Swaps & Swaptions. by Ying Ni
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1 Swaps & Swapions by Ying i Ineres rae swaps. Valuaion echniques Relaion beween swaps an bons Boosrapping from swap curve Swapions Value swapion by he Black 76 moel
2 . Inroucion Swaps- agreemens beween wo companies o exchange cash flows in he fuure accoring o a preeermine formula. Currency Ineres rae Swapions- opions o ener ino a swap Usually an ineres rae swap 2
3 2. Ineres Rae Swaps he paries o an ineres rae swap Pary A Pays fixe Receives floaing Fixe ineres rae Floaing ineres rae Pary B Receives fixe Pays floaing oional principal will no be exchange Floaing-rae - Linke o i.e. 6-monh LIBOR raes 3
4 2.Ineres Rae Swapscomponens of an Ineres rae swap. oional principal 2. Ineres raes for he paries Fixe rae Floaing rae 3. Paymen frequency Semi-annual Quarerly 4. Duraion of he swap or enor, mauriy 4
5 2. Ineres Rae Swaps- Example : Cash paymens in a swap Diagram of cash paymens-2-y, semi-annual, $, r*, r ½ r* a 0 ½ r* a 0,5 ½ r* a ½ r* a,5 ½r ½r ½r ½r 0 0.5,5 2 ime 5
6 3. Comparaive avanage argumen wo companies wan o borrow money hey are quoe fixe an floaing raes such ha: by exchanging paymens beween hemselves hey benefi, a he same ime benefiing he inermeiary who pus he eal ogeher 6
7 4. he Relaion beween Swaps & Bons Fixe-sie sum of zero-coupon bons Z, i ; r s -fixe rae; principal. PV fix r s i Z ; i. 7
8 4. he Relaion beween Swaps & Bons Floa sie: A single floaing leg & he replicaing porfolio Perio τ LIBRO $ + LIBRO $ τ τ i -τ i $ $ 8
9 4. he Relaion beween Swaps & Bons Floa sie: PV All floaing legs fl Z ; $ 9
10 4. he Relaion beween Swaps & Bons Value of he swap a iniiaion: receiver of he fixe sie V s r s Z ; i + i Z ; 0
11 5. Swap curve & Boosrapping wih Swaps -Swap curve Obain he par swap rae by + i i s i i s s Z Z r e i Z Z r V ; ;.. 0 ; ;
12 2 5. Swap curve & Boosrapping wih Swaps -Boosrapping wih Swaps Obain Z, by ; : ; ; ; k s k i i k s k s s r Z r Z r Z Z Z r M
13 6. Valuaion of swaps A iniiaion: swap has value of 0 Some ime afer iniiaion: swap may have posiive or negaive value. Suppose- A: paying floaing B: receive fixe he swap for A a long posiion in a fixe-rae bon + a shor posiion in a floaing-rae bon V s B fix B fl 3
14 6. Valuaion of swaps value he floaing-rae bon: Suppose: oional principal L, ex paymens a ime i K i : Floaing paymen a ime i Immeiaely afer he paymen B fl L Immeiaely before he paymen B fl L+K i floaing-rae bon an insrumen proviing a single cash flow of a ime i. value of he floaing-rae bon oay L+k i exp-r i 4
15 7. Swapions Swapion: righ o ener ino a swap a a specific ae in he fuure a a paricular fixe rae for a specifie erm Componens:. Mauriy of he opion 2. Srike rae 3. Payer or receiver 4. ype: American, European or Bermuan 5. All componens of a swap 5
16 7. Swapions Payer swapions: opion o ener ino a swap paying fixe an receiving floaing Benefi of he pre-se srike rae if he marke raes are higher, expires worhless if hey are lower. Receiver swapion: opion o a swap receiving fixe & pay floaing he opposie is rue 6
17 7. Swapions- Example 3: In-5-for-0 payer swapion-srike rae 7% Decision of a payer swapion holer om Year 0: om buys a swapion Year 5: Exercise ae Exercise! if 0-year swap rae is above 7%, om pays fixe 7%, an receives floaing. -Oherwise, o no Exercise! Year 5 7
18 8 8. Valuaion of Swapions- Black 76 Opion Pricing Moel he unerlying is a forwar on a swap K F K F e P K F e P r pu r call σ σ σ ; 2 / / ln
19 9 8. Valuaion of Swapions- Value European Swapions use Black 76 [ ] [ ] / / 2 2 F K e F m F p K F e F m F c r m r m τ τ
20 9. Conclusion Swaps can be ecompose ino zero-coupon bons Yiel curve are ofen boosrappe from swap curve Afer iniiaion, Swaps can be value in erms of fixe-rae an floaing-rae bon Swapions are value using he Black 76 opion pricing formula 20
21 hank You! 2
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