Lecture 1

Question 1

What is a derivative?

Answer 1

A derivative is a financial instrument whose value depends on the value of other underlying variables.

Question 2

Name some examples of derivatives.

Answer 2

Options, forward contracts, futures contracts, interest rate swaps, credit default swaps, collateralized debt obligations, and mortgage-backed securities

Question 3

What are the three main uses of derivatives?

Answer 3

To hedge, speculate and arbitrage

Question 4

What is a forward contract?

Answer 4

An agreement to buy or sell an asset at a future date for a predetermined price.

Question 5

How does a forward contract differ from a spot contract?

Answer 5

A forward contract is settled in the future, whereas a spot contract is an immediate exchange.

Question 6

What does it mean for the forward contract’s initial value to be zero?

Answer 6

The delivery price is set so that no money changes hands initially between the two parties.

Question 7

What is a “replicating portfolio”?

Answer 7

A portfolio constructed to have the same payoff as a forward contract, allowing it to be used to price the forward.

Question 8

Why do hedgers use forwards?

Answer 8

To lock in a future price and reduce price risk (uncertainty) from market volatility.

Question 9

How can forwards be used for speculation?

Answer 9

By taking on leveraged positions to profit from future price movements without immediate capital outlay.

Question 10

What is the forward price formula for a non-dividend-paying asset?

Answer 10

Forward price at time t = Spot price at time t * e ^ Risk-free rate * (T-t)

Question 11

What are the assumptions for pricing futures and forwards?

Answer 11

No transaction costs, no taxes, borrowing and lending at the risk-free rate, and risk-averse investors.

Question 12

How is the present value (PV) of a future amount calculated with continuous compounding?

Answer 12

PV = X*e ^ -rT, where X is the future amount, r is the rate, and T is the time to maturity.

Question 13

What is “contango” in futures markets?

Answer 13

When the forward price is higher than the spot price, often due to storage and interest costs exceeding any convenience yield.

Question 14

What is “backwardation” in futures markets?

Answer 14

When the forward price is lower than the spot price, typically when convenience yield outweighs storage and interest costs.

Question 15

What is an arbitrage opportunity in the context of forwards?

Answer 15

When a discrepancy between the forward price and the cost of the replicating portfolio allows risk-free profit.

Question 16

How can an investor gain from an undervalued forward contract?

Answer 16

By buying the forward and creating a short position in the replicating portfolio to profit from the mispricing.

Question 17

Define “convenience yield” in commodity futures.

Answer 17

The benefit received by holding a physical asset, which is often absent in financial contracts.

Question 18

How does storage cost affect forward pricing in commodity markets?

Answer 18

It increases the forward price by adding a cost of carry, which forward holders must pay indirectly.

Question 19

What is the modified pricing formula for a commodity forward with convenience yield and storage cost?

Answer 19

F0 = S0 * e ^ (r + u - y) * T, where r is interest rate, u is storage cost and y is convenience yield.

Question 20

Explain the “cash-and-carry” strategy in futures markets.

Answer 20

Buying the underlying asset while borrowing funds to pay for it, to replicate the forward’s payoff.

Question 21

What factors affect the structure of commodity futures prices?

Answer 21

Interest rates, storage costs, and convenience yields.

Question 22

What historical example illustrates early option trading?

Answer 22

The Duke of Chandos purchased a call option on South Sea stocks in 1718.

Question 23

How does a forward contract gain or lose value over time?

Answer 23

It reflects changes in the spot price of the underlying asset as the contract approaches maturity.

Question 24

What are “investment assets” in the context of forwards and futures?

Answer 24

Assets held mainly for investment purposes, like stocks, for which the cost of carry and risk-free rates influence pricing.

Question 25

What distinguishes “consumption assets” from investments assets?

Answer 25

Consumption assets are primarily for use rather than investment, and holding them can offer convenience yields.

Question 26

What does a “forward short” position entail?

Answer 26

Agreeing to sell the underlying asset at a future date for a specified price, gaining if the asset’s market price drops below this price.

Question 27

Why might energy suppliers engage in long-term natural gas forward contracts?

Answer 27

To hedge against future price fluctuations and offer price stability for households.

Question 28

Describe an example of hedging with forwards in the airline industry.

Answer 28

Airlines lock in fuel prices for peak travel times, like Christmas, to manage costs despite market volatility.

Question 29

Why might backwardation occur in commodity markets?

Answer 29

When the benefit of physically holding the commodity (convenience yield) is higher than storage and interest costs.

Question 30

What role does Euler’s number play in forward pricing?

Answer 30

Euler’s number (e) is used for continuous compounding in calculating present and future values.