Spreadsheet: 1d93c970-dd01-40a2-827f-ad7ad1c1276f
Sheet: Sheet1

Black-Swaption | Unnamed: 1 | Unnamed: 2 | © copyright THC 2003. All rights reserved by [NAME], New York, NY. USA      www. thomasho.com       [EMAIL] | Unnamed: 4 | Unnamed: 5 | Unnamed: 6 | Unnamed: 7 | Unnamed: 8 | Unnamed: 9 | Unnamed: 10 | Unnamed: 11 | Unnamed: 12 | Unnamed: 13 | Unnamed: 14 | Unnamed: 15 | Unnamed: 16 | Unnamed: 17 | Unnamed: 18 | Unnamed: 19 | Unnamed: 20 | Unnamed: 21 | Unnamed: 22 | Unnamed: 23 | Unnamed: 24 | Unnamed: 25 | Unnamed: 26 | Unnamed: 27 | Unnamed: 28 | Unnamed: 29 | Unnamed: 30 | Unnamed: 31 | Unnamed: 32 | Unnamed: 33 | Unnamed: 34 | Unnamed: 35 | Unnamed: 36 | Unnamed: 37 | Unnamed: 38 | Unnamed: 39 | Unnamed: 40 | Unnamed: 41 | Unnamed: 42
reference number | 32 | classification# | 60204
Version | 2 | level | intermediate |  | Instructions
publication date | 2003-06-05 00:00:00 |  |  |  | Use "cspline_interp" function of Xnumbers freeware package to interpolate the yield curve and volatility curve.
author | [NAME]. |  |  |  | Unzip xnumber31.zip at local directory (D:). 1) Open Excel 2) Select <Addins...> from the <Tools> menu
affiliation | Hanyang University |  |  |  | 3) Once in the Addins Manager, search for and select XNUMBERS.XLA 4) Click OK and have fun!
email address | [EMAIL] |  |  |  | input | notional principal, swaption maturity, swap tenor, compounding frequency, strike, volatility of forward swap rate, initial yield curve
last revised date | 2004-03-11 00:00:00 |  |  |  | output | swaption value
references | Jamshidian, F., 1989, An Exact Bond Option Formula, Journal of Finance, Vol.44, 205-209.
 | Ch. 6 of "The Oxford Guide to Financial Modeling" by [NAME] and [NAME], 2003, Oxford University Press
Descriptions
financial model class | Implied Volatility Surface: Calibrating the Models
issuer/[NAME] | practitioner
model type | Price Quotes of Benchmark Securities
risk sources | forward swap rate
risk distribution | lognormal
economic assumptions | perfect capital market
technical assumptions | continuous compounding interest rate
key words | arbitrage-free interest rate model
Links
data | http://www.federalreserve.gov/
financial models | 7. Bond Arithmetic, 8. Bond Model
freeware | http://digilander.libero.it/foxes/
Inputs
notional principal | F | 10000
swaption maturity (year) | OT | 5
tenor of swap (year) | ST | 3
total maturity (year) | T | 8 | T=OT+ST, 0 < T ≤ 10, The maximum total maturity is 10, that is, we can choose both swaption maturity and tenor of swap arbitrarily on condition that the sum of them is less than or equal to 10.
compounding frequency/year | m | 2 | We can choose the compounding frequency among 1, 2, and 4.
the number of periods | n | 16 | n=Tm, 0 < n ≤ 40, The maximum number of periods is 40 since the maximum values of total maturity and compounding frequency are 10 and 4 respectively.
