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Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
9
Equity Swaps (page 767-768)
Total return on an equity index is exchanged periodically for a fixed or floating return When the return on an equity index is exchanged for LIBOR the value of the swap is always zero immediately after a payment. This can be used to value the swap at other times.
CMS swaps
Swap rate observed at time ti is pபைடு நூலகம்id at time ti+1 We must
make a convexity adjustment because payments are swap rates (= yield on a par yield bond) Make a timing adjustment because payments are made at time ti+1 not ti
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
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Variations on Vanilla Interest Rate Swaps
Principal different on two sides Payment frequency different on two sides Can be floating-for-floating instead of floating-forfixed It is still correct to assume that forward rates are realized How should a swap exchanging the 3-month LIBOR for 3-month CP rate be valued?
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
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Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
10
Swaps with Embedded Options
(page 769-771)
Accrual swaps Cancelable swaps Cancelable compounding swaps
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 4
Currency Swaps
In theory, a swap where LIBOR in one currency is exchanged for LIBOR in another currency is worth zero In practice it is sometimes the case that LIBOR in currency A is exchanged for LIBOR plus a spread in currency B This necessitates a small adjustment to the “assume forward LIBOR rate are realized” rule
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
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Compounding Swaps (Business Snapshot
33.2, page 762-763)
Interest is compounded instead of being paid Example: the fixed side is 6% compounded forward at 6.3% while the floating side is LIBOR plus 20 bps compounded forward at LIBOR plus 10 bps. This type of compounding swap can be valued (approximately) using the “assume forward rates are realized” rule. Approximation is exact if spread over LIBOR for compounding is zero
Fi 2si2 (ti 1 ti )ti 1 Fi i
when valuing a LIBOR-in-arrears swap
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 7
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 5
More Complex Swaps
LIBOR-in-arrears swaps CMS and CMT swaps Differential swaps
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
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Other Swaps (page 771-772)
Indexed principal swap Commodity swap Volatility swap Bizarre deals (for example, the P&G 5/30 swap in Business Snapshot 33.4 on page 772)
These cannot be accurately valued by assuming that forward rates will be realized
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
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LIBOR-in Arrears Swap (Equation 33.1,
page 764-765)
Rate is observed at time ti and paid at time ti rather than time ti+1 It is necessary to make a convexity adjustment to each forward rate underlying the swap Suppose that Fi is the forward rate between time ti and ti+1 and si is its volatility We should increase Fi by
Chapter 33 Swaps Revisited
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Valuation of Swaps
The standard approach is to assume that forward rates will be realized This works for plain vanilla interest rate and plain vanilla currency swaps, but does not necessarily work for non-standard swaps
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
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Differential Swaps
Rate is observed in currency Y and applied to a principal in currency X We must make a quanto adjustment to the rate
