Derivatives are financial instruments whose value is based on an underlying asset. The three main types of participants in derivatives markets are hedgers who use derivatives to reduce risk, speculators who try to profit from price movements, and arbitrageurs who take advantage of temporary price differences. Common derivatives include forward contracts which require delivery of the asset, and futures contracts which are exchange-traded and involve daily settlement. Options provide the right but not obligation to buy or sell the underlying asset and have non-linear payoffs. Key models for pricing derivatives include the cost-of-carry model and Black-Scholes options pricing formula.

1. DERIVATIVES
PRESENTED BY
SIMRAN KAUR

2. DERIVATIVES
O Derivatives are instruments which include
(a) security derived from a debt
instrument, share, loan, risk instrument or
contract for differences or any other form
of security and (b) a contract that derives
its value from the price/index of prices of
underlying securities
O Variants of derivatives are Forwards,
Futures and Options

3. 3 CATEGORIES OF
PARTICIPANTS
O Hedgers
O Speculators
O Arbitrageurs

4. HEDGERS
O Hedgers face risk associated with the
price of an asset
O They use futures or options markets to
reduce/eliminate this risk

5. SPECULATORS
O Speculators wish to bet on future
movements in the price of an asset
O Futures 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

6. ARBITRAGEURS
O Arbitrageurs are in business to take
advantage of a discrepancy between
prices in two different markets
O If, for example, they see the futures price
of an asset getting out of line with the
cash price, they will take offsetting
positions in the two markets to lock-in a
profit

7. ECONOMIC FUNCTIONS OF
DERIVATIVES
O They help in the discovery of the future as
well as current prices
O They transfer risk to those who have an
appetite for them
O The underlying cash markets witness high
trading volumes
O Speculative trades shift to a more
controlled environment
O They help increase savings and
investment in the long run

8. FORWARD CONTRACT
O Forward contract is an agreement to
buy(long position) or sell(short position)
an asset/security on a specified date for a
specified price; settlement happens at the
end of the period
O Other contract details like delivery date,
price and quantity are negotiated
bilaterally by the parties to the contract

9. FEATURES OF FORWARD
CONTRACT
O They are bilateral contracts and, hence,
exposed to counterparty risk
O Each contract is customer designed, and,
hence, is unique in terms of contract size,
expiration date and asset type and quality
O The contract price is generally not
available in public domain
O On the expiration date, the contract has to
be settled by delivery of the asset

10. LIMITATIONS OF FORWARD
CONTRACT
O Liquidity
O Counterparty risk (possibility of default by
any one party to the transaction)

11. FUTURE
CONTRACTS/FUTURES
O Future contracts/Futures is an agreement
between two parties to buy/sell an
asset/security at a certain time in future; it
follows daily settlement
O Futures are standardized and stock
exchange traded
O It may be offset prior to maturity by
entering into equal and opposite
transaction

12. STANDARDIZED ITEMS IN
FUTURES
O Quantity of the underlying
O Quality of the underlying
O The date/month of delivery
O The units of price quotation and minimum
price change
O Location of settlement

13. TERMINOLOGY IN FUTURES
O SPOT PRICE: The price at which an
instrument/assets trade in the spot market
O FUTURE PRICE: The price at which the
futures contract trade in the future market
O CONTRACT CYCLE: The period over
which a contract trades
O EXPIRY DATE: The last day, specified in
the futures contract, on which the contract
will be traded, at the end of which it will
cease to exist

14. TERMINOLOGY IN FUTURES
O CONTRACT SIZE: The amount of asset
that has to be delivered under one
contract
O BASIS: The futures price minus the spot
price
O COST OF CARRY: The relationship
between futures price and spot prices can
be summarized in terms of the 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

15. TERMINOLOGY IN FUTURES
O INITIAL MARGIN: The amount that must
be deposited in the margin account at the
time a futures contract is first entered into
O MARKING TO MARKET: In the 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

16. TERMINOLOGY IN FUTURES
O 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

17. PAYOFF FOR THE FUTURES
O Payoffs is the likely profit/loss that should
accrue to the market participant with
change in the price of the underlying asset
O Futures contracts have linear payoffs
O Linear payoffs implies losses as well as
profits for both the buyer and seller of
futures are unlimited

18. PRICING FUTURES
O The Cost-of-Carry Model
O Pricing equity index futures
O Pricing stock futures

19. COST OF CARRY MODEL
O Cost of carry model explains the dynamics
of pricing that constitute the estimation of
the fair value of futures
O According to this model, using discrete
compounding, where interest rates are
compounded at discrete intervals, the
price of the contract is defined as
F = S + C

20. COST OF CARRY MODEL
O Other formulae for the model include
F = S(1 + 𝑟) 𝑇
F = S𝑒 𝑟𝑇

21. TERMS IN COST OF CARRY
MODEL
O F = future price
O S = spot price
O C = holding costs or carry posts
O r = cost of financing
O T = time till expiration
O e = 2.71828

22. PRICING EQUITY INDEX
FUTURES
O Index futures is a future contract that
gives the owner the rights/obligations to
buy/sell the portfolio of stocks
characterized by the index
O The differences between commodity and
equity index features are : (i) There are no
costs of storage involved in holding equity
and (ii) equity comes with a dividend
stream

23. PRICING EQUITY INDEX
FUTURES
O GIVEN EXPECTED DIVIDEND AMOUNT:
The pricing of index futures is also based
on the cost-of-carry model, where the
carrying cost is the cost of financing the
purchase of the portfolio underlying the
index, minus the present value of
dividends obtained from the stocks in the
index portfolio