time increment | dt | 0.5 | dt = T/n
strike | K | 0.05063024104885768
volatility of forward swap rate | σ | 0.2
time period (year) |  | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10
yield curve (continuous compounding) |  | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05
Outputs
swaption value | 191.9421818268761
Interim Calculations
adjusted time period (t-year) | t | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 | 5.5 | 6 | 6.5 | 7 | 7.5 | 8 | 8.5 | 9 | 9.5 | 10 | 10.5 | 11 | 11.5 | 12 | 12.5 | 13 | 13.5 | 14 | 14.5 | 15 | 15.5 | 16 | 16.5 | 17 | 17.5 | 18 | 18.5 | 19 | 19.5 | 20
interpolated yield curve | r(t) | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05
discount function | P(t) | 1 | 0.9753099120283326 | 0.951229424500714 | 0.9277434863285529 | 0.9048374180359595 | 0.8824969025845955 | 0.8607079764250578 | 0.8394570207692074 | 0.8187307530779818 | 0.7985162187593771 | 0.7788007830714049 | 0.7595721232249685 | 0.7408182206817179 | 0.7225273536420722 | 0.7046880897187134 | 0.6872892787909722 | 0.6703200460356393 | 0.6537697851298473 | 0.6376281516217733 | 0.62188505646502 | 0.6065306597126334 | 0.5915553643668151 | 0.5769498103804866 | 0.5627048688069557 | 0.5488116360940264 | 0.5352614285189903 | 0.522045776761016 | 0.5091564206075492 | 0.4965853037914095 | 0.4843245689553624 | 0.4723665527410147 | 0.4607037809989658 | 0.4493289641172216 | 0.4382349924649492 | 0.4274149319487267 | 0.4168620196785084 | 0.4065696597405991 | 0.3965314190749928 | 0.3867410234545012 | 0.3771923535631569 | 0.3678794411714423
one period forward rate | f(t-dt,t) |  | 0.05000000000000011 | 0.04999999999999988 | 0.05000000000000011 | 0.05000000000000011 | 0.04999999999999966 | 0.05000000000000011 | 0.04999999999999988 | 0.05000000000000011 | 0.04999999999999988 | 0.05000000000000011 | 0.05000000000000011 | 0.04999999999999988 | 0.04999999999999988 | 0.05000000000000011 | 0.04999999999999988 | 0.05000000000000011 | 0.05000000000000011 | 0.04999999999999988 | 0.05000000000000034 | 0.04999999999999988 | 0.04999999999999988 | 0.05000000000000034 | 0.04999999999999988 | 0.05000000000000011 | 0.04999999999999966 | 0.05000000000000011 | 0.04999999999999988 | 0.05000000000000034 | 0.05000000000000011 | 0.04999999999999988 | 0.04999999999999988 | 0.05000000000000011 | 0.05000000000000011 | 0.04999999999999988 | 0.04999999999999988 | 0.04999999999999988 | 0.05000000000000011 | 0.05000000000000011 | 0.04999999999999988 | 0.04999999999999988
one period forward price | F(t-dt,t) |  | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283326 | 0.9753099120283328 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283325 | 0.9753099120283327 | 0.9753099120283327 | 0.9753099120283325 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283328 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283325 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283327 | 0.9753099120283327 | 0.9753099120283326 | 0.9753099120283326 | 0.9753099120283327 | 0.9753099120283327
zero-coupon bond price with t-maturity | B(t) | 10000 | 9753.099120283327 | 9512.29424500714 | 9277.434863285529 | 9048.374180359595 | 8824.969025845954 | 8607.079764250579 | 8394.570207692073 | 8187.307530779818 | 7985.162187593771 | 7788.007830714048 | 7595.721232249684 | 7408.182206817179 | 7225.273536420722 | 7046.880897187134 | 6872.892787909723 | 6703.200460356394 | 6537.697851298473 | 6376.281516217733 | 6218.8505646502 | 6065.306597126334 | 5915.553643668151 | 5769.498103804866 | 5627.048688069557 | 5488.116360940264 | 5352.614285189903 | 5220.457767610161 | 5091.564206075492 | 4965.853037914095 | 4843.245689553624 | 4723.665527410147 | 4607.037809989658 | 4493.289641172216 | 4382.349924649492 | 4274.149319487266 | 4168.620196785084 | 4065.696597405991 | 3965.314190749928 | 3867.410234545012 | 3771.923535631569 | 3678.794411714423
checking swap period |  | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
forward discount function | 5.502325119903213 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.9753099120283326 | 0.951229424500714 | 0.927743486328553 | 0.9048374180359596 | 0.8824969025845955 | 0.8607079764250578 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
the last discount function | 0.8607079764250578 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.8607079764250578 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
calculate A | 2.142607556047042 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.3797860616124842 | 0.3704091103408589 | 0.3612636768210361 | 0.3523440448593567 | 0.3436446393954861 | 0.3351600230178197 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
forward swap rate | 0.05063024104885768
d1 | 0.223606797749979
d2 | -0.223606797749979