The document discusses pricing models for future contracts. It describes the expectancy model, which states that futures prices are expected future spot prices. It also describes the cost of carry model, where the price is the spot price plus the net cost of carry, which includes financing costs, storage costs, and convenience yield. The relationship between spot and futures prices depends on factors like costs of carry and interest rates. As the delivery date approaches, futures prices converge to the spot price to avoid arbitrage opportunities. However, inherent risks and uncertainties remain due to changing future variables.

1. General
Approach to
Future Pricing
Hedging Risk with Future Contracts

2. Content
Future Contracts and Its Market
Mechanics
Component of Future Contracts
Pricing of Future Contract
Expectancy Model
Cost of Carry Model
 Salient Features
 Concept of Carrying Cost
 Function and Component of Carrying Cost
 Other Factors influencing carrying cost
Relationship: Spot and Future Market
 Spot vs Futures Prices: An Overview
 Basis and Convergence
 Example: Gold Futures
Uncertainties: Inbuilt Residual Inherent Risk
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3. Future Contracts and Its Market Mechanics
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What Are Future Contracts?
Future contracts are standardized legal exchange trade derivative
(ETD) contract to buy or sell underlying asset at a certain time in
future at predetermined price. Due to its flexibility, it is widely
used in derivative market. It may be used for wide range of
underlying assets including commodities (Gold, Silver, Coal, Crude
Oil) and Currencies (often called currency futures). The key
purpose of using future contracts is to take a counter position
against any adverse impact in current transaction.
Market Mechanics:
Just like other markets, Future markets are driven by demand
and supply. If future demand is high in the market, the price
tends to be higher which makes the market more lucrative and
attract future seller to enter in to market which ultimately
correct situation. Future contract ingredients includes Underlying
Asset, Standardized Contract Size, Delivery Arrangement and
Delivery Month.

4. Components of Future Contracts
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Standardized Future Contracts have following specified
components:
• Asset
• Contract Size
• Delivery Arrangement (Exchange Regulated)
• Delivery Months
• Price Quotes
• Price Limits and Position Limits
Assets:
In General , It is broad range of standardized product traded in
numerous futures exchanges of the global financial markets. It
includes but not limited to Commodities, Stocks, and Currencies
Assets
Delivery Date
Contract Size
Price Quotes

5. Components of Future Contracts
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Assets
Delivery Date
Price Quotes
Contract Size:
Contract size refers to the quantity of underlying asset which is
supposed to be delivered in the future under one contract. In
General, Contract size depends on several component including User
class, underlying asset and future exchange regulation.
Delivery Date/Delivery Months:
In practical market, most of the user of future markets generally sell
prior to its delivery however, delivery of the future is a unique feature
of this contract. Further, Futures Exchange specify the precise period
during the month when delivery is made however, for many future
contract , delivery period is whole month.
Delivery Arrangement:
Arrangement of delivery is specified by the exchange because all of
the product do not carry same transportation cost.
Price Quotes and Price Limits:
Price Quotes and Price Limits are merely the decision of exchange.
Price limit refer to upper and lower lock of future in order to prevent
any speculative move and protect the interest of stakeholders.
Contract Size

6. Pricing of Future Contracts
Future Contract derived their value largely from the underlying asset or index.
Due to several component including volatility in underlying asset price, investor
risk-appetite and risk-return ratio, futures are priced on the basis of different
theoretical model.
Two famous model that are used to Price Future contracts are:
• Expectancy Model
• Cost of Carry Model

7. Pricing of Future Contracts
Expectancy Model:
In this model, it is argued that futures prices are actually expected spot price of an asset
in the future. The Key features of this model are :
 This theory gives more emphasis on the concept that future price and cash market
price are unrelated to each other.
 There is a bond between expected spot price and price of the future contract.
 In general, future contracts are settled at cash market price on the date of maturity.
At the date of expiration, future price and spot price are converged.
 Futures price provide market participant an indicative expected directional
movement of spot price in the future.

8. Pricing of Future Contracts
Expectancy Model:
 If such indicator provides rising effect in future market as compare to spot market,
such expectedly rising market called “Cotango”.
 There is a bond between expected spot price and price of the future contract.
 where indicators are showing decline in future market as compare to spot market
with respect to an asset, such market is known as “Backwardation market”.

9. Pricing of Future Contracts
Expectancy Model:
Formula:
F = S x (1+ Rf (X/365)
where,
F= Expected Future Price
S= Spot Price
Rf = Risk-Free rate
X=no of days to expiry
This model widely used by individual due to its simplicity and rationale.

10. Pricing of Future Contracts
Expectancy Model:
Example:
Assume ABC Corporation spot is trading at $2,280.5 with 7 more days to expiry. Actual Future
are being traded in the market at $2284. The Risk-Free Rate is 8.3528%. what should ABC’s
current month futures contract be priced at using Expectancy Model and “Spot-Future Parity”
Function?
Calculation:
Futures Price = Spot price * [1+ Rf*(x/365) – d]
Futures Price = 2280.5 * [1+8.3528 %( 7/365)] – 0=$2283
ABC is not expected to pay any dividend over the next 7 days, hence It is assumed dividend as 0.
Solving the above equation, the future price turns out to be $2283. This is called the ‘Fair value’
of futures .However, the actual futures price is $2284. The actual price at which the futures
contract trades is called the ‘Market Price’.

11. Pricing of Future Contracts
Cost of Carry Model:
Salient Features:
It is a bitter complex method in comparison to Expectancy model. The Key Features
of this models are as follows:
 This model advocates that imperfections in pricing between cash market and
future market is eliminated by arbitrage.
 The only difference that is residual impact after considering all imperfections is
due to a factor called “The Cost of Carry”.
 This model also assumed that future contract will be held till maturity.

