low in one market and selling
high in other market)
4. Protection of securities against price fluctuations.
5. The most important use of these derivatives is the transfer of
market risk from risk-averse investors to those with an appetite
for risk.
6. The objective of firms using derivatives is to reduce the cash
flow volatility and thus to diminish the financial distress costs.
7. Some firms use derivatives not for the purpose of hedging risk
but to speculate about future prices.
USES OF DERIVATIVES:

24. PARTICIPANTS OF DERIVATIVE MARKETS:
Hedgers: The practice of offsetting the price risk inherent in any cash
market position by taking the opposite position in the futures market;
hedgers use the market to protect their businesses from adverse price
changes.
Speculators: Speculators who wish to bet on future movements in the
price of an asset. Future and options contracts can give them an extra
leverage, that is, they can increase both the potential gains and
potential losses in a speculative venture.
Arbitrageurs: Arbitragers are interested in locking in a minimum
risk profit by simultaneously entering into transactions in two or more
markets. If the price of the same asset is different in two markets,
there will be operators who will buy in the market where the asset
sells cheap and sell in the market where it is costly.
Intermediaries and Investors are also participants of Derivative Markets.

25. TYPES - DERIVATIVE PRODUCTS:
Forwards: A forward contract is a customized contract between two
entities, where settlement takes place on a specific date in the future at
today’s contracted specific price; forward contract is not traded on an
exchange.
Future: A futures contract is an agreement between two parties to buy or
sell a specified quantity and quality of an asset at a certain time in the future
at a certain price. Futures contract are standardized exchange-traded
contracts. Such contracts were originally protection against price volatility
by buyers and sellers of commodities such as grain, oil and precious metals.
Leaps: The acronym means Long-Term Equity Anticipation Securities.
These are options having a maturity of up to three years.
Options: An option is a contract which gives the right, but not the
obligation, to buy or sell the underlying asset at a specific price for a
specified time. Stocks are traded on BSE or Bombay Online Trading
(BOLT) system and options are traded on Derivatives Trading and
Settlement System (DTSS). Calls n Puts are 2 types of options.

26. Call Option: A call option is a contractual agreement which gives the
owner (holder) of the option the right but on the obligation to purchase a
stated quantity of the underlying asset (commodities, shares, indices, etc.)
at a specific price (called the strike price), on the expiry date.
Put Option: A put option is a contractual agreement which gives the
owner (holder) of the option the right but on the obligation to sell a stated
quantity of the underlying asset (commodities, shares, indices, etc.) at a
specific price (called the strike price), on the expiry date.
Warrants: Options worldwide generally have lives of up to one year, the
majority of options traded an option exchanges having a maximum
maturity of nine months. Longer-dated options are called warrants and are
generally traded over-the-counter.
Baskets: Basket options are options on portfolios of underlying assets.
The underlying asset is usually a moving average of a basket of assets.
Equity index options are a form of basket options.

27. Swaps: Swaps are private arrangements between two parties to exchange
cash flows in the future according to a prearranged formula. They can be
regarded as portfolio of forward contracts. Swaps can be of Interest rate
swaps and currency swaps.
Interest rate Swaps: These entail swapping only the interest related cash
flows between the parties in the same currency.
Currency Swaps: These entail swapping both principal and interest
between the parties, with the cash flows in one direction being in a
different currency than those in the opposite direction.
Swapations: Swapations are options to buy or sell a swap that will
become operative at the expiry of the options. Thus a Swaptions is an
option on a forward swap. Rather than have calls and puts, the Swaptions
market has receiver Swaptions and payer Swaptions. A receiver
Swaptions is an option to receive fixed and pay floating. A payer
Swaptions is an option to pay fixed and receives floating.

