UNIT 3

FINANCIAL DERIVATIVES

A forward contract is a customized contract

between two parties to buy or sell an asset at a
specified price on a future date. A forward
contract can be used for hedging or speculation,
although its non-standardized.
Here's a more detailed look at the key features:
1. Customization:
Forward contracts are highly customizable.
The terms, including the asset, quantity, price,
and delivery date, can be tailored to the specific
needs of the buyer and seller.
2. Over-the-Counter (OTC):
They are not traded on a centralized exchange.
This means the agreements are negotiated
directly between the two parties, offering more
flexibility but also potentially higher counterparty
risk.
3. Hedging:
Forward contracts are frequently used by
businesses to hedge against price fluctuations.
By agreeing to a fixed price in advance, they can
protect themselves from potential losses due to
adverse price movements.
4. No Margin Requirement:
Unlike futures contracts, which require margin
payments, forward contracts generally do not.
This makes them more flexible for participants
and can be beneficial for businesses that prefer
not to tie up capital.
5. Counterparty Risk:
Since forward contracts are private agreements,
there is a higher risk that one party might default.
This is because there's no central clearinghouse
to guarantee performance.
6. Settlement:
Forward contracts can be settled either through
physical delivery of the asset or by a cash
settlement.
The terms of the settlement are determined in the
contract.
7. Flexibility:
The terms of the contract can be adjusted to the
preferences of the contracting parties, including
payment terms, delivery location, and other
variables.
8. No Daily Settlement:
Unlike futures contracts, forward contracts are
not marked to market daily.
This means there is no daily fluctuation in the
value of the contract until the settlement date.
Here's a breakdown of the common types of
forward contracts :
Based on Underlying Asset:
Currency Forward Contracts:
Used to hedge against exchange rate fluctuations
when dealing with international trade or
investment.
Commodity Forward Contracts:
Used by producers and consumers of
commodities like oil, gold, or agricultural
products to protect against price volatility.
Interest Rate Forward Contracts:
Help companies lock in future interest rates,
providing protection against rising borrowing
costs.
Equity Forward Contracts:
Allow investors to hedge or speculate on stock
prices, enabling them to lock in a sale or
purchase price.
Based on Settlement Method:
Fixed Forward Contracts: Settlement occurs on a
specific future date.
Open Forward Contracts: Settlement can happen
at any time up to the maturity date.
Window Forward Contracts: Settlement can take
place within a defined period before the maturity
date.
Other Types:
Non-Deliverable Forwards (NDFs):
These contracts settle in cash, without the
physical transfer of the underlying asset.
Flexible Forwards:
Allow for flexibility in the settlement date, often
within a window of time.
Long-Dated Forwards:
Contracts with longer maturities, often beyond
one year.
Closed Outright Forwards:
Contracts where the exchange rate is agreed
upon at the time of the transaction, based on the
spot rate plus a premium.

A futures contract is a legally binding agreement

to buy or sell a specific asset (like a commodity,
stock, or currency) at a predetermined price on a
specific date in the future. These contracts are
standardized and traded on exchanges, providing
a way to hedge against price fluctuations or
speculate on future price movements.
Here's a more detailed breakdown of the
features:
Standardization:
Futures contracts have standardized terms like
contract size, quality of the underlying asset, and
delivery date, making them easier to trade and
more liquid than forward contracts.
Exchange-Traded:
They are traded on regulated exchanges like CME
Group, Intercontinental Exchange, or BSE in
India, ensuring transparency and reducing
counterparty risk.
Daily Settlement (Mark-to-Market):
Daily gains or losses are settled based on the
contract's current market value, reducing the risk
of significant losses accumulating over time.
Margin Requirements:
Traders are required to deposit margin, which
serves as collateral to ensure they can meet their
settlement obligations.
Clearinghouse Involvement:
A central clearinghouse acts as an intermediary
between buyers and sellers, guaranteeing the
performance of contracts and mitigating
counterparty risk.
Leverage:
Futures contracts allow traders to control a large
amount of an asset with a relatively small amount
of capital, providing leverage.
Expiry Date:
Every futures contract has a specific expiration
date by which the contract must be settled or
closed.
Versatility:
Futures contracts can be based on a wide range
of assets, including stocks, commodities,
currencies, and indices.
Hedging and Speculation:
Futures can be used by producers/hedgers to
mitigate price fluctuations or by speculators to
bet on price movements.

