WWW.DISSERS.RU


...
    !

Pages:     | 1 ||

[,T ]e-r(T - ) t [, T ] r11 + r22 rT = -rf /T Cov(R1, RT ) = Cov(R1, 1R1 + 2R2) = 11 + S(t) 2 Cov(R1, R2) T K P (t) 2 r1T - Cov(R1, RT )(rT - rf ) - rf T = 0.

P (t) Ke-r(T -t) - S(t).

(r1 - rf )T = (rT - rf ) Cov(R1, RT ).

-t) Ke-r(T A(A, rA) B(B, rB) A < B t rA > rB A1 A A 2 T = 1A1 + 2A2 + 3 A3 1 = 0.3 2 = 0.4 3 = 0. ln K/S() + n t Cov(R1, RT ) = 230 Cov(R2, RT ) = 280 Cov(R3, RT ) = j0.

2 t T nt = T - A(0.067, 0.18) B(0.14, 0.32) F ln K/S() - (r - 2/2)(T - ) j0 - np.

0.09 Cov(RB, RT ) = 0.0007 T 2 t 0. npq n/0. A B ln K/s( ) - (r - 2/2)(T - ) j0 - np -d2.

npq nt (x) = 1 - (-x) b( j0, n, p) (d2).

A B 470 A 1. b( j0, n, p ) (d1) B 1 30% e-q(T - ) 20% t = T - ) - ) e-q(T eq(T = [,T ] S()e-q(T - ) t = [,T ] t = T -) er(T [,T ] = S()e-q(T - )er(T -) S0(t), S(t), F (t) 10% $20 $ 10% t (t) = 0, e-q(T -t), -1.

S t S S() S = St, T K [, T ] n t t 0 (T - )/n n S = S.

n S(T ) = S(0)eT S(T ) c n T j0 ln K/(S(t)dn) / ln(u/d) n j0 - np j0 - np b( j0, n, p) 1 -, b( j0, n, p ) 1 -, npq np q w(t) w(0) = x w(t1 +s)-w(t1) w(t2 +s)-w(t2) 1 (x) = e-t /2 dt - 2 u d n s t1 t2 s c = S()(d1) - Ke-r(T - )(d2), (t1, t1 + s) (t2, t2 + s) h > ln(S()/K) + (r + 2/2)(T - ) Wh(t) t = 0 h d1 =, T - 2h... W (0) = 0 Wh = Wh (k+1)h -Wh(kh) h ln(S()/K) + (r - 2/2)(T - ) d2 = = d1 - T -.

T - Wh - P 1/2 1/ Wh (k+ 1)h Wh(kh) x2 ex = 1 + x + +....

Wh M(Wh) = 0 D(Wh) = 2 u d p q h D(Wh) h ert - e t w(t) p =. Wh(t) h e t - e- t t Wh(t) h t + (r - 2/2)t t - (r - 2/2)t p, q.

[0, 1] h = 0.2 t 2 t j = 0 p + q = 1 n Cn(pu)j(qd)n-je-nrt j=j b( j0, n, p ) j n p S = Sw, c = S(t)b( j0, n, p ) - Ke-nrtb( j0, n, p).

w(t) > S(t + t) - S(t) /S(t) S $20 $100 P (t1) P(t2) t S(t) = S(t)t + S(t)w, t2 2-t1) M P (t2) = er(t M P (t1).

t M S(t + t) = S(t)ert.

p Y (t) q Y S(t+t) = S(t)u S(t+t) = S(t)d Y = at + bw, M S(t + t) = S(t)up + S(t)d(1 - p) a b w S(t)up + S(t)d(1 - p) = S(t)ert.

t [0, T ] T t [0, T ] ert - d p =.

t Y u - d u d Y (t) = Y (0) + at + bw(t) - bw(0).

ln(S(t + t)) - ln(S(t)) 2t t Y (t) u d Y bw 1 u = e t, d = = e- t.

M Y = at + b M w = at, u y c cd u c = e-2rt cuup2 + 2cudpq + cddq2, 1. cuu = max u2S(t) - K, 0 cud = max udS(t) - K, 0.cdd = max d2S(t) - K, 0. n 0 2 4 6 t n Y (t) a = 0.1 b = 0. t = 0.n j c = e-nrt Cnpjqn-j max ujdn-jS(t) - K, 0.

j= w M Y (t) = at + Y (0) M Y (2t) = j0 at+M Y (t) = a2t+Y (0) 0 uj dn-j S(t) > K j0 M Y (T ) = aT + Y (0).

ln(K/S(t)dn)/ ln(u/d) Y j j0 max ujdn-jS(t) - K, 0 = 0 bw j > jD(Y ) = b2 D(w) = b2t.

max ujdn-jS(t) - K, 0 = ujdn-jS(t) - K.

c Y (T ) n D Y (T ) = b2T.

j c = e-nrt Cnpjqn-j ujdn-jS(t) - K.

j=j w Y Y (t) t > Y (t) n n j j t c = S(t) Cn(pu)j(qd)n-je-nrt - Ke-nrt Cnpjqn-j.

Y (0) + at j=j0 j=j b2t n j Cnpjqn-j b( j0, n, p) j=j j0 n p p = pue-rt, q = qde-rt f(S, t) S(t)uu,c uu S S(t)u,c u t w S(t), c S(t)ud,c ud f f 1 2f f f = S w + S + 2S2 + t + (t).

S(t)d,cd S S 2 S2 t S(t)dd,cdd f(S, t) = ln S f 1 2f 1 f =, = -, = 0.

S S S2 S2 t t (t) t (t) = (t+t)e-rt (ln S) = - t + w.

