Spreadsheet: 239159d1369835985-question-about-addin-and-a-special-function-52vasicek-model-v3
Sheet: furtherex1,2

[NAME] |  |  | © copyright THC 2003. All rights reserved by [NAME], NY, NY. |  |  |  |  |  | www.thomasho.com |  | [EMAIL]
reference number | 16 | classification# | 50302 |  | Instructions
Version | 1 | level | basic |  | Use "data-table" to generate the discount function and the term structure.
publication date | 2003-05-19 00:00:00
author | [NAME].
affiliation | Hanyang University |  |  |  | input | current short term interest rate, long-term mean, mean reverting speed, the volatility of short rate, maturity date, current date
email address | [EMAIL]
last revised date | 2003-12-07 00:00:00 |  |  |  | output | discount function and term structure
references | [NAME], O., 1977, An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, [NAME], 177-188.
 | Ch.5 of "The Oxford Guide to Financial Modeling" by [NAME] and [NAME], 2004, Oxford University Press
Descriptions
financial model class | Interest Rate Derivatives: Interest Rate Models
issuer/[NAME]
model type | Equilibrium Models
risk sources | interest rate
risk distribution | normal
economic assumptions | equilibrium
technical assumptions | continuous compounding
key words
Links
data
financial models
Inputs
the level of short rate (r(t)) | 0.06
the long-term mean (b) | 0.08
the mean reverting speed (a) | 0.2
the volatility of short rate (σ) | 0.02
bond maturity (T) | 1
current date (t) | 0
option expiration (OT) | 0.6
bond face value (F) | 100
exercise price (K) | 90
Outputs
European bond option value |  | 7.035891041467324
 |  | Monte-carlo simulation
Interim Calculations
time to maturity |  | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30
P(t,T) | 0.940056275243874 | 1 | 0.940056275243874 | 0.8810573009516471 | 0.8239004994540895 | 0.7691339367004132 | 0.7170672400309374 | 0.6678486619954512 | 0.621518268671486 | 0.5780445405813084 | 0.5373495361345882 | 0.4993261898843852 | 0.4638501995557121 | 0.4307881808183406 | 0.4000032383763802 | 0.3713587411022408 | 0.3447208438252474 | 0.3199601316113122 | 0.2969526484592412 | 0.2755804941075043 | 0.2557321185633212 | 0.237302406308507 | 0.2201926157192347 | 0.2043102205674385 | 0.1895686871846965 | 0.1758872113523345 | 0.1631904321260957 | 0.1514081348423873 | 0.1404749519495444 | 0.1303300676838056 | 0.1209169306972732 | 0.1121829773517296
r(t,T) | 0.06181553822934455 | 0.06 | 0.06181553822934455 | 0.06331630717662358 | 0.06456850315120129 | 0.06562253867019857 | 0.06651713261980594 | 0.06728228083528796 | 0.0679414248542708 | 0.0685130441811828 | 0.06901183232685228 | 0.06944957096479397 | 0.06983578406062772 | 0.07017823079188194 | 0.0704832796896905 | 0.07075619474483692 | 0.07100135585470678 | 0.07122242997905205 | 0.07142250504043321 | 0.07160419546916497 | 0.07176972601240664 | 0.07192099876136428 | 0.07205964712774172 | 0.07218707959811782 | 0.0723045154252067 | 0.07241301391506905 | 0.07251349859396304 | 0.07260677725488753 | 0.07269355866818233 | 0.07277446657547412 | 0.07285005145908156 | 0.07292080048038294