12. Pricing of Future Contracts
Cost of Carry Model:
Concept of Carrying Cost:
“Carrying Cost” refers to the cost related to the carrying value of an investment. It
includes but not limited to:
 Financial cost including interest cost of bonds;
 Financial cost margin accounts
 Storage cost involved in holding a physical asset
 Opportunity cost of using own funds.

13. Pricing of Future Contracts
Cost of Carry Model:
Function and Component of Carrying Cost:
Considering assumption of removal of imperfection, a fair future price can be simplified as follows:
Fair Price = Spot Price + Net Cost of Carry
Net Cost of Carry = Cost of Financing – revenues + cost of Storage
On the Other Side , the function under cost of carry model can be written as
F = Se ^ ((r + s - c) x t)
Where
F = the future price of the commodity S = the spot price of the commodity
e = the base of natural logs
r = the risk-free interest rate
s = the storage cost, expressed as a percentage of the spot price
c = the convenience yield
t = time to delivery of the contract, expressed as a fraction of one year

14. Pricing of Future Contracts
Cost of Carry Model:
Function and Component of Carrying Cost:
Cost of Financing includes a finance raise buy such future. It is to be considered that it
really depends on cost of finance for each buyer.
Cost of Storage includes cost of physical inventory storage, insurance and any potential
losses from obsolescence and normal wear and tear.
Convenience Yield is a unique component of this function. It refers to the benefit or
premium associated with holding an underlying product rather than the associated
derivative security or contract. In real world, it is noted that convenience yield basically
described that commodity prices and storage levels are inversely correlated.

15. Pricing of Future Contracts
Cost of Carry Model:
Other Factors:
Although cost of carry contains significant impact over decision making related to future
pricing however, there are several factors of “Cost-of-Carry” that investor should accounted for
including:
Margin: Using margin can require interest payments, since a margin is essentially borrowing.
As such, interest borrowing costs would need to be subtracted from total returns
Short Selling: In short selling, an investor may want to account for foregone dividends as a
type of opportunity cost.
Other Borrowing: When making any type of investment with borrowed funds, the interest
payments on the loan can be considered a type of carrying cost that reduces total return.
Trading Commissions: Any trading costs involved with entering and exiting a position will
reduce the overall total return achieved.

16. Relationship: Spot and Future Market
Spot vs Futures Prices: An Overview
The spot price of a commodity is the local cash price for immediate delivery of the commodity
whereas futures price locks in the cost of a future delivery of the commodity.
The difference between the spot price and futures price in the market is called the basis. The
basis is the difference between the local spot price of a deliverable commodity and the price of
the futures contract for the earliest available date. "Local" is relevant here because futures
prices reflect global prices for any commodity and are therefore a benchmark for local prices.
In Simple Terms, futures prices and spot prices are different numbers because the market is
always forward-looking.
What cause the difference in a commodity's spot price and the future price at
any given time?
Basically, it is attributable to the cost of carry and interest rates.

17. Relationship: Spot and Future Market
Basis and Convergence
Convergence and Basis Risk is the crucial concept and underlying principal to understand the
relationship between Spot and Future Market relationship.
Convergence:
Convergence is the movement of the price of a futures contract toward the spot price of the
underlying cash commodity as the delivery date approaches. The Future Price and Spot Price
must converge at the date of expiration of contract otherwise, an arbitrage opportunity exists
and the possibility for a risk-free profit.
Convergence happens because the market will not allow the same commodity to trade at two
different prices at the same place at the same time. For example, you rarely see two Fuel
stations on the same road with two very different prices for gas at the pump. Car owners will
simply drive to the place with the lower price.

18. Relationship: Spot and Future Market
Basis and Convergence
As the delivery period for a futures contract is approached, the futures price converges
to the spot price of the underlying asset. When the delivery period is reached, the
futures price equals—or is very close to—the spot price.
Relationship between futures price and spot price as the delivery period is approached:
(a) Futures price above spot price;
(b) Futures price below spot price.

19. Relationship: Spot and Future Market
Basis and Convergence
Basis:
Basis is a crucial concept for portfolio managers and traders because this relationship between
cash and futures prices affects the value of the contracts used in hedging.
The basis is not necessarily accurate. There are typically gaps between spot and relative price
until the expiry of the nearest contract. Product quality also can vary, making basis an
imperfect indicator.
Further, the prices of commodities futures are not always higher than spot prices. Futures
prices take into account expectations of supply and demand and production levels, among
other factors.
Example: assume the spot price for crude oil is $50 per barrel and the futures price for crude
oil deliverable in two months' time is $54. The basis is $4, or $54 - $50.

20. Relationship: Spot and Future Market
Example: Gold Futures
Assume the spot price of gold is $1,200 per ounce and it costs $5 per ounce to store the gold
for six months. What is the price of six-month futures contract on gold, given a risk-free
interest rate of 0.25%,?
The Price of the Future is $1,206.51 which can be calculated as follows:
=(($1,200+$5)*e^(0.0025*0.5))
As per KITCO,
Current Gold Price is $1878.7/Ounce in NYSE whereas Gold Continuous Contract is $1882.6
reflecting future expectation of fall Gold Price.

21. Uncertainties: Inbuilt Residual Inherent Risk
Due to inclusion of several futuristic variable, Future markets have several
uncertainties which affect adversely key stake holders and market players of the
future markets.
It observed in S&P 500 and several other well renowned exchange of the world that
future price are highly affected and it anomalous behavioral pattern badly create a
financial impact to all the players including Hedger and Speculator.
Comprehensive survey and research have been done to understand such behavior
and mitigate such variation to an acceptable level but still there is a mile to go!
Conclusively, it can be said that the concept of perfect market in this practical world is
still theory.