Week 3 Flashcards
Currency Prepaid Forward
Prepaid Forward = x(0)e^(-r(y)*T)
- x(0) is the current ($/Y) exchange rate
- r(y) is the yen-dominated exchange rate
Currency Forward
F = FV(Prepaid Forward) = x(0)e^[(r - r(y))T]
- x(0) is the current ($/Y) exchange rate
- r(y) is the yen-dominated exchange rate
- r is the dollar-dominated exchange rate
Forward Rate Agreements (FRAs) Definition
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
Different FRAs Settlements
In arrears: [r-r(FRA)]*notional principal
At time of borrowing: notional principal*[r-r(FRA)]/(1+r)
Forward Curve
The set of prices for different expiration dates
Upward sloping => market is in contango
Downward sloping => market is in backwardation
Lease Rate
Like the dividend, for a commodity owner who lends the commodity
The lease rate is only earned if the commodity is loaned
Annualized Lease Rate Formula
δ(l) = r - (1/T)ln(F/S(0))
How do we view storage costs in commodity forwards?
A negative dividend
Convenience Yield
Holders of a commodity receive benefits from physical ownership
Forward Price of a Commodity Forward
F = S(0)e^[(r+λ-c)T]
c: the continuously compounded convenience yield
Commodity Lease Rate
δ(l) = c - λ
2 common types of basis risk
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
Swap Definition
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
Prepaid Swap
A single payment today to obtain multiple deliveries in the future
Market Value of a Swap
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
Prepaid Swap Formula
ΣF*P(0,ti)
Fixed Swap Payment
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