Futures contracts are broadly categorized into

commodity, currency, interest rate, and stock
market index futures. These contracts are
agreements to buy or sell an asset at a
predetermined price on a specific date in the
future.
Here's a more detailed breakdown:
Commodity Futures:
These contracts are based on physical
commodities like agricultural products (wheat,
corn), metals (gold, silver), and energy (oil,
natural gas).
Currency Futures:
These contracts involve the exchange of one
currency for another at a predetermined
exchange rate on a specific future date.
Interest Rate Futures:
These contracts are tied to the value of debt
instruments like bonds or Treasury bills.
Stock Market Index Futures:
These contracts are based on the value of a stock
market index, such as the Nifty 50 or the S&P 500.
Stock Futures:
These contracts allow traders to buy or sell
individual shares of a company at a
predetermined price on a future date.
 Forward Contract Futures Contract

Standardization Standardization
Customized, non-standardized Standardized, with fixed terms.
agreements.
Trading Venue
Trading Venue Traded on exchanges.
Over-the-counter (OTC),
privately negotiated. Settlement
Daily mark-to-market, with
Settlement gains and losses settled daily.
Settlement occurs at the end
of the contract period. Regulation
Heavily regulated by bodies
Regulation like SEBI.
Minimal regulation.
Transparency
Transparency More transparent, with publicly
Less transparent, as prices are available prices on exchanges.
privately agreed upon.

Margin Margin
Typically no margin Margin accounts are required
requirements. to cover potential losses.
A forward price is the predetermined price agreed
upon by a buyer and seller in a forward contract,
specifying the future delivery of an asset. This
price is set at the beginning of the contract, with
the intention of it being zero in initial value.
However, the forward price can fluctuate as the
market price of the underlying asset changes,
potentially leading to a positive or negative value
for the contract.
Here's a more detailed breakdown:
Definition:
The forward price is the price at which an asset,
commodity, or currency will be bought or sold at
a future date, as agreed upon in a forward
contract.
Contract Value:
Initially, when the forward contract is
established, the forward price is set so that the
contract's value is zero. This is because the price
is a pre-determined agreement.
Fluctuations:
As the market price of the underlying asset
changes, the forward price also fluctuates. This
can cause the value of the forward contract to
move up or down, potentially leading to gains or
losses for the buyer and seller.
Relationship to Spot Price:
The forward price is influenced by the current
spot price of the underlying asset, as well as
factors like interest rates, storage costs, and
dividends.
• The formula to calculate the forward price
typically involves:
• Spot price (S): The current price of the asset.
• Interest rate (r): The risk-free rate or the rate of
return available in the market.
• Time to maturity (T): The length of time until the
contract expires.
• Cost of carry: This includes storage costs for
commodities or dividends for stocks (if
applicable).
For a simple asset, the forward price F can be
calculated using the formula:
F= S×(1+r) T
Where:
• F is the forward price.
• S is the spot price.
• r is the risk-free interest rate or carrying cost.
• Tis the time to maturity, usually expressed in
years.
For commodities or more complex assets, the
formula may need to incorporate factors like
storage costs, dividends, or convenience yield
(for commodities).
Example: Forward Price of a Stock
Let's say we want to calculate the forward price
for a stock. Here are
the details:
• Spot price (S) = $100 (current price of the
stock),
• Risk-free interest rate (r) = 5% per year (or 0.05),
• Time to maturity (T) = 1 year (since the forward
contract expires in
one year).
• Now we can plug these values into the formula:
F=100×(1+0.05)1
=100×1.05
=105
So, the forward price of the stock for a 1-year
forward contract
would be $105.
• This means that the buyer and seller of the
forward contract have
agreed to buy and sell the stock at $105 one year
from now, regardless of what the spot price is at
that time.

