Book 4_Derav_READING 71_ARBITRAGE, REPLICATION, AND THE COST OF CARRY IN PRICING DERIVATIVES

Question 1

Valuation of derivative securities

Answer 1

based on a no-arbitrage condition
- When the forward price is too high, the arbitrage is to sell the forward and buy the underlying asset.
- When the forward price is too low, the arbitrage is to buy the forward and sell short the underlying asset.
Arbitrage will move the forward price toward its no_x0002_arbitrage level.

Question 2

Arbitrage

Answer 2

refers to a transaction in which
- an investor purchases one asset or portfolio of assets at one price
- and simultaneously sells an asset or portfolio of assets
=> that has the same future payoffs, regardless of future events, at a higher price, realizing a risk-free gain on the transaction.

Question 3

Replication

Answer 3

• Refers to creating a portfolio with cash market transactions that has the same payoffs as a derivative for all possible future values of the underlying.
• Replication allows us to calculate the no-arbitrage forward price of an asset.

Question 4

Long forward replication

Answer 4

Borrow 30 at 5% and buy a share, the pay-off = S1 - 30x1.05 = S1 - 31.5 (fw price = 31.5)

Question 5

Short forward replication

Answer 5

Short a share and invest 30 at 5%, the payoff = 31.5 - S1 (fw price 31.5)

Question 6

the forward price that will prevent arbitrage is

Answer 6

the spot price compounded at the risk-free rate over the time until expiration.

Question 7

The cost of carry

Answer 7

is the benefits of holding the asset minus the costs of holding the asset.

Question 8

Greater costs of holding an asset

Answer 8

increase its no-arbitrage forward price

Question 9

Greater benefits of holding an asset

Answer 9

decrease its no-arbitrage forward price

Question 10

the no-arbitrage forward price for an asset in case of no benefits of holding the asset and no costs of holding the asset

Answer 10

F0 (T) = S0 (1 + Rf) T

Question 11

the no-arbitrage forward price for an asset if there are benefits of holding the asset and costs of holding the asset

Answer 11

S0 + PV0 (costs) - PV0 (benefit) T .

Question 12

Forward exchange rate (p/b)

Answer 12

= (1+ interest p)/(1+interest b) x spot rate

Question 13

convenience yield

Answer 13

refers to nonmonetary benefits from holding an asset. One example of convenience yield is the advantage of owning an asset that is difficult to sell short when it is perceived to be overvalued