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Urey
04-28-2004, 03:57 AM
I think they are essentially the same questions requiring the application of the knowledge in the book "Valuation of Interest-Sentive..." Chapter 3, Page 26~39. But I just cannot get the right answer. Please point out the mistakes in my calculation:

2002.MC.28
1+γ=exp(0.20)=1.2214
r1u=0.06*1.2214=0.0733
r1d=0.06/1.2214=0.0491
r2u=0.06*1.22142=0.0895
r2m=0.06*1.2214/1.2840=0.06
r2d=0.06/1.22142=0.0402
Short rate Cash out-flow
1 2 3 1 2 3
0.0895 -0.95
0.0733 0
0.06 0.06 0 0
0.0491 0.09
0.0402 0.98
Thus the price of the floor:
[(-0.95/1.0733/2+0)+ (0.98/1.0491/2+0.09)]/1.06/2=0.0540
But the answer is C: 0.328

2001.MC.26
1+γ=exp(0.25)=1.2840
r1u=0.04*1.2840=0.5136
r1d=0.04/1.2840=0.3115
r2u=0.04*1.28402=0.0659
r2m=0.04*1.2840/1.2840=0.04
r2d=0.04/1.28402=0.0243
Short rate Cash flow
1 2 3 1 2 3
0.0659 0
0.5136 0
0.04 0.04 0 0
0.3115 0.385
0.0243 1.07
Thus the price of the floor:
(1.07/1.03115/2+0.385)/1.04/2=0.4345
But the answer is C: 0.363

Thank you !

Urey
04-28-2004, 04:04 AM
Sorry. It seems that the format has some problems. So I re-post my calculation here:

2002.MC.28

1+γ=exp(0.20)=1.2214
r1u=0.06*1.2214=0.0733
r1d=0.06/1.2214=0.0491
r2u=0.06*1.22142=0.0895
r2m=0.06*1.2214/1.2840=0.06
r2d=0.06/1.22142=0.0402

Short rate
1: 0.06
2: 0.0491, 0.0733
3: 0.0402, 0.06, 0.0895

Cash Out-flow
1: 0
2: 0.09, 0
3: 0.98, 0, -0.95

Thus the price of the collar:
[(-0.95/1.0733/2+0)+ (0.98/1.0491/2+0.09)]/1.06/2=0.0540
But the answer is C: 0.328

2001.MC.26

1+γ=exp(0.25)=1.2840
r1u=0.04*1.2840=0.5136
r1d=0.04/1.2840=0.3115
r2u=0.04*1.28402=0.0659
r2m=0.04*1.2840/1.2840=0.04
r2d=0.04/1.28402=0.0243

Short rate
1: 0.04
2: 0.3115, 0.5136
3: 0.0243, 0.04, 0.0659

Cash Out-flow
1: 0
2: 0.385, 0
3: 1.07, 0, 0

Thus the price of the floor:
(1.07/1.03115/2+0.385)/1.04/2=0.4345
But the answer is C: 0.363

Thank you!

torrent
04-28-2004, 04:10 AM
Use the multiplicative binomial mode.

ru=r(1+gamma)^(1/t)
rd=r/(1+gamma)^(1/t)

They provided the formula in both questions.

Urey
04-28-2004, 10:05 AM
I do use the formula in my calculation. For example,

2002.MC.28
1+γ=exp(0.20)=1.2214

By applying "ru=r(1+gamma)^(1/t)", I have the following

"r1u=0.06*1.2214=0.0733"

How much is t? Isn't it 1?

BC
04-28-2004, 10:57 AM
I think we may have talked about 28 two years almost two years ago and come to the conclusion that the SOA had messed up - that they actually added the values at the two nodes rather than taking the difference.

See Here:

http://actuary.ca/phpBB/viewtopic.php?p=83175&highlight=#83175

torrent
04-28-2004, 11:45 AM
Short rates:

1+γ=1.2
r1u=0.06*1.2=0.072
r1d=0.06/1.2=0.05
r2u=0.06*1.2*1.2=0.0864
r2m=0.06*1.2/1.2=0.06
r2d=0.06/(1.2*1.2)=0.04167

V=(0.64*0.5*0.5) / (1.072*1.06) + (0.833*0.5*0.5) / (1.05*1.06) = 0.328

Dr T Non-Fan
04-28-2004, 02:37 PM
I think we may have talked about 28 two years almost two years ago and come to the conclusion that the SOA had messed up - that they actually added the values at the two nodes rather than taking the difference.

See Here:

http://actuary.ca/phpBB/viewtopic.php?p=83175&amp;highlight=#83175
Wow, was I wrong about Rachel and Joey!

BC
04-28-2004, 03:05 PM
Maybe, but Joey is getting his own show, so it still could be in the future...

Dr T Non-Fan
04-28-2004, 04:16 PM
No. Ross and Rachel will get together. Unless, of course, Friends has become a drama instead of a comedy. Don't want any sad endings. Maybe Gunther could die. Or Gunther gets Rachel.