Chapter 2:Background and Motivation
In this chapter, we provide the finance background inherent to the various option pricing and dynamic trading strategies
examined throughout the website and motivating issues.
Recently explosive changes in corporate bank and investment finance have been observed by financial engineers
and a new set of financial instruments came into existence, called
financial derivative.
According to Oxford dictionary the derivative is defined as:
1. A word formed by derivation i.e. something derived.
2. The limit of the ratios of change in a function to the corresponding changes in its independent variable
as the latter changes to zero.
3.
(a) A chemical substance related structurally to another substance and theoretically derivable from it.
(b) A substance that can be made another substance in one or more steps.
Definition (1) suggests that a financial derivative is a financial instrument which is derived from the cash market or
plain vanilla( Standardized financial instrument). A cash market instrument is regarded as market
instrument that involves paying a principal sum upfront. For this, the buyer obtains the right to interest and return of
principal after a period of time (a loans, deposit or bond or for a part of ownership of a company).
Definition (2) is similar to ubiquitous Greek delta ($\delta$ ) i.e. ratio in the pricing and hedging of options and is also
defined as change in the price of an option on a particular financial instrument, with respect to the change in the price
of the underlying financial instrument.
Definition (3) suggests that financial derivative have taken a life of their own, their prices are structurally related to the
prices of theoretically constituent components.
In view of all above suggestions a financial derivative is defined as "Derivative is a financial contract whose
value/price dependents on the behavior of the price of other underlying assets". These agreements, made on the trading
screen of stock exchanges, to buy or sell an asset in future at a predetermined price and these asset can either be a share,
index, interest rate, bond, rupee-dollar exchange rate, sugar,crude oil, soybean, cotton, coffee and what have we.
The concept of derivative can easily be understood with the help of a very simple example of derivative of milk. The price
of curd depends upon the price of milk, which in turn depends upon the demands and supply of milk.
There are two types of derivative instruments -
1. Exchange traded instruments: Future and options.
2. Over the counter (OTC) market traded instruments: forward, options and swaps.
A
exchange is a market where individuals trade standardized contracts that have been defined by
exchange. In 1848, the first exchange was established in U.S.A. as "The Chicago Board of Trade" (CBOT), and
its main task was to standardize the quantities and qualities of the grains that were traded. Now a day's
exchanges exist all over the world. Future and options traded on exchange.
Over the counter {OTC} market is a network of telephone and computer. The traders of over
the counter market do not physically meet, all the conversation between two parties on the telephone are
usually taped, and in the case of dispute about what was agreed, the tapes are replayed to solve the issue.
In the OTC, the market participants are free to negotiate any mutually attractive deal .
The main difference between two types of derivative instruments is in counter party risk and liquidity. The instruments traded
in the exchange are more liquid and have not counter party risk, while the instruments which traded in OTC are less liquid
and have always a counter party risk.
Forward contract
A
forward contract is an agreement between two parties, one party agrees to deliver a specified date
(called maturity) in future at a specified price
(called strike price) of a
financial assets. All the terms and condition of contracts are mutually decided and contracts are thus tailor
made. A business organization can use the forward contract to hedge the price of purchase or sale of the financial assets on
the future date.
For example - In 19th Century, sugar that was produced in India and exported to England for use, to take
months to reach its destination. There was no way to knowing how the price of sugar would move, while the commodity was
being shipped. If prices fell significantly, the sugar had to be sold at a loss, thus bringing ruin to its producer. The
producer, therefore, sought to avoid the price risk by selling their sugar "forward" albeit at prices somewhat lower than what
they expected to get by waiting for the sugar to arrive at the market months latter. The forward contract provides some
immunity from price variation.
For example- A manufacturer of soaps and detergents who uses oil as raw material cannot change the
prices of his product as when oil prices change. Hence he has to face the risk of oil prices rising in the future. In order
to prevent this, he will want to take a forward contract to buy oil at a predetermined price for a certain period of time.
Future contracts
Future contracts are similar to forward contract in all except some respects. Future contract is a highly standarlised forward
contracts having specific quantity of underlying known as lot-sized traded on organized future exchanges with a clearing
association that acts as a middleman between the contracting parties. The contracting parties pay an initial margin to
clearing house as a performance bond. A part from the initial margin, the contracting parties also have to pay a daily mark
to market margin. This margin is equal to the notional net loss of the position of the market participant. This is done on a
daily basis. The profiting party is credited with the profit, whereas the losing party is debited by the loss amount
.
Example for future contract - Mr. X is dealing in March 2010 Satyam future contract, he know that the market
lot size is 1200 shares of Satyam, the contract would expiry on March 28, 2010, the price is quoted per share, the minimum
fluctuation is 5 paise per share i.e. $1200 \times 0.5$ = Rs $60$ per contract/lot, the contract would be settled in cash
and the losing price in the cash market on expiry day would be the settlement price.
Options are contract between two parties in which one party has the right but not obligation to buy or sell
a fixed quantity of an underlying asset at a particular date (or period) at a fixed price. In other words, in an option
contract one person who has the right to buy or sell any asset or commodity at a fixed price in the future and no obligation
by paying some upfront fee to second person, is known as holder. While the second person who has sold the right to
holder by getting some upfront free has not right only an obligation, is known as option writer. Options can be traded
both on an exchange and over the counter (OTC). There are two types of option are
call and
put
options.
