55.Double-UpSinkingFundBondModel1129

81.906 83.408 84.940 86.390 87.784 89.205 5
Case 3: no double-up at 4th, double-up at 5th principal to be retired at each year
Outstanding amount at the beginning of each year
92.144 93.834 95.558 97.090 98.484 99.905 5
100 0.0
Remaining principal at the ending of each year
coupon
100 100 7.0
100 100 7.0
100 100 7.0
10 100 90 7.0
10 90 80 6.3
numerator of convexity adjustment at time n denominator of convexity adjustment at time n
####### 1.98069 3.88562 7.55045 14.5343 1.98069 3.88562 7.55045 14.5343 27.7185
10 80 70 5.6
Sinking Fund Bond in case 2 year
99.633 100.908 ####### 103.702 107.518 ####### 101.021 111.908 114.228 ####### 0 1 2 3
####### ####### ####### ####### ####### 4
r (n, i 1, T ) r (n, i, T ) (T ) 2 fi n (T )
n i
Time-varying forward volatility lattice year
0
0.15 1
0.15 0.15 2
0.15 0.15 0.15 3
0.15 0.15 0.15 0.15 4
Outstanding amount at the beginning of each year
100 0.0
Remaining principal at the ending of each year
coupon
100 100 7.0
100 100 7.0
100 100 7.0
20 100 80 7.0
####### ####### ####### ####### ####### 4
81.906 83.408 84.940 86.277 87.472 88.690 5
Case 2: double-up at 4th, no double-up at 5th principal to be retired at each year
100 0.0
Remaining principal at the ending of each year
coupon
100 100 7.0
100 100 7.0
100 100 7.0
20 100 80 7.0
20 80 60 5.6
Sinking Fund Bond in case 1 year
99.633 100.896 ####### 103.665 107.449 ####### 100.945 111.783 114.031 ####### 0 1 2 3
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initial yield curve, lognormal spot volatility of interest rate, the number of partitions, time to maturity at each node, face value, 4 cases of principal repayment schedule, coupon rate, bond maturity, double-up sinking fund bond lattice ling " by Thomas S.Y. Ho and Sang Bin Lee, 2003, Oxford University Press
#######
92.144 93.834
Sinking Fund Bond in case 4 year convexity adjustment
99.633 ####### 95.558 100.915 ####### ####### 97.203 103.755 107.625 ####### ####### 98.796 101.155 112.143 114.616 ####### ####### 100.420 0 1 2 3 4 5 1.00000 1.98069 1.96175 1.94318 1.92496 1.98069 1.96175 1.94318 1.98069 1.96175 1.98069 1.90710 1.92496 1.94318 1.96175 1.98069
Double-Up Sinking Fund Bond Model reference number Version publication date author affiliation email address last revised date references Descriptions financial model class issuer/modeler model type risk sources risk distribution economic assumptions technical assumptions key words Links data financial models Inputs year initial yield curve (continuous compounding) initial discount function p(n) forward curve lognormal spot volatility (σS) f lognormal forward volatility (σ ) the number of partitions (m) time to maturity (T) at each node forward price delta (δ) face value coupon rate (annual compounding) bond maturity Outputs
Outstanding amount at the beginning of each year
99.633 100.904 ####### 103.718 107.557 ####### 101.079 112.017 114.419 ####### 0 1 2 3
####### ####### ####### ####### ####### 4
investment grade corporate bonds N/A sinking fund bond interest rate normal contingent claim model m=1 arbitrage-free interest rate model, contingent claim
© copyright THC 2003. All rights reserved by Thomas Ho 55 classification# 80304 Instructions 1.0 level basic May-03 Hanyang Financial Engineering Lab. Hanyang University input initial yield curve, lognormal leesb@hanyang.ac.kr 4 cases of principal repayme Nov-03 output double-up sinking fund bond Ch.8 of "The Oxford Guide to Financial Modeling " by Thomas S.Y. Ho and S
100 0.0
Remaining principal at the ending of each year
coupon
100 100 7.0
100 100 7.0
100 100 7.0
10 100 90 7.0
20 90 70 6.3
Sinking Fund Bond in case 3 year Case 4: no double-up at 4th and 5th year principal to be retired at each year
ri n (T )
ln Pi n (T ) T
0.065 0
Interest rate lattice year
0.09468 0.08469 0.07518 0.0748 0.06519 0.05568 0.0553 0.04569 0.03618 1 2 3
0.10476 0.08526 0.06576 0.04626 0.02676 4





n
100 源自文库.07 6
Double-up Sinking Fund Bond Lattice year Interim Calculations Case 1: double-up at 4th, double-up at 5th
99.633 100.896 104.757 103.665 107.449 109.675 100.945 111.783 114.031 114.395 0 1 2 3
####### =Min(case1,case2,case3,cas ####### ####### ####### ####### 4
principal to be retired at each year
Outstanding amount at the beginning of each year
http://www.federalreserve.gov/ 7. Bond Arithmetic, 8. Bond Model, 21. Extended Ho-Lee Model, 53. Callable
0 1 2 3 4 5 0.065 0.065 0.065 0.065 0.065 0.065 1.0000 0.9371 0.8781 0.8228 0.7711 0.7225 0.065 0.065 0.065 0.065 0.065 0.065 0 0.15 0.15 0.15 0.15 0.15 0 0.15 0.15 0.15 0.15 0.15 1 f s f (n 1) n 1 n 1 r (n 1) n 1 n r (n) s 1 0.9371 0.9371 0.9371 0.9371 0.9371 0.9371 1 0.98069 0.98069 0.98069 0.98069 0.98069
P (n 1) 1 n 1 n 2 1 1 n 1 2 i Pi n (1) n P (n) 1 n 1 1 n 2 1 n
Discount function lattice year
####### 0.91880 ####### 0.92793 0.93689 ####### 0.93707 0.94620 0.95534 ####### 0 1 2 3
####### ####### ####### ####### ####### 4
0.89142 0.90897 0.92687 0.94513 0.96374 0.98271 5 0.11494 0.09544 0.07594 0.05644 0.03694 0.01744 5 0.15 0.15 0.15 0.15 0.15 5