24. PRICING EQUITY INDEX
FUTURES
O GIVEN EXPECTED DIVIDEND YIELD: If
the dividend flow throughout the year is
generally uniform, it is useful to calculate
the annual dividend yield
F = S(1 + 𝑟 − 𝑞) 𝑇
Where F = futures price, S = spot price, r =
cost of financing, q = expected dividend
yield, T = holding period

25. PRICING STOCK FUTURES
O Stock futures is a future contract that
gives its owner the right/obligation to
buy/sell the stocks(shares)
O The main difference between commodity
and stock futures are that (i) There are no
costs of storage involved in holding stock
and (ii) Stocks come with a dividend
stream

26. PRICING STOCK FUTURES
WHEN NO DIVIDEND EXPECTED: The
pricing of stock futures is based on the cost-
of-carry model, where the carrying cost is
the cost of financing the purchase of the
stock, minus the present value of dividends
obtained from the stock. If no dividends are
expected during the life of the contract,
pricing futures on that stock is very simple. It
simply multiplies the spot price by the cost
of carry

27. PRICING STOCK FUTURES
WHEN DIVIDENDS ARE EXPECTED:
When dividends are expected during the life
of the futures contract, pricing involves
reducing the cost of carry to the extent of
the dividends. The net carrying cost is the
cost of financing the purchase of the stock,
minus the present value of dividends
obtained from the stock

28. OPTIONS/OPTIONS
CONTRACT
O Option/option contract is a contract that
gives the holder the right but not the
obligation to buy/sell an asset/security
O The purchase of option requires an up
front payment

29. TERMINOLOGY IN OPTION
O STOCK OPTIONS: Options on individual
stocks
O BUYER OF AN OPTION: One who by
paying the option premium buys the right
but not the obligation to exercise his
option on the seller/writer
O WRITER OF AN OPTION: One who
receives the option premium and is
thereby obliged to sell/buy the asset if the
buyer exercises the option on him

30. TERMINOLOGY IN OPTION
O CALL OPTION: It gives the holder the
right but not the obligation to buy an asset
by a certain date for a certain price
O PUT OPTION: It gives the holder the right
but not the obligation to sell an asset by a
certain date for a certain price
O OPTION PRICE/PREMIUM: Price that the
option buyer pays to the option seller

31. TERMINOLOGY IN OPTION
O EXPIRATION DATE: The date specified in
the options contract is known as the
expiration date, the exercise date, the
strike date or maturity
O STRIKE PRICE: The price specified in the
options contract
O IN-THE-MONEY OPTION: Option that
would lead to a positive cashflow to the
holder if it were exercised immediately

32. TERMINOLOGY IN OPTION
O AT-THE-MONEY OPTION: Option that
would lead to zero cashflow if it were
exercised immediately
O OUT-OF-THE-MONEY OPTION: Option
that would lead to a negative cashflow if it
were exercised immediately
O INTRINSIC VALUE OF AN OPTION: The
amount of option in ITM(In-the-money
option)

33. TERMINOLOGY IN OPTION
O TIME VALUE OF AN OPTION: Difference
between its premium and its intrinsic value

34. OPTIONS PAYOFF
O The optionality characteristics of options
results in a non-linear payoff
O Non-linear payoff implies the losses for
the buyer of the option are limited but
profits are potentially unlimited; profits to
the writer of the option are limited to the
option premium but losses are potentially
unlimited
O Option premium is the price that the
option buyer pays to the option seller

35. BLACK-SCHOLES OPTION
PRICING
O Black and Scholes start by specifying a
simple and well known equation that
models the way in which stock prices
fluctuate
O Also called Geometric Brownian Motion
O It implies that stock returns will have a
lognormal distribution, meaning that the
logarithm of the stock’s return will follow
the normal (bell-shaped) distribution

36. BLACK-SCHOLES OPTION
PRICING
O The option’s price is determined by only
two variables that are allowed to change:
time and the underlying stock price
O The other factors, namely, volatility,
exercise price and risk free rate do affect
the option’s price but they are not allowed
to change

37. BLACK-SCHOLES OPTION
PRICING
Black-Scholes formulae for the prices of
European calls and puts on a non-dividend
paying stock are
C = SN(𝑑1) − 𝑋𝑒−𝑟𝑇N(𝑑2)
P = X𝑒−𝑟𝑇 𝑁 −𝑑2 − 𝑆𝑁 −𝑑1
where 𝑑1 =
ln
𝑆
𝑋
+ 𝑟+
𝜎2
2
𝑇
𝜎 𝑇
𝑑2 = 𝑑1 − 𝜎 𝑇

38. TERMS IN BLACK-SCHOLES
OPTION PRICING
O N() is cumulative normal distribution
O N(𝑑1) is called the delta of the option
O σ is a measure of volatility
O X is the exercise price
O S is the spot price
O T is the time to expiration measured in
years

39. FACTORS AFFECTING
OPTION PRICES
O STOCK PRICE: The payoff from a call
option will be the amount by which the
stock prices exceeds the strike price
O STRIKE PRICE: In the case of a call, as
the strike price increases, the stock price
has to make a larger upward move for the
option to go in-the-money
O TIME TO EXPIRATION: Both put and call
options become more valuable as the time
to expiration increases

40. FACTORS AFFECTING
OPTION PRICES
O VOLATILITY: The volatility of a stock price
is a measure of how uncertain we are
about future stock price movements
O RISK FREE INTEREST RATE: The affect
of the risk free interest rate is less clear
cut
O DIVIDENDS: They have the effect of
reducing the stock price on the ex-
dividend date. This has a negative affect
on the value of call options and a positive
effect on the value of put options

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