Forwards and Futures Flashcards
What is a forward contract
A forward contract is an agreement to buy/sell a specified quantity of a given asset (underlying) at a known future date (delivery date) at a price determined today (delivery or forward price). The party that agrees to buy the underlying assumes a long position, while the party that agrees to sell the underlying assumes a short position.
Let S_T be the spot price of the asset at maturity and K be the delivery price, the payoff is then given:
The payoff of a long position is: X=S_T-K
The payoff of a short position is: X=K-S_T
It is customary to set up the contract, such that its initial value is zero. A forward contract is traded in the over-the-counter market and can be used to hedge foreign currency risk or Air-lines hedge fuel prices; changes in fuel price lead to large variations in profits if Airline does not hedge.
What is a future contract?
A futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future for a certain price. Unlike forward contracts, future contracts are normally traded on an exchange. The exchange specifies certain standardised features of the contract. It will also provide a mechanism that gives the two parties guarantee that the contract will be hon-oured.
WHat are options?
Options are traded both on exchanges and in the OTC market. The price in the contract is the exercise price or strike price, while the date in the contract is the expiration date or maturity.
A call option on an asset S gives the holder (of a long position) the right, but not the obligation, to buy the asset before a future date T for a predetermined price K.
A put option on an asset S gives the holder (of a long position) the right, but not the obligation, to sell the asset before a future date T for a predetermined price K.
What is a Swap?
A swap is an agreement between two parties A and B to exchange cashflows in the future. There are prespecified dates for when the cashflows are to be exchanged. Common cashflows are floating (variable) interest or the return on a stock (or an index) is exchanged for a fixed in-terest rate. Contracts are usually set up such that its initial value is zero.
Forward vs Option contracts
Forward contracts neutralise risk by fixing the price paid or received for the underlying asset. Option contracts provide insurance and can protect investors against adverse price movements in the future while still allowing them to benefit from favourable price movements.
Mechanics of future markets - Delivery
In the case of a commodity, taking delivery usually means accepting a warehouse receipt in re-turn for immediate payment. Some financial futures are settled in cash because it is inconven-ient to deliver the underlying asset. The final settlement price is the spot price of the underly-ing asset at either the open or close of trading that day. There are 3 critical days for a futures contract:
(1) First notice day: The first day on which a notice of intention to make delivery can be sub-mitted
(2) Last notice day: The last such day
(3) Last trading day: Is generally a few days before the last notice day.
Most futures do not lead to delivery, as traders close out their positions prior to the delivery period. To avoid having to take delivery, a long investor should close out prior to the first no-tice day.
Settlement Price, Trading Volume, Open Interest
The settlement price is the price used for calculating daily gains and losses and margin re-quirements. It is calculated as the price at which the contract traded immediately before the end of a day. The trading volume is the number of contracts traded in a day. Open interest is the number of contracts outstanding, i.e., the number of long (short) positions.
Convergence of futures price to spot price
As the delivery period for a futures approach, the futures price converges to the spot price of the underlying. When the delivery period is reached, the futures price equals the spot price. If the futures price was to be above the spot price during the delivery period, traders have an arbitrage opportunity. As this is exploited, the futures price will fall. If the futures price was below, companies interested in acquiring the asset will find it attractive to enter a long futures contract and then wait for delivery to be made. This will make the futures price rise.
Margin accounts
Margin accounts help the exchange organise trading to avoid contract defaults by ensuring funds are available to pay traders when they make a profit. Minimum margin levels are deter-mined by the variability of the price of the underlying. The higher the variability, the higher the margin level. Margin requirements also depend on the objectives on the trader and the risk of defaults. Most brokers pay investors interest on the balance in a margin account. To satisfy the initial margin requirements, but not subsequent margin calls, an investor can also deposit securities with the broker.
Margin accounts - Daily Settlements
The broker will require an investor to deposit funds in a margin account. When the contract is entered the amount deposited is the initial margin. At the end of each trading day, the margin account is adjusted to reflect the investor’s gain or loss, which is known as daily settlement (or marking-to-market). This is opposed to a forward contract that is settled at the end of its life. If there is an increase in futures price, brokers for parties with short positions pay money to the exchange clearing house and brokers for parties with long positions receive money, and vice versa.
The investor is entitled to withdraw any balance more than the initial margin. To ensure the margin never becomes negative, a maintenance balance (lower than the initial margin) is set. If the balance in the margin account falls below this, the investor receives a margin call and is expected to top up the margin account to the initial margin. The extra funds deposited are known as variation margin.
Investment vs. Consumption Asset
This distinction impacts the pricing of derivatives. While it is “easy” to replicate monetary pay-offs, it is generally not possible to replicate utility.
An investment asset does not provide utility beyond monetary payoffs, e.g., stocks, bonds, gold.
A consumption asset does provide utility beyond monetary payoffs, e.g., copper, crude oil, corn.
Assumptions Derivatives
(1) No arbitrage: The minimal assumption regarding market rationality. Implies that market par-ticipants take advantage of arbitrage opportunities as they occur, thus they disappear quick-ly.
(2) No transaction costs or short-sale restrictions: There are many transaction costs associated with trading such as bid-ask spreads on both forward and the underlying, brokerage commis-sions, and differential borrowing and lending rates. Usually we assume they do not exist
(3) Same borrowing and lending rate: The same risk-free rate for all market participants.
(4) No default risk: If the contract has positive value and your counterparty defaults, you lose money, which implies that counterparty credit risk may affect the forward price. This can be mitigated with either posting of collateral or via netting.
(5) No taxes: If market participants are subject to the same tax rate on all net trading profits, taxes do not matter for the forward price
Cost of Carry
The relationship between futures and spot prices can be summarised as the cost of carry measuring the storage cost plus the interest paid to finance the asset less the income earned on the asset.
For a non-dividend paying stock, the cost of carry is r; for a stock index it is r-q; for a currency it is r-r_f; for a commodity with income at rate q and requiring storage at rate u, it is r-q+u.
Define the cost of carry as c. For an investment asset, the futures price is F_0=S_0 e^cT
For a consumption asset it is F_0=S_0 e^(c-y)T
Forward vs. Future Price
When interest rates are certain, the futures price equals the forward price. This is also the case if interest rates are uncorrelated with the futures price.
When interest rates are unpredictable (real world) forward and futures prices are in theory no longer the same. When the price of the underlying asset S is strongly positively correlated with interest rates, futures prices will tend to be higher than forward prices. When S is strongly negatively correlated with interest rates, forward prices will tend to be higher than futures prices.
Intuition: The buyer of futures receives cash when futures price goes up, which she would like to invest. Interest rate turns out to be high when she wants to invest. This positive cor-relation between cash flow and the interest rate makes the futures more attractive than the forward.
Empirically, for most futures (where underlying is not a fixed-income asset), correlation be-tween futures price and interest rates are small. Traders prices futures as if they were forwards. We can therefore use all the pricing insights from forwards.
What are two derivative pricing cases?
Main idea: replicate payoffs of the derivative using spot markets: price of derivative contract must equal to the cost of replicating strategy.
Two cases:
(1) Static (model free) replicating strategy: forwards, futures, plain vanilla swaps
(2) Dynamic (model dependent) replicating strategy: options, exotics, etc.
