2 - Pricing of futures and forwards

Question 1

What are the two fundamental assumptions when seeking to price futures and forwards?

Answer 1

1. No arbitrage
2. Replication

Question 2

No arbitrage meaning ?

Answer 2

Markets are efficient and arbitrage cannot persist

Question 3

Replication meaning?

Answer 3

The payoffs of the derivative product (in this
case the future or the forward) are
determined by price movements in the
underlying assets.
The derivative can be “replicated” by using
the underlying assets

Question 4

Time notation:
0
T

Answer 4

0 - current date
T - Maturity Date of the Forward (yrs)

Question 5

Price notation:
S0
ST
F

Answer 5

S0 - Current price of the underlying asset
ST - The price of the underlying asset at time = T
Is the maturity price of the forward
F - Delivery price of a forward

Question 6

PV(F)=PV(S)

Answer 6

PV(F) - Forward strategy
This is, at time = 0, the present value of the single payment under the futures contract upon delivery of the asset

PV(S) - Replication strategy
Involves:
1. Holding benefits e.g. dividends or coupons
2. Holding costs e.g. storage or insurance cists

Question 7

Formula for replication strategy which includes Net holding costs?

Answer 7

PV(S)=S0 + M

S0 - spot price at time T = 0
M - Net holding costs (replication strategy)
= PV(holding costs) - PV(holding benefits)

Question 8

Formula for for forward strategy which includes Net holding costs?

Answer 8

PV(F) = S0 + M

Question 9

What are the principle assumptions when using pricing futures and forwards?

Answer 9

• No transaction costs
• No restrictions on short sales
• The rates of interest are the same for borrowing and lending

Question 10

PV(F)>S0 +M meaning?

Answer 10

The futures is over-valued and the spot is undervalued
Therefore, to arbitrage the position the arbitrageur must short the futures and long the spot

Question 11

PV(F)<S0 + M meaning?

Answer 11

The futures is under-valued and the spot is over-valued
Therefore, to arbitrage the position the arbitrageur must long the futures and short the spot

Question 12

What does short the futures and long the spot mean?

Answer 12

Enter a position to sell asset in the future.
Borrow money for the period of the futures instrument
Buy x unit(s) of asset on the Spot Mkt
Repay borrowings when the futures settles

Question 13

What does long the futures and short the spot mean ?

Answer 13

Enter a position to buy asset in the future. Sell x unit(s) of asset on the Spot Mkt
Invest proceeds for the period of the futures instrument
Buy back x unit(s) of asset on the Spot Mkt

Question 14

what does the model PV(F)<S0 + M assume?

Answer 14

Assumes that you hold assets, have spare available and want it back or can borrow and then return assets

Question 15

What are the pricing model limitations?

Answer 15

.Delivery Options
.Margining (Daily Marking to Market)
.Transaction costs
.Restrictions on Short Sales
(e.g. catastrophe futures where the underlying is not traded & electricity where the cost to hold it is
prohibitively expensive)
.Different rates of interest for borrowing and lending
(incl. the default-free or risk-free rate of interest)

Question 16

What is the hedging strategy for this model:
PV(F) NOT= Smid + M

Answer 16

Hedging strategy
1. Take advantage of the price mismatch (using the SPOT market)
2. Seek to trade out of the position
3. Hold the original position

Question 17

What are the practical issues when hedging?

Answer 17

1. There may be an asset and delivery mismatch
2. Margining for futures contracts would have to be considered

Question 18

What are asset mismatches?

Answer 18

The assets underlying the original contract may not be available

Question 19

What are delivery mismatches?

Answer 19

It may be impossible to absolutely match the delivery criteria of the original contract in the current market

Question 20

What are hedges?

Answer 20

A way of protecting oneself against financial loss or other adverse circumstances

Question 21

What are short hedges?

Answer 21

An attempt to manage risk using an agreement to sell an asset/assets at a point in the future

Question 22

What are long hedges?