A
call option give the holder the right to
buy the underlying asset at a
specified price during a specified period, and a
put option give the holder the right to
sell the underlying asset at a specified price during a specified period.
Example of call option: - Suppose you have a right to buy 1000 shares of Hindustan Lever at Rs 250 per share
on before March 28, 2010. In other word you are a holder of a call option on Hindustan Lever shares at Rs 250 per share. The
option writer who gives you that right to buy from him is under obligation to sell 1000 shares of Hindustan Lever at Rs 250 per
share on before March 28, 2010 whenever asked.
Example of put option: - Suppose you have the right to sell 1600 shares of Bharat Heavy Electrical at Rs. 140
per share on before March 28, 2002. In other word you are a holder of a put option on Bharat Heavy Electrical. The options
give you the right to sell 1600 shares. You have the right to sell Bharat Heavy Electrical shares at Rs 140 per share. The
writer of this put option, who has give you the right to sell to him is under obligation to buy 1600 shares of Bharat Heavy
Electrical at Rs 140 per share on or before March 28, 2010, whenever asked.
For the purpose of the pricing, financial instruments (options)can be broadly be classified into two fundamental types. The
first type consists of those whose cash flows cannot be influenced by the holder of the instrument. These are referred
to as
European instruments (Options). TheEuropean financial instrument, the application of the
arbitrage pricing principle reduces the valuation of the instrument to the computation of an
expectation over the space of the underlying factors that determine the instrument's price.
The second type includes those whose cash flows can be influenced by the holder of the instrument. These are referred
to as
American instruments (Option). For an American instrument, application of the
arbitrage
pricing principle reduces the pricing problem to the computation of the
maximum, over all exercise
strategies, of an expectation over the space of the underlying factors that determined the instrument's price.
If the optimal exercise strategy were known, the pricing of an American instrument would ne no different than the pricing of a
European instrument. Because the optimal exercise strategy is not known in advance, the analytic pricing of American-style
instruments is far more difficult than that of European ones.
An option on future is an option that has a future contract as its underlying asset, in contract with options on physical
assets. The structure of an options on future is similar to its counterpart on the physical side and settlement of an option on
futures is not physical handling of the asset is required. A future option is the right but not the obligation, to enter
into a future contract at a certain future price by a certain date. Specifically, a
call future option is the right to enter
into a long future contract at a certain price, a
put future option is the right to enter into a short future contract at a
certain price.
Example: - An investor buys a July call future option contract o gold. The contract size is 100 ounce. The
strike price is 300. The investor exercises when the July gold future price 340recent settlement price is 338. The investor
receive a long futures contract plus a cash amount equal to (338-300)X100=3800. The investor decides to closed out
the long futures position immediately for a gain of $(340-338)X100=200. The total payoff from the decision to
exercise is 4000.
A forward contract on interest rate is called
forward rate agreement and it is an
OTC
version of interest rate future. In other words, a contract between bank and depositor/borrower in which Bank guarantees to
depositor/borrower a fixed rate of interest for a term. The depositor/borrower can lock in on future interest rate. In this
contract bank need not necessarily be a lender in the transaction.
A swap is a contract between two or more parties to exchange sequences of cash flows over a period in the future. These
parties are called counter parties. If the cash flows are pegged to the value of debt instruments is called an
interest rate swap. In case of foreign currency, it is called
currency swap.
In an interest rate swap, a party agrees to pay the other party interest at a fixed rate on a notional principal for a number
of years. In return, it receives interest at a floating rate on the same notional principal for the same period of time. An
interest rate swap can be used to transform a floating-rate loan into a fixed-rate loan or vice versa. It can also be used
to transform a floating-rate investment to a fixed-rate investment, or vice versa.
Example: - Consider a three year swap initiated on March 1, 2007 between, SBI and BHEL. Let SBI agrees to pay
to BHEL an interest rate 6.2\%per annum on a notional principal of Rs. 100 Cr. and in return BHEL agrees to pay SBI the six
month LIBOR rate on the same notional principal.
In a currency swap, one party agrees to pay interest on a principal amount in one currency. In returns, it receives
interest on a principal amount in another currency. A currency swap can be used to transform a loan in one currency into a
loan in another currency. It can also be used to transform a investment dominated in one currency into an investment
denominated in another currency.
Example: - Consider a five year currency swap agreement between VSNL and Indian Overseas Bank entered into on
March5, 2007. Indian Overseas Bank agrees to pay to VSNL \$15 million at rate of 6\% annum and in return VSNL agrees to pay
Indian Overseas Bank Rs.720 Cr. an interest rate 5.9\% annum.
Example :- Swaps is that a party agree to pay of Rs 1 billion to a second party annually for three year's and
other party is agree to pay the first party a floating rate of interest on the same notional principal, annually for three
years.
While, principal amount is not usually exchanged in an interest rate swap. In a currency swap principal amount is usually
exchanged at both the beginning and the end of the life of swap. For a party paying interest in the foreign currency, the
foreign principal is received, and the domestic principal is paid at the beginning of the life of the swap. At the end of
the life of the swap, the foreign principal is paid and the domestic principal is received. In Swap, counter parties are
able to negotiable terms and conditions based on their needs due to this flexibility swaps are growing rapidly but swap
market also suffers from counter party risk and liquid constraint like forward market.