-
(
(
)
50
-
50
60
50
6010)
40
0
(S X)+ max{S X, 0}
-
A =0
> 0
-
4
max{0, }
-
-
2
-
2
0 S0
1 S1
n Sn2
S2
(0,0)
(1,0)
(2,0)
(1,1)
(2,2)
(2,1)
(3,0)
(3,1)
(3,2)
(3,3)
u
d
d2
u2
ud 1-p
dS
ud = 1
p
uS
-
2
0 S0
1 S1
n Sn2
S2
(0,0)
(1,0)
(2,0)
(1,1)
(2,2)
(2,1)
(3,0)
(3,1)
(3,2)
(3,3)
i
-
O(n2)
Hull-White(1993), Neave (1997)
Chalasani et al.(1999), Dai et al.(2002)
-
(0,0)
(1,0)
(2,0)
(1,1)
(2,2)
(2,1)
(3,0)
(3,1)
(3,2)
(3,3)
-
(0,0)
(1,0)
(2,0)
(1,1)
(2,2)
(2,1)
(3,0)
(3,1)
(3,2)
(3,3)
-
(0,0)
(1,0)
(2,0)
(1,1)
(2,2)
(2,1)
(3,0)
(3,1)
(3,2)
(3,3)
-
O(n4/)
-
(0,0)
f0,0(S0)
T=S0+S1++Si
-
T(n+1)X
1/(n+1)
0,0S
0,1S
1,1S
0,2S
1,2S
2,2S
0,nS
nnS ,
)(, Tf jn0,1nS
1,nS
-
jiS ,1+
1,1 ++ jiS
jiS ,
-
T(i+1)X
1/(i+1)
-
T
-
T
-
2
(n-1)0
T
T
T
p
(1-p)
+
-
T
)(, Tf ji
T
)(, Tf ji
-
)(, Tf ji
)()1( , Tf ji+)(, Tf ji)()1( , Tf ji+
(n-1)0 (1+)n < 1+
n2/ =
1 1+
-
1
0a
0)1( a+
)(, Tf ji
)()1( , Tf ji+
1a
1)1( a+0)1( a+
1)1( a+
2a
2)1( a+
2)1( a+
-
)(, Tf ji
)()1( , Tf ji+
0)1( a+
0a
0)1( a+
1a
1)1( a+
-
0.995
1
1.005
1.01
1.015
1.02
1.025
1.03
0 5 10 15 20 25 30
n
Alg1
Alg2
=0.2
1
-
)(, Tf ji
)()1( , Tf ji+
)(, Tf ji
)()1( , Tf ji+
-
0
50
100
150
200
250
300
0 10 20 30 40 50 60 70 80
n
sec Alg1
Alg2
1
-
O(n4/)
