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# Valuation of swaps

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### Valuation of swaps

1. 1. Chapter 32Swaps Revisited Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 1
2. 2. 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, 8th Edition, Copyright © John C. Hull 2012 2
3. 3. Variations on Vanilla Interest RateSwaps Principal different on two sides Payment frequency different on two sides Can be floating-for-floating instead of floating-for- fixed 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, 8th Edition, Copyright © John C. Hull 2012 3
4. 4. Compounding Swaps (Business Snapshot32.2, page 735) 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 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 4
5. 5. 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, 8th Edition, Copyright © John C. Hull 2012 5
6. 6. More Complex Swaps LIBOR-in-arrears swaps CMS and CMT swaps Differential swaps These cannot be accurately valued by assuming that forward rates will be realized Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 6
7. 7. LIBOR-in Arrears Swap (Equation 32.1,page 738) 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 i is its volatility We should increase Fi by Fi 2 2 i(ti 1 ti )ti 1 Fi i when valuing a LIBOR-in-arrears swap Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 7
8. 8. CMS swaps Swap rate observed at time ti is paid 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, 8th Edition, Copyright © John C. Hull 2012 8
9. 9. 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 Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 9
10. 10. Equity Swaps (page 740-741) 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. Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 10
11. 11. Swaps with Embedded Options(page 742-744) Accrual swaps Cancelable swaps Cancelable compounding swaps Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 11
12. 12. Other Swaps (page 744-745) Indexed principal swap Commodity swap Volatility swap Bizarre deals (for example, the P&G 5/30 swap in Business Snapshot 32.4 on page 733) Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 12