Derivatives

DERIVATIVE SECURITY – is a financial instrument whose value depends on the value of one
or more underlying assets. Derivative contracts can be stock derivatives, interest derivatives,
commodity derivatives (e.g. a derivative contract on gold depends on the price of gold), etc.

Exchange-traded derivatives – derivatives that are standardized (fixed) and traded
on an exchange (FUTURES)

Over-the-counter (OTC) derivatives – derivatives that are customized (tailor-made)
as per the needs of the participating parties who negotiate the terms of the contract
(FORWARD)


THE 3 GENERAL TYPES OF DERIVATIVES:

1) FORWARD – is an agreement to buy/sell the underlying asset at a certain future
date for a certain price, and traded over-the-counter. It comes in non-standardized
form with customizable contract size (e.g. number of barrels of oils is negotiable),
expiry date and price (as per the needs of the users). The details of the asset and the
price to be paid at the forward contract expiration date are set at time 0, so the
price of the forward contract becomes fixed over the life of the contract! Market
participants take a position in forward contracts because the future (spot) price or
interest rate on the asset is uncertain. Such a contract lets the market participants
hedge the risk that future spot prices of an asset will move against them by
guaranteeing a future price for the asset today.

2) FUTURE – is similar to forward but is traded on an exchange (e.g. CBOT). It comes in
standardized form with fixed expiry date, contract size and price. But, the price of
the future contract changes daily as the market value of the underlying asset
fluctuates. One difference between forwards and futures is that forward contacts
are bilateral (counterparty) contracts subject to counterparty default risk, but the
default risk on futures is significantly reduced by the futures exchange guaranteeing
to indemnify (хохирлыг барагдуулах) counterparties against credit or default risk.
Another difference relates to the contract’s price, which in a forward contract is
fixed over the life of the contract, whereas a futures contract is marked to market
daily. This means that the contract’s price is adjusted each day as the price of the
underlying asset changes and as the contract approaches expiration. Therefore,
actual daily cash settlements occur between the buyer and seller in response to
these price changes. This trade is monitored by a clearing house, who keeps track of
and guarantees the transactions on the exchange, so that the traders do not have to
worry about the creditworthiness of the people they are trading with. The clearing
house takes care of credit risk by requiring each of the 2 traders to deposit funds
(known as margin) to ensure that they will live up to their obligations.


Long position – buyer of the underlying asset
Short position – seller or writer of the underlying asset



Forward/Futures price – is the price fixed today




1

, Spot/Cash market – is a public financial market in which spot assets are traded for
immediate delivery.
Forward/Futures market – is a public financial market for forward and futures contracts in
which underlying spot assets are traded for deferred delivery.


FUTURES CONTRACTS: MARGINS, “MARKING TO MARKET” AND PROFIT & LOSS (P&L)

The P&L in a FORWARD contract is realized entirely at expiry, in a FUTURES contract this is
realized on a daily basis though the “MARKING TO MARKET” mechanism. In other words, for
the FORWARD contract no money changes hands until the contract expires, whereas for the
FUTURES contract money changes hand daily according to the movements in the futures
price.

Margin/Initial margin – a security deposit, which must be posted when entering the
contract
Maintenance margin – the minimum acceptable balance in the margin account
Margin call – if the balance of the account falls below the maintenance level, the exchange
makes a margin call upon the individual who must then restore the account to the level of
the initial margin before the start of trading the following day
Variation margin – the extra funds added to deposit to restore to the initial margin
CONTRACT VALUE = POINT VALUE * FUTURES PRICE

LONG POSITION = FT – F0
SHORT POSITION = F0 – FT


COST-OF-CARRY relationship for FUTURES price

COST-OF-CARRY – is the cost of ‘carrying’ (taking) a certain position. E.g. the costs related to
buying the spot asset and holding it up to time T. Such as:
FINANCE COSTS - such a cost would be the interest rate that has to be paid to the
bank at time T for borrowing money today to finance the immediate purchase of the
asset.
The amount owed to the bank at time T = S 0 * erT
If we ignore the storage costs, F0 = S0 * erT
COST-OF-CARRY relationship is based on the following assumptions:
- no market frictions, e.g. no transaction costs (brokerage fees, delivery fees), no
taxes, no restrictions
- no credit risk: everyone is guaranteed to satisfy his/her obligations, hence lending
and borrowing rates are equal
- competitive markets: market operators are price takers (individual investors cannot
affect the market price)
- rational agents: market participants prefer more to less
- arbitrage opportunities are eliminated!!!

If the COST-OF-CARRY relationship (F0 = S0 * erT) does not hold, then:
1) F0 > S0 * erT, we say that ‘futures are rich to cash’: SELL FUTURES, BUY SPOT
ARBITRAGE profit: F0 – S0 * erT > 0
2) F0 < S0 * erT, we say that ‘futures are cheap to cash’: BUY FUTURES, SELL SPOT
ARBITRAGE profit: S0 * erT – F0 > 0



2