Interest Rate Swaps Lecture

# Interest Rate Swaps Lecture - Debt Instruments and Markets...

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Debt Instruments and Markets Professor Carpenter Interest Rate Swaps 1 Interest Rate Swaps Concepts and Buzzwords Swaps Swap Spreads Credit Risk of Swaps Swap Spreads vs. Credit Spreads Counterparty Notional amount Plain vanilla swap Swap rate Synthetic Duration Readings Veronesi, Chapter 5 Tuckman, Chapter 18 Krishnamurthy, “How Debt Markets Have Malfunctioned in the Crisis”

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Debt Instruments and Markets Professor Carpenter Interest Rate Swaps 2 Description of a Swap An interest rate swap is a contract which commits two counterparties to exchange, over an agreed period, two streams of interest payments, each calculated using a different interest rate index, but applied to a common notional principal amount. A plain vanilla or generic swap is a fixed-for- floating swap with constant notional principal, constant fixed interest rate, floating 6-month interest rate, and semi-annual payments. The swap rate is the quoted fixed rate. Which Side is Which? Institutionally, we can just call one counterparty the fixed payer and one counterparty the fixed receiver. For valuation, duration, and swaption analysis, it is convenient to identify one side as long the swap and the other short the swap. We’ll say the fixed receiver is long the swap and the fixed payer is short the swap. Some people use the opposite convention.
Debt Instruments and Markets Professor Carpenter Interest Rate Swaps 3 Swap Cash Flows Every six months until maturity, the party who is long the swap receives a fixed rate k , and pays the 6-month rate set 6-months earlier. If the notional amount of the swap is N and the maturity is T , the time t cash flow to this party is N ( k - t-0.5 r t )/2 for t = 0.5, 1, 1.5, ..., T . Note that no principal is exchanged. Class Problem Consider a long position in 5.5% 2-year swap with \$100 notional amount. Suppose the 0.5-year rates over the life of the swap turn out as follows: What are the cash flows to long swap position? 0 0.5 1 1.5 2 5.54% 6.00% 5.44% 6.18% 0 0.5 1 1.5 2

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Debt Instruments and Markets Professor Carpenter Interest Rate Swaps 4 Consider again the cash flows of the plain vanilla swap with fixed rate k , notional amount N and maturity T : N ( k - t-0.5 r t )/2 for t =0.5, 1, 1.5, …, T . These are the same as the cash flows from a portfolio consisting of a long position in a T -year fixed rate note with par amount N and coupon rate k , and a short position in a T -year floating rate note with par amount N . The difference between the coupons of the two notes equals the swap payment, and the difference between their principal payments is zero. ! swap( k , T ) = fixed rate note( k , T ) – floating rate note Swap as Bond minus Floater Swap = Long a fixed rate bond, short a floater Swap value = value of bond – value of floater = value of bond – 100 Swap dollar duration = dollar duration of bond – dollar duration of floater Swap dollar convexity = dollar convexity of bond – dollar convexity of floater Swap Value and Interest Rate Risk
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