f(t,T) |  |  | 0.06181553822934455 | 0.06481707612390261 | 0.0670728951003567 | 0.06878464522719042 | 0.07009550841823547 | 0.07110802191269798 | 0.0718962889681678 | 0.07251437946956686 | 0.07300213749220814 | 0.07338921870626922 | 0.07369791501896521 | 0.07394514483567843 | 0.07414386646339301 | 0.07430409046174037 | 0.0744336113928849 | 0.07453854184423102 | 0.07462370602253161 | 0.07469293275760494 | 0.07474927579075669 | 0.07479518099155943 | 0.07483261445529056 | 0.07486316147601603 | 0.07488810362116226 | 0.07490847918190281 | 0.07492513088741903 | 0.0749387437779992 | 0.07494987541384754 | 0.07495898007235215 | 0.0749664282000902 | 0.07497252209812261
B(t,T) | 0.9063462346100909
A(t,T) | 0.9925928053397293
P(t,T) | 0.940056275243874
r(t,T) | 0.06181553822934455
B(t,OT) | 0.5653978164142126
A(t,OT) | 0.9972487904185413
P(t,OT) | 0.9639856502653986
σP | 0.005615298830269215
h | 14.28946450465243
European call option | 7.246919000501535 | closed-form
the number of periods (n) | 5
dt=T/n | 0.2
time to maturity |  | 0 | 0.2 | 0.4 | 0.6000000000000001 | 0.8 | 1
Generate interest rate paths | 1 | 0.06 | 0.05034171052269572 | 0.0557229419104336 | 0.06727997569347878 | 0.08437510273786575 | 100
 | 2 | 0.06 | 0.05104290880908038 | 0.05153000655277785 | 0.06033030519869804 | 0.06522902260680642 | 100
 | 3 | 0.06 | 0.06585439783730543 | 0.06654994096287219 | 0.06206153099271898 | 0.05126273288492292 | 100
 | 4 | 0.06 | 0.07368398013986673 | 0.07059150180873325 | 0.0829236140608493 | 0.09180002812613455 | 100
 | 5 | 0.06 | 0.03880793848703572 | 0.04129737761032461 | 0.03618344567200864 | 0.03280975759956826 | 100
 | 6 | 0.06 | 0.06265585344618821 | 0.07419938674994753 | 0.08014297612831797 | 0.06661395248892286 | 100
 | 7 | 0.06 | 0.07405444083463691 | 0.06975254059315884 | 0.07008575132067325 | 0.06996151720276432 | 100
 | 8 | 0.06 | 0.06328147915073472 | 0.06229861228029751 | 0.06923127367866069 | 0.05680209013459427 | 100
 | 9 | 0.06 | 0.06356047468104309 | 0.06472237765229616 | 0.07903963401462336 | 0.1006290697116135 | 100
 | 10 | 0.06 | 0.06782613527381885 | 0.0827155342643325 | 0.07291472421479762 | 0.07160286321448955 | 100
 | 11 | 0.06 | 0.05780393206420003 | 0.04863967659676823 | 0.05624016893641896 | 0.07245085295196013 | 100
 | 12 | 0.06 | 0.06029848002368125 | 0.07752635553056006 | 0.08131501603417839 | 0.08057282067946875 | 100
 | 13 | 0.06 | 0.07314585970490813 | 0.08593563130736888 | 0.07871708133480408 | 0.06684214631570481 | 100
 | 14 | 0.06 | 0.06594852402964677 | 0.08137655088328583 | 0.09234082688295904 | 0.08969138365290737 | 100
 | 15 | 0.06 | 0.06194024790784281 | 0.05236108257146169 | 0.05392229845540381 | 0.06566873145732303 | 100
 | 16 | 0.06 | 0.04583845908235344 | 0.05465460874399919 | 0.03696050768015401 | 0.04466139438170772 | 100
 | paths | r(t) |  |  |  |  | F
calculate bond option value |  | PV(Pay-offs) |  |  | Pay-offs
 |  | 6.783357110250639 |  |  | 7.012435401489867
 |  | 7.279501513762137 |  |  | 7.520081454001598
 |  | 7.466104939067331 |  |  | 7.759006547327644
 |  | 6.303035026567517 |  |  | 6.565878825274439
 |  | 8.391157981661243 |  |  | 8.629612421144913
 |  | 6.833124834369551 |  |  | 7.107518255377627
 |  | 6.948821794110486 |  |  | 7.237917417223784
 |  | 7.237173992335666 |  |  | 7.510836286245166
 |  | 6.231297861503572 |  |  | 6.470421194764512
 |  | 6.856153579168021 |  |  | 7.151019369091898
 |  | 7.214806061974764 |  |  | 7.459019966177635
 |  | 6.549761623529281 |  |  | 6.814097464764245
 |  | 6.825083906688415 |  |  | 7.130782195289001
 |  | 6.163872290124409 |  |  | 6.424830271574848
 |  | 7.374931001183484 |  |  | 7.636556735418623
 |  | 8.116073147180671 |  |  | 8.38081402000239