28. CLASSIFICATION OF DERIVATIVES MARKETS:
Over the Counter (OTC) derivatives are that which are privately
traded between two parties and involves no exchange or
intermediary. Non-standard products are traded in the so-called
over-the-counter (OTC) derivatives markets. The Over the counter
derivative market consists of the investment banks and include
clients like hedge funds, commercial banks, government sponsored
enterprises etc. Ex: OTCEI
Exchange Traded Derivatives Market - A derivatives exchange is
a market where individual’s trade standardized contracts that have
been defined by the exchange. A derivatives exchange acts as an
intermediary to all related transactions, and takes initial margin
from both sides of the trade to act as a guarantee. Ex: BSE, NSE,
etc.

29. Forwards: A forward contract is a customized contract or an
agreement between two entities, where settlement takes place on a
specific date in the future at today’s contracted specific price; forward
contract is not traded on an exchange and they popular on the Over
the Counter (OTC) market. Forward contracts are very useful in
hedging and speculation.
Features of Forward Market:
 They are bilateral contracts and, hence, exposed to counter party
risks.
 Each contract is customer designed and, hence, is unique in terms
of contract size, expiration date and the asset type and quality.
 The contract price is generally not available to public domain.
 On the expiration date, the contract has to be settled by delivery of
the asset.
 If a party wishes to reverse the contract, it has to compulsorily go
to the same counterparty, which often results in high price being
charged.

30. Limitations of Forward Contracts:
 Lack of centralization of trading.
 Liquidity. (Non-Tradable)
 Counterparty risk. (Default in Payment)
 Too much of flexibility and generality.
Futures: A futures contract is an agreement between two parties to buy
or sell a specified quantity and quality of an asset at a certain time in the
future at a certain price. Futures contract are standardized exchange-
traded contracts. Such contracts were originally protection against price
volatility by buyers and sellers of commodities such as grain, oil and
precious metals. Two types of future categories / types:-
Commodity Futures: Where the underlying is a commodity or physical
asset such as wheat, cotton, etc. such contracts began trading on Chicago
Board of Trade (CBOT) in 1860s.
Financial Futures: Where the underlying is a financial asset such as
foreign exchange, interest rates, shares, Treasury bill or stock index.

31. STANDARDIZED ITEMS IN A FUTURE CONTRACT:
1. Quantity & Quality of the underlying instrument.
2. The date and month of delivery.
3. Location of settlement or place of delivery.
4. The Underlying asset or instrument.
5. The type of settlement and last trading date.
6. The currency in which the futures contract is quoted.
7. The units of price quotation and minimum price change.
FUTURE TRADING FUNCTIONS:
 Price Discovery
 Price Risk Management.
 Information dissemination by exchanges.
 Improved product standards.
 Facilities access to credit / financing.
Contract Contract size Exchange
Corn 5,000 bushels Chicago Board of Trade (CBT)
Crude Oil 1,000 barrels New York Mercantile Exchange
STANDARDIZATION IN FUTURES CONTRACT:

32. Spot Price: The price at which an instrument/asset trades in the spot
market.
Future Price: The price at which the futures contract trade in the future
market.
Contract Cycle: The period over which a contract trades. For
instance, the index futures contracts typically have one month, two
months and three months expiry cycles that expire on the last Thursday
of the month.
Expiry Date: It is the date specified in the futures contract. (Last
Thursday)
Contract Size: The amount of asset that has to be delivered not be less
than one contract. For instance, the contract size of the NSE future
market is 200 Niftiest.
Basis: Basis is defined as the futures price minus spot price. There will
be a different basis for each delivery month for each contract. In a
normal market, basis will be positive. This reflects that futures prices
normally exceed spot prices.
FUTURE TERMINOLOGIES:

33. Cost of Carry: The relationship between futures prices and spot prices
can be summarized in terms of cost of carry. This measures the storage
cost plus the interest that is paid to finance the asset, less the income
earned on the asset. (Cost of Carrying: Storage, Insurance, Transport
cost, Finance costs (Interest)
Future Price = Spot Price + Cost of Carrying
Initial Margin: The amount that must be deposited in the margin
account at the time a futures contract is first entered into is the initial
margin.
Marking to Market: In futures market, at the end of each trading day,
the margin account is adjusted to reflect the investor’s gain or loss
depending upon the futures closing price.
Maintenance Margin: This is somewhat lower than the initial margin.
This is set to ensure that the balance in the margin account never
becomes negative. If the balance in the margin account falls below the
maintenance margin, the investor receives a margin call and is expected
to top up the margin account to the initial margin level before trading
commences on the next day.

