38.OptiononFowardContract1204
year
01234initial yield curve
0.0600.0600.0600.0600.060initial discount function p(n) 1.00000.94180.88690.83530.78661-year forward curve 0.0600.0600.0600.0600.060lognormal spot volatility (σS)00.20.20.20.2lognormal forward volatility (σf)the number of partitions (m)
forward price 0.94180.94180.94180.94180.9418
delta (δ)10.9762860.9762860.9762860.976286exercise price 0.8
Outputs
0.00000.00050.00110.01380.02910.0609option on forward contract lattice
0.03320.05660.08970.1251year
1
2
3
Interim Calculations
convexity adjustment of 1-year bond
1.00000 1.97629
1.95313 1.93053 1.908461.97629
1.95313 1.930531.97629
1.953131.97629
numerator of convexity adjustment at time n 1.0000 1.9763 3.86007.4518denominator of convexity adjustment at time n
1.9763 3.86007.451814.2214year
1
2
3
4
0.89660.90790.91840.91920.92990.94070.93050.94150.95250.96351-year discount function lattice
0.94180.95310.96440.97570.9869year 0
1
2
3
4
0.109150.096650.085150.084290.072650.061150.072070.060290.048650.037151-year interest rate lattice
0.060000.048070.036290.024650.01315year
1
2
3
4
0.20.20.20.20.20.2Time-varying forward volatility lattice
0.20.20.20.2year
1
2
3
4
0.64400.61410.70890.60050.69240.78030.60200.69350.78070.85898-year zero coupon bond price
0.61880.71210.80090.88020.9455year 0
1
2
3
4
0.8966
0.82390.9184
0.77590.86440.9407
0.74890.83380.90690.9635 5-year zero coupon bond price0.74080.82440.89610.95150.9869 year01234
003. All rights reserved by Thomas Ho Company, New York, NY. USA www. https://www.wendangku.net/doc/8b5803198.html, tom.ho@https://www.wendangku.net/doc/8b5803198.html,
Modeling
del, 21. Extended Ho-Lee Model,
567
8910111213140.0600.0600.0600.0600.0600.0600.0600.0600.0600.0600.74080.69770.65700.61880.58270.54880.51690.48680.45840.43170.060
0.0600.0600.0600.0600.0600.0600.0600.0600.0600.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.2
0.94180.94180.94180.94180.94180.94180.94180.94180.94180.94180.9762860.9762860.9762860.9762860.9762860.9762860.9762860.9762860.9762860.976286
1.88692 1.86589 1.84535 1.825311.90846 1.88692 1.86589 1.845351.93053 1.90846 1.88692 1.865891.95313 1.93053 1.90846 1.88692
1.97629 1.95313 1.93053 1.90846
1.97629 1.95313 1.93053
1.97629 1.95313
1.97629 14.221426.834750.07059
2.3977 26.834750.070592.3977########
5678
0.8516
0.86280.8723
0.87410.88380.8935 0.88530.89530.90530.9152 0.90680.91710.92730.9374 0.92890.93930.94980.9602 0.95140.96210.97290.9835 0.97450.98550.9965 1.0074 0.9982 1.0095 1.0207 1.0319
5678
0.16060
0.147520.13660
0.134590.123520.11260 0.121800.110590.099520.08860 0.097800.086590.075520.06460 0.073800.062590.051520.04060 0.049800.038590.027520.01660 0.025800.014590.00352-0.00740 0.00180-0.00941-0.02048-0.03140
5678
0.2
0.20.2
0.20.20.2 0.20.20.20.2 0.20.20.20.2 0.20.20.20.2 0.20.20.20.2 0.20.20.20.2
5678
1.0000
0.8628 1.0000
0.76330.8838 1.0000 0.69240.80090.9053 1.0000 0.74410.84030.9273 1.0000 0.79970.88160.9498 1.0000 0.85940.92490.9729 1.0000 0.92350.97040.9965 1.0000 0.9925 1.0181 1.0207 1.0000
5678
1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 5 0.6924 0.7441 0.7997 0.8594 0.9235 0.9925 5
https://www.wendangku.net/doc/8b5803198.html,
1516
0.0600.060
0.40660.3829
0.060
0.20.2
0.2
0.9418
0.976286