1 2 A A 1. ([1]3 3[ ])
2 A A 3 A 2. A [2] A A A A 4 [3]
Xi 1 1 2 1 () () 1 n () 1 n 0 i i = 1 1 S = S +! X S ( ) 02 n 1 2 Xi 1 0 2 ( ) ( 2) n ( 2) n 0 i i = 1 2 S = S +! X 0 k Xip 1 (1-p) 1 ( ) n n k Pr % S 2 = k/ = C p ( 1 -p) k n - k A( ) [2] 1 A p n A r Pr Pr = ncr p ( 1 - p) r n - r 2 3 Xi u (u>0), d (d>0) 3 Xi ( ) ( 3) n ( 3) n 0 i i = 1 3 S = S % X k 0 ( 3) ( 3) ( - ) k n - k n 0 k n k Pr % S = S u d. = nck p ( 1 -p) 3 4 Xi log u, log d ln S S ( 4) n ( 4) 0 n =! X i = 1 ( 4) i
( ) ( 4 ) n ( 4 ) n 0 i i = 1 4 S = S exp d! X n 4 e A A 1 1 A ( B)( C) 1 [2] U A P(A) P( A) A = U [4] P A) P( )=1 B P( B) $ 0 3 3 B) {An} P(, A ) =! P( A ) P n = 1 n n = 1 n [5]
A [6] EXCEL [7] [4] [8] Shreve [9] [10] [10] 2 A A A ()
[2] [11] WEB [12, 13] 3. ( ) 3
15 3 {1,2,3,4,5,6} 6 { } 2 1 3 2 { } 3 1,2,3,4,5,6, 2 2
( 1 2) 2 3 1 10 A, B, C 10 A 5 B 3 C 2 3 A 2 C 1 A B, C A: 50 %, B: 30%, C: 20% 1 A 2 C 1 A 2 C U ( 50, 50 ) A1 A2 U 10 3 () 10C3 A 2 C 1 5C2 2C1 U 10C3
2 2: 2 6 2 3 2 6 U 36 A 41/9 2 1/9 3 3 3 2 3 2 1 A 1 A 1
7 3 3 ( ) U 3 7 7C3 A 4C2 3C14C2 3C1 7C3 4. 2 A A
[1] Luenberger, D.G., Investment Science. 1998: Oxford University Press. [2], A. 2003:. [3],. 2009:. [4],. (. 1999:. [5],. 2004:. [6],. 2005:. [7],. EXCEL 1. 1995:. [8],. 5. 2003:. [9] Shreve, S.E., Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. 2004, New York: Springer- Verlag [10],. 2002:. [11], A. 1998:. [12] (, CFV21. http://www.cfv21.com/math/probability.htm (2010 7 27 ). [13],. http://kakuritsu.hp.infoseek.co.jp/mokufr.html (2010 7 27 ).