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LOS b: Explain the equivalence of 1) interest rate swaps to a series of off-market forward rate agreements (FRAs) and 2) a plain vanilla swap to a combination of an interest rate call and an interest rate put.

The fixed-rate payer in an interest-rate swap has a position equivalent to a series of:

A)	long interest-puts and short interest-rate calls.

B)	long interest-rate puts and calls.

C)	short interest-rate puts and long interest-rate calls.

The fixed-rate payer has profits when short rates rise and losses when short rates fall, equivalent to writing puts and buying calls.

The fixed-rate receiver in a plain vanilla interest rate swap has a position equivalent to a series of:

A)	long interest-rate puts and short interest-rate calls.

B)	long interest-rate puts.

C)	short interest-puts and long interest-rate calls.

The fixed-rate receiver has profits when short rates fall and losses when short rates rise, equivalent to buying puts and writing calls.

For a 1-year quarterly-pay swap, an equivalent position with short puts and long calls would involve:

A)	put-call combinations expiring on each of the four settlement dates.

B)	three put-call combinations on the last three settlement dates of the swap.

C)	three put-call combinations expiring on the first three settlement dates of the swap.

Interest rate options pay one period after exercise. Options expiring on settlements at t = 1,2,3, will mimic the uncertain swap payments at t = 2,3,4.

Writing a series of interest-rate puts and buying a series of interest-rate calls, all at the same exercise rate, is equivalent to:

A)	being the floating-rate payer in an interest rate swap.

B)	a short position in a series of forward rate agreements.

C)	being the fixed-rate payer in an interest rate swap.

A short position in interest rate puts will have a negative payoff when rates are below the exercise rate; the calls will have positive payoffs when rates exceed the exercise rate. This mirrors the payoffs of the fixed-rate payer who will receive positive net payments when settlement rates are above the fixed rate.

A)	provides a series of payments.

B)	has a positive value at contract initiation.

C)	cannot be priced with market rates.

An off-market FRA has a contract rate that differs from the zero-value rate at the inception of the contract; by definition, it has a positive value to one of the parties to the FRA.

Since the fixed rate on the swap is the same at every settlement date, a series of FRAs at those fixed rates will have values that differ from zero to the extent the fixed rate and the zero-value rate differ. This makes them off-market FRAs.

The floating-rate payer in a simple interest-rate swap has a position that is equivalent to:

A)	a series of short FRAs.

B)	issuing a floating-rate bond and a series of long FRAs.

C)	a series of long forward rate agreements (FRAs).

The floating-rate payer has a liability/gain when rates increase/decrease above the fixed contract rate; the short position in an FRA has a liability/gain when rates increase/decrease above the contract rate.

Which of the following is equivalent to a plain vanilla receive fixed currency swap?

A)	A short position in a foreign bond coupled with a long position in a dollar-denominated floating rate note.

B)	A long position in a foreign bond coupled with the issuance of a dollar-denominated floating rate note.

C)	A short position in a foreign bond coupled with the issuance of a dollar-denominated floating rate note.

A long position in a fixed rate foreign bond will receive fixed coupons denominated in a foreign currency. The short floating rate note requires U.S. dollar denominated floating-rate payments. Combined, these are the same cash flow as a plain vanilla currency swap.

Which of the following is equivalent to a plain vanilla receive-fixed interest rate swap?

A)	A short position in a bond coupled with a long position in a floating rate note.

B)	A long position in a bond coupled with the issuance of a floating rate note.

C)	A short position in a bond coupled with the issuance of a floating rate note.

A long position in a fixed rate bond pays fixed coupons. The short floating rate note requires floating-rate payments. Together, these are the same cash flow as a receive-fixed swap.

A plain vanilla interest-rate swap to the fixed-rate payer is equivalent to issuing a fixed-rate bond and:

A)	buying a floating-rate bond.

B)	selling a series of interest rate puts.

C)	selling a series of interest rate calls.

Paying fixed and receiving floating in a swap is equivalent to issuing a fixed-rate bond and investing the proceeds in a floating rate bond.