Answer 22

An attempt to manage risk using an agreement to buy an asset/assets at
a point in the future

Question 23

State which are fixed and variable:
The Original Forward Price
The Present Value of the Forward
The Spot Market Price

Answer 23

Fixed
Variable
Variable

Question 24

What are the assumptions underlying the process of valuing alternative strategies mid-term for futrures and forward agreements. When looking to value strategies mid-term, your essentially considering how changes in market might affect your position and whether its worth switching strategy. Key assumptions:

Answer 24

. Market conditions are constant or predictable- assume market will behave similarly in the future unless there are shocks

No arbitrage - Assume here’s no risk-free profit (arbitrage) to be made by taking advantage of price differences between the spot market and the futures market. If arbitrage exists, you would adjust your strategy to take advantage of it.

Transaction costs are negligible - In theory, trading futures and forwards is frictionless — there are no significant transaction costs, commissions, or fees that would affect the profit or loss of the strategy.

Interest rates and holding costs are constant -
If you are borrowing or lending money as part of the strategy, you assume that interest rates will stay the same. Similarly, any costs related to holding the asset (storage, insurance, etc.) are assumed to be predictable.

Hedging effectiveness - You assume that the hedge will be effective at protecting against adverse price movements. This is where you calculate how well the futures position will offset losses or gains in the underlying asset.

Question 25

What are holding costs/benefits?

Answer 25

Refer to the financial impact of owning and maintaining an asset (such as a commodity) until the future date when it will be sold or delivered under a futures or forward contract. Holding Costs: Storage Costs: The cost of physically storing the commodity (like grain, oil, etc.) until the contract's maturity. Insurance: Costs to insure the asset while it is stored. Financing Costs: If you have to borrow money to finance the purchase of the asset, there will be interest costs. Holding Benefits: Price Appreciation: If the price of the asset increases while you're holding it, that’s a benefit. For instance, if you hold wheat and the price rises, you gain value in the asset. Dividends or Interest: For some assets, like stocks or bonds, there may be an income stream (such as dividends or interest) while holding the asset. In futures and forwards, these costs and benefits are important when you’re considering whether to hold the underlying asset or use the contract to hedge.

Question 26

Long hedge

Answer 26

A long hedge is used when you expect the price of the asset to rise in the future, but you want to lock in a price today. It’s typically used by buyers of the underlying asset. Example: If you are a wheat buyer and you expect the price of wheat to rise before you need to buy it, you would take a long position (buy a futures contract) today at the current price to lock in the price for future delivery. At the future time when you need to buy the wheat, you either: Take delivery of the wheat at the agreed futures price (which is fixed). Or you close out the futures position (sell the contract) and buy the wheat at the market price. The profit from the futures contract compensates for the higher price of wheat in the spot market.

Question 27

Short hedge

Answer 27

A short hedge is used when you expect the price of the asset to fall, and you want to lock in a selling price today. It’s typically used by sellers of the asset. Example: If you are a farmer and you expect the price of wheat to fall before harvest time, you would take a short position (sell a futures contract) today to lock in the price for your wheat. At the future time when you sell the wheat, you either: Sell the wheat at the market price and make a profit from the futures contract (as you sold the futures at a higher price). Or you close out the futures position (buy the contract back) and sell the wheat at the market price. The profit from the futures contract compensates for the lower price you receive in the spot market.

Question 28

Perils of hedging using futures/forwards

Answer 28

Basis Risk: Basis risk arises when the futures price doesn’t move perfectly in sync with the spot price of the underlying asset. For example, if you're hedging wheat, but the wheat futures price doesn’t move exactly in line with the spot price of wheat (due to supply issues, local weather changes, etc.), your hedge might not be fully effective. You could still experience a loss even with the hedge in place. Liquidity Risk: Futures and forward markets may not be highly liquid, especially for certain commodities or contracts. If you want to close your position early, you might not be able to find a buyer/seller at a favorable price. Counterparty Risk: Futures: In a futures market, this risk is generally low because the exchange itself acts as the counterparty. However, in a forward contract, you face counterparty risk, meaning the other party may default on the contract. Over-hedging: Over-hedging happens when you take a position that is larger than necessary to protect against your risk. This can result in more risk than you intended, as you may end up with losses if the price moves contrary to your position. Mispricing: Hedging is based on the assumption that futures and forwards are priced correctly. However, mispricing can occur due to factors like interest rates, unexpected economic events, or incorrect expectations about future prices. Cost of Hedging: Hedging with futures/forwards involves some costs (such as transaction fees, margin requirements, or opportunity costs), and if these costs exceed the benefits of hedging, the strategy may not be worthwhile.