Example: Forward Price for a Commodity

(with Storage Costs)
• In the case of a commodity, additional factors
like storage costs, dividends, or convenience
yields can affect the forward price. Let's go
through an example where we also have
storage costs.
• Spot price (S) = $50 per barrel of oil,
• Risk-free interest rate (r) = 3% per year (0.03),
• Time to maturity (T) = 1 year,
• Storage costs = $2 per barrel for 1 year.
The formula for the forward price becomes:
• F= (S + Storage costs) ×(1+r) T
= (50+2) × (1+0.03)1
=52×1.03
=53.56F
So, the forward price for the oil, considering
storage costs, would be $53.56.
• This forward price is slightly higher than the
spot price due to the cost of storing the oil for
a year.
A Forward Rate Agreement (FRA) is a financial
derivative contract where two parties agree to
exchange fixed and floating interest rate
payments for a predetermined future period. It
essentially allows parties to lock in a specific
interest rate for a future borrowing or lending
transaction, providing protection against interest
rate fluctuations.
Here's a more detailed breakdown:
Purpose:
FRAs are primarily used to hedge against interest
rate risk, meaning they help mitigate the potential
impact of rising or falling interest rates on future
borrowing or lending costs.
Mechanism:
In an FRA, one party agrees to pay a fixed interest
rate on a notional principal amount, while the
other party agrees to pay a floating interest rate
based on a reference rate like LIBOR.
Benefits:
Hedging: FRAs allow businesses to lock in a fixed
interest rate for a future borrowing, reducing the
risk of rising rates.
Speculation: They can also be used by investors
to speculate on future interest rate movements.
Matching Assets and Liabilities: Institutions can
use FRAs to match their future borrowing or
lending rate with their assets or liabilities.
Example:
Imagine a company plans to borrow money in six
months, but is worried about potential interest
rate increases. They could enter into an FRA to fix
the interest rate for that borrowing period,
protecting them against higher borrowing costs if
rates rise.
OTC contracts:
FRAs are over-the-counter (OTC) contracts,
meaning they are negotiated directly between
two parties and not traded on a centralized
exchange.
Key terms:
Notional principal: The agreed-upon amount of
money that the interest rate applies to.
Forward rate: The fixed interest rate that is agreed
upon for the future period.
Settlement date: The date when the FRA expires
and any net payments are made.
VALUATION OF FORWARD CONTRACT :-
The value of a forward contract is determined by
the difference between the current spot price of
the underlying asset and the present value of the
forward price. At initiation, the value of a forward
contract is zero because neither party pays the
other any money.
Initial Value:
A forward contract is a contract between two
parties to buy or sell an asset at a future date for
a predetermined price.
At the time the contract is initiated, the value is
zero because no exchange of money occurs.
Value During the Life of the Contract:
The value of a forward contract changes
throughout its life as market conditions
(specifically the spot price of the underlying
asset) fluctuate.
The formula to calculate the value V(t) of a
forward contract at time t is:
V(t)=S(t)−F0×e−r(T−t)

• Where:
• S(t) = Spot price of the underlying asset at time
t,
• F0 = Initial forward price agreed at the time the
contract was entered into,
• r = Risk-free interest rate (continuously
compounded),
• T = Time to maturity (expiry date) of the forward
contract,
• t = Current time (the time you are calculating
the value for),
• e−r(T−t) = Discount factor, accounting for the
time value of money.
Key Points in Forward Contract Valuation:
• When S(t)>F0: The holder of a long forward
contract has a gain (the contract is in-the-
money).
• When S(t)<F0: The holder of a long forward
contract has a loss (the contract is out-of-the-
money).
Valuation of Futures Contract
• The valuation of a futures contract is generally
similar to forward contracts, except that
futures are marked-to-market daily. This
means that the value changes every day based
on the difference between the future price
and the spot price.
• Formula for Valuation of Futures Contract:
Vt=(Ft−St) × e
• Where:
• Vt= Value of the futures contract at time t.
• Ft= Futures price at time t.
• St = Spot price of the underlying asset at time t.
• r = Risk-free interest rate.
• T = Time to maturity.
• t = Current time (in years)
• Futures contracts are settled daily, so the value
changes with fluctuations in the spot price of the
underlying asset. Futures prices are influenced
by the same factors as forward contracts (spot
prices, interest rates, and dividends), but since
futures are traded on exchanges, they are also
influenced by market liquidity and investor
sentiment.