34. Future Trading Functions:
 Basic Functions:
- Price Discovery
- Price Risk Management.
 Other Functions:
 Information dissemination by exchanges.
 Improved product standards
 Facilities access to credit / financing.
Objectives and Benefits of Commodity Futures are as follows:
Hedging: Price risk management by risk mitigation.
Speculation: Take advantage of favorable price movements.
Leverage: Pay low margin to enjoy large exposure.
Liquidity: Ease of entry and exit to market.
Price Discovery: For taking farming and business decisions.
Price stabilization along with balancing demand and supply
position.
Facilities integrated price structure.

35. DIFFERENCES BETWEEN FUTURES AND FORWARD CONTRACT:
Delivery: Delivery tendered in case of futures contract should be of a
standard quantity and quality as per contract specification, at designated
delivery centers of the exchanges. Delivery in case of forward contract is
carried out at delivery center specified in customized bilateral agreement.
Trading Place: Futures contract is entered on the centralized trading
platform of the exchange; forward contract is OTC in nature.
Size of the Contract: Futures contract is standardized in terms of quantity
and quality as specified by the exchange. Size of the forward contract is
customized as per the terms of agreement between the buyer and seller.
Transparency in Contract Price: Contract price of futures contract is
transparent as it is available on the centralized trading system of the
exchange. Contract price of forward contract is not transparent, as it is not
publicly disclosed.
Counter Party Risk: In futures contract the clearing house becomes a
counter party to each transaction, which is called ‘Novation’, making
counter party risk nil. In forward contract, counter party risk is high due to
decentralized nature of the transaction.

36. Regulation: Futures contract is regulated by a government regulatory
authority and the exchange. Forward contract, is not regulated.
Settlement: Futures contract can be settled in cash or physical delivery.
Forward contract is generally settled by physical delivery.
Valuation of Open position (Mark to Market Position): In case of futures
contract, valuation of open position is calculated as per the official closing
price on a daily basis and ‘mark-to-market’ margin requirement exists. In
case of forward contract, valuation of open position is not calculated on a
daily basis and there is a no provision of ‘mark-to-market’ requirement.
Organized futures Exchange: Forward contracts are contracts between
two parties, called the counterparties and they are not traded in any
exchange. Future contracts are traded in the organized future exchanges. As
stated earlier, future contracts are forward contract traded on the futures
exchanges.
Margin: The Buyers and sellers of the future contracts are required to
deposit some cash or securities as margin. This is done to ensure that the
buyers and sellers honor the deal.
Liquidity: Futures contract is more liquid as it is traded on the exchange.
Forward contract is less liquid due to its customized nature.

37. OPTION TERMINOLOGIES:
Index Options: These options have the index as the underlying. Some
options are European while other is American.
Stock Options: stock options are options on individual stocks. A
contract gives the holder the right to buy or sell shares at the specified
price.
Buyer of an Option: The buyer (Holder) of an option is the one who by
paying the option premium buys the right not the obligation to exercise
his option on the seller (Writer).
Options Premium: Option price is the price that the option buyer pays
to the option seller. It is also referred to as the option premium.
Expiration Date: The date specified in the options contract is known as
the expiration date, the exercise date, and the strike date of the maturity.
Strike Price: The price specified in the options contract is known as the
strike price or the exercise price.
OPTIONS: An option is a contract which gives the right, but not the
obligation, to buy or sell the underlying asset at a specific price for a
specified time.