(t) = S(t)+c c = c(t) ln S S(t)(u - d) cud - cdu S(t) - c = S(t) e-rt ln S(T ) - ln S(t) cu - cd cu - cd (-2/2)(T - t) 2(T - t) N(m, s2) ert - d u - ert c = e-rt(cup + cdq), p =, q =.

m s2 u - d u - d 2 ln S(T ) N ln S(t) + - (T - t), 2(T - ).

K S(t)u cu S0(t), S1(t),..., Sn(t), D1(t),..., Dm(t) Dj(t) cu = e-rt(cuup + cudq).

S0(t)... Sn(t) Si(t) i t cd = e-rt(cudp + cddq).

Dj(t) j t c cd u c(t) P (t) Si t dS0(t) = r(t)S0(t)dt dSi(t) = iSi(t)dt + iSi(t)dw.

S0 r(t) t S (t) t t + t S(t + t) S(t)u S(t)d u > 1 d < 1 c t + t K S(t)u, c u S(t+t) K c(t + t) S(t), c c(t + t) = max S(t + t) - K, 0 S(t)d, cd t 1 = 0(t), 1(t),..., n(t), n+1(t), n+m(t).

t + t S(t+t) S(t + t) = S(t)u S(t)u + cu 0... n S(t + t) = S(t)d t t + t S(t)d + cd (t) S(t)u + cu = S(t)d + cd.

(t) = 0(t)S0(t)+...+n(t)Sn(t)+n+1(t)D1(t)+...+n+m(t)Dm(t).

S(t)(u - d) =.

cd - cu d(t) = 0(t)dS0(t)+...+n(t)dSn(t)+n+1(t)dD1(t)+...+n+m(t)dDm(t).

t+t t+t (t) K > 0 (t) -K S(t)cu(u - d) S(t)(cud - cdu) t+t = S(t)u - =.

cu - cd cu - cd I 0 t0 [,T ] = S() - I er(T - ).

t1 > t0 (t1) 1 q% P (t1) > 0 > [,T ] = S()e(r-q)(T - ) 2 2/3 2 1/ 6 24 4 2/ 24 4 c(t) C6 (2/3)4(1/3)2 = 0, T 1 wt wt c(T ) = max S(T ) - K, 0.

P (t) T f 1 2f f f(t, w) = + t + w.

P (T ) = max K - S(T ), 0.

t 2 w2 w f 2f 1 f(t, w) = w2 f = 0 w = w = S (t) T 2 t w K c(t) P (t) 1 wt = wtw + t.

2 c(t) + Ke-r(T -t) = P (t) + S(t).

S(0) = $40 = 16% = 20% S(T ) 1/ t1 t2 S(T ) 1/ t1 0. t2 (t2) t = 0. (t2) ln S(T ) N(3.759, 0.142).

t2 t t2 t t2 S(T ) 0. 2-t1) t2 = er(t t1.

P ln S(T ) - M(ln S(T ))| 1.96 = 0.95.

ln S(T ) T 3.759-1.960.14 < ln S(T ) < 3.759+1.960.14 S(T ) [32.5, 56.6].

Y T = [,T ] F[,T ](t) Y = 2t + 3w.

T t 0.95 t T t r Y (0.75) m = 2 0.75 + Y (0) = 1.5 + Y (0) F[,T ](t) = [t,T ] - [,T ] e-r(T -t). 2 = 9 0.75 = 6. P{Y (0.75) > 0} = 0. Y (0.75) - m m F[,T ]() = 0 F[,T ](T ) = S(T )-[,T ] P > - = 0.95.

Y (0.75)-m N(0, 1) [,T ] Y (0.75) - m m m P > - =, [,T ] = S()er(T - ).

(x) (m/) = 0.95 F[,T ](t) m/ = 1.645 1.5 + Y (0) = t 1.645 6.75 Y (0) = 2. F[,T ](t) = S(t) - [,T ]e-r(T -t). 2.7738 1 C t 1 /(t) = e-x d x dC = Cdt + Cdw, t (t) t (t) t (t) t (t) 1.5 = 1.0.0 0.500000 1.0 0.841345 2.0 0.977250 3.0 0. C0 = 0.1 0.539828 1.1 0.864334 2.1 0.982136 3.1 0. C 0.0.2 0.579260 1.2 0.884930 2.2 0.986097 3.2 0. C 0.3 0.617911 1.3 0.903200 2.3 0.989276 3.3 0.0.4 0.655422 1.4 0.919243 2.4 0.991802 3.4 0.dC = Cdt + Cdw, 0.5 0.691462 1.5 0.933193 2.5 0.993790 3.5 0.0.6 0.725747 1.6 0.945201 2.6 0.995339 3.6 0.999841 1.1 = 1. 0.7 0.758036 1.7 0.955435 2.7 0.996533 3.7 0. 0.95 0.8 0.788145 1.8 0.964070 2.8 0.997445 3.8 0. 0.9 0.815940 1.9 0.971283 2.9 0.998134 3.9 0. S(t) S = t + w.

3 = 2 = 3 2 3/5 = 3 = 4 S(0) 2 2/5 S S S(6) S 36.5% 1.04 3/ S(0) = $40 1.06 2/ = 18% 20% S ln S(T ) T = 0.S 99% S(T ) V1 V 2 V6 - P{Vi = 1} = 1/2 X V1 + V2 +... + V V1 V 2 V8 P{Xi = -1} = 1/2 P{Xi = 1} = 1/ r = r(t) X1 + X2 + X3 + X4 = 0 X1 +... + X8 = S twt wt 2-t1) S0(t2) = er(t S0(t1)

Pages:     | 1 ||



2011 www.dissers.ru -

, .
, , , , 1-2 .