加載中. ..
PDF
103
F4607
________________
25
( )
10
ydxdy
?y
4
t
t
tdzdt
S
dS
t
dz
Weiner
0
t
dzE
tdzVar t
drift
diffuse
Ito 7
random walk Weiner 6
T
ZTTr
TeSS
2
2
1
0
Z
KSP T
8
S 100 K 100
u=1.1181 d=0.9354 4.88%
5
8
12
(non--dividend--paying) (underlying asset)
(European call option) A B
S=50
(geometric Brownian motion)
(risk-free annual rate of interest) =5%
(volatility) =30%
A
1T
65K
5969.0)(,7405.0)( 11
dNdN
2
12
S
ln r T
K
dT
21
d d T
2/2
() 2
w
de
N d dw
B
0.5T
55K
Delta 0.5931,Gamma 0.0436,Vega 16.36
A 5
A B
Delta 0,Gamma 50, Vega 20,000
A B (risk free) Gamma Vega
8 Delta 5
Delta 7
0
S
T
T
S
(risk-free annual rate of
interest)
r
T
(forward contract)
0,T
F
0,T
F
0
S
(arbitrage) 4
6
()
T
ES
T
S
()
T
ES
0
S
(risk neutrality)
4
0
S
=100
r
1%
1T
80 120
p
p
6
T
0
uS
0
dS
ud
0
uS
p
p
5