Week 3

Question 1

Currency Prepaid Forward

Answer 1

Prepaid Forward = x(0)e^(-r(y)*T)

• x(0) is the current ($/Y) exchange rate
• r(y) is the yen-dominated exchange rate

Question 2

Currency Forward

Answer 2

F = FV(Prepaid Forward) = x(0)e^[(r - r(y))T]

• x(0) is the current ($/Y) exchange rate
• r(y) is the yen-dominated exchange rate
• r is the dollar-dominated exchange rate

Question 3

Forward Rate Agreements (FRAs) Definition

Answer 3

Over-the-counter contracts that guarantee a borrowing or lending rate on a given notional principal amount

They can be settled at maturity (in arrears) or the initiation of the borrowing or lending transaction

They can be synthetically replicated using zero-coupon bonds

Question 4

Different FRAs Settlements

Answer 4

In arrears: [r-r(FRA)]*notional principal

At time of borrowing: notional principal*[r-r(FRA)]/(1+r)

Question 5

Forward Curve

Answer 5

The set of prices for different expiration dates

Upward sloping => market is in contango
Downward sloping => market is in backwardation

Question 6

Lease Rate

Answer 6

Like the dividend, for a commodity owner who lends the commodity

The lease rate is only earned if the commodity is loaned

Question 7

Annualized Lease Rate Formula

Answer 7

δ(l) = r - (1/T)ln(F/S(0))

Question 8

How do we view storage costs in commodity forwards?

Answer 8

A negative dividend

Question 9

Convenience Yield

Answer 9

Holders of a commodity receive benefits from physical ownership

Question 10

Forward Price of a Commodity Forward

Answer 10

F = S(0)e^[(r+λ-c)T]

c: the continuously compounded convenience yield

Question 11

Commodity Lease Rate

Answer 11

δ(l) = c - λ

Question 12

2 common types of basis risk

Answer 12

Cross hedging: crude oil futures to hedge jet fuel price risk (similar prices, but not exactly)

Stack and role: Hedge distant obligations with near-term futures

Question 13

Swap Definition

Answer 13

A contract calling for exchange of payments, on one or more dates, determined by the difference in two prices

Provides a means to hedge a stream of risky payments

A single-payment swap is the same thing as a cash-settled forward contract

Question 14

Prepaid Swap

Answer 14

A single payment today to obtain multiple deliveries in the future

Question 15

Market Value of a Swap

Answer 15

Zero at interception

Once swap is struck no longer zero

It is the difference in the PV of payments between the original and new swap rates

Question 16

Prepaid Swap Formula

Answer 16

ΣF*P(0,ti)

Question 17

Fixed Swap Payment

Answer 17

R = [Σf(0)*P(0,ti)]/ΣP(0,ti)

Substitutes for f:

• f(0) = r0(t(i-1), t(i)) for interest rate swap
• f(0) = R*F(0) for currency swap (annuity)
• f(0) = F(0) for commodity swap