38. In-the Money Option: An in-the money (ITM) option is an option that
would lead to a positive cash flow to the holder if it were exercised
immediately. A call option on the index is said to be in-the-money when
the current index stands at a level higher than the strike price. (that is, spot
price > strike price)
At-the-Money Option: An at-the money (ATM) option is an option that
would lead to zero cash flow if it were exercised immediately. An option
on the index is at-the –money when the current index equals the strike
price (that is, spot price = strike price)
Out-of-the Money Option: An out-of-the-money (OTM) option is an
option that would lead to a negative cash flow if it were exercised
immediately. A call option on the index is out-of-the-money when the
current index stands at a level is less than the strike price (that is, spot
price < strike price)
Intrinsic value of an option: The intrinsic value of a call is the amount
the option is ITM, if it is ITM. If the call is OTM, it intrinsic value is zero.
Time value of an Option: The time value of an option is the difference
between its premium and its intrinsic value. Both calls and puts have time
value.

39. Differences between Futures and Options:
Futures Options
Exchange traded, with novation Same as futures
Exchange defines the product Same as futures
Price is zero, strike price moves Strike price is fixed, price moves
Price is zero, Linear payoff Price is always positive, Nonlinear payoff
Both long and short at risk Only short at risk
Differences between Forwards and Options:
• Forward contract, both the buyer and seller are bound by the
contract, under option, the buyer has a right to decide whether or
not he/she would exercise the option.
• Forward contracts are flexible; but not in options.
• Option premium required to be paid, where in forward no
premium amount is required to be paid.

40. SWAPS:
Swaps are similar to futures and forwards contracts in providing
hedge against financial risk. A swap is an agreement between two
parties, called counterparties, to trade cash flows over a period of
time. Swaps arrangements are quite flexible and are useful in many
financial situations. The two most popular swaps are currency swaps
and interest rate swaps. These two swaps can be combined when
interest on loans in two currencies are swapped. The interest rate and
currency swap markets enable firms to arbitrage the differences
between capital markets.
CURRENCY SWAPS: Currency swaps involve an exchange of cash
payments in one currency for cash payments in another currency;
most international companies require foreign currency for making
investments in abroad. These firms fin difficulties in entering new
markets and raising capital at convenient terms. Currency swap is an
easy alternative for these companies to overcome this problem.

41. INTEREST RATE SWAPS: The interest rate swaps can be used by
portfolio managers and pension fund managers to convert their bond
or money market portfolios from floating rate (or fixed rate) to
synthetic fixed rate (or synthetic floating rate). There are many other
possible applications of the interest rate swaps.
BACK TO BACK LOAN:
Currency swaps are a form of back to back loan. For example, an
Indian company wants to invest in Singapore. Suppose the
government regulations restrict the purchase of Singapore dollars for
investing abroad but the company is allowed to lend rupees abroad
and borrow Singapore dollars. The company could find a Singapore
company that needs Indian rupees to invest in India. The Indian
company would borrow Singapore dollars and simultaneously lend
rupees to the Singapore Company. Currency swaps have replaced the
back to back loans. Back to back loans developed in UK when there
were restrictions on companies to buy foreign currency for investing
outside the country.

42. PRICING OF FUTURE CONTRACT – COST OF CARRY MODEL:
The cost of carry model expresses the forward price (or,
as an approximation, the futures price) as a function of the
spot price and the cost of carry.
Where:
F is the forward price,
S is the spot price,
e is the base of the natural logarithms,
r is the risk-free interest rate,
s is the storage cost,
c is the convenience yield, and
t is the time to delivery of the forward contract (expressed as a fraction
of 1 year).
The same model in currency markets is known as interest rate parity. We can
also use the below mentioned formulas for calculation of future prices.

43. PRICING OF OPTIONS CONTRACT –
BLACK SCHOLES MODEL CALL & PUT OPTION FORMULA:
Assumptions of Black Scholes Model:
• It is possible to short sell the underlying stock.
• There are no arbitrage opportunities.
• Trading in the stock is continuous.
• There are no transaction costs or taxes.
• All securities are perfectly divisible (e.g. it is possible to buy 1/100th
of a share).
• It is possible to borrow and lend cash at a constant risk-free interest
rate.