微观经济学分析

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5 years ago
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1 A

2 100 S S

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7 A S

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10 1 ( ) θ 2 W 0 3 R j i i i i

11 j i

12 ( ) 7 4 i j j i

15 S 3 V S

16 R

18 A.3 (Moigliani) (Miller) MM MM (Stiglitz)

20 θ[0, 1] W 0 0 W 0 θ U=W 1 W 1 W 0 W 0 W

21 K y=f(k)>0 r w f(k)(1+r)k+w w w=

22 p p=θ W 0 >K W 0 θ r) K] (1 [f(k) r) 2r(1 r) (1 W B 0 + +

23 K=50r=0.1f(50)=60 B 0 W K= f(50) f(50)=55 B 0 W 0 f(50)=67.3 B 0 W 50.3 K=50 p=θ f(k)

25 A.4 (Cox)(Ross) (Rubinstein) 1979 (Black) (Scoles)1973 B-S Cox, J. C., S. A. Ross an M. Rubinstein Option Pricing: A Simplifie Approac. Journal of Financial Economics 7: Black, F. an M. Scoles, Te Pricing of Options an Corporate Liabilities. Journal of Political Economy 81 (3):

26 B-S B-S u-1-1 S us S r u>1+r> C C u us C S K C u =max[0, us-k]c =max[0, S-K] A.1

27 A B AS+B AuS+(1+r)B us AS+(1+r)B S A B A B us S AuS+(1+r)B=C u AS+(1+r)B=C. r) )(1 (u C uc B, )S (u C C A u u + = = A B C C=AS+B= r) /(1 ) C u 1 r u C u r 1 ( r) )(1 (u C uc u C C u u u = + +

28 1+ r p= u u r1 1-p= u C=[pC u +(1-p)C ]/(1+r) u>1+r> 1>p>0 p p 1-p C p p(us)+(1-p)(s)=(1+r)s A.2 A.2 C uu C C u C u C u C u =[pc uu +(1-p)C u ]/(1+r)

29 C =[pc u +(1-p)C ]/(1+r) C=[pC u +(1-p)C ]/(1+r) C=[p 2 C uu +2p(1-p)C u +(1-p) 2 C ]/(1+r) 2 ={p 2 max[0, u 2 S-K]+2p(1-p)max[0, us-k]+(1-p) 2 max[0, u 2 S<K C=0 2 S-K]}/(1+r) 2. u 2 S>K>uS C=p 2 (u 2 S-K)/(1+r) 2 us>k> 2 S C=[p 2 (u 2 S-K)+2p(1-p)(uS-K)]/(1+r) 2 K< 2 S C=[p 2 (u 2 S-K)+2p(1-p)(uS-K) +(1-p) 2 ( 2 S-K)]/(1+r) 2 n n n! C = [ j= 0 j!(n p j)! j (1 p) n j max(0, u j n j S K)]/(1 + r) j S*=u j n-j S K a u a n-a S>K a a log[k/(s n )]/log(u/) j<a ja max(0, u j n-j S-K)=0 max(0, u j n-j S-K)= u j n-j S-K n

30 = S[ n j= a C = n [ j= a n! p j!(n j)! n! j!(n j p j)! (1 p) (1 p) j n j j u n j n j (1+ r) n (u j n j ] K(1+ r) S K)] /(1+ r) n [ n j= a n n! j!(n p j)! j (1 p) p*=pu/(1+r)p*>01-p*=(1-p)/(1+r)>0 0<p*<1 n n n! j n j n n! C = S[ p* (1 p *) ] K(1 + r) [ p j!(n j)! j!(n j)! j= a =S[a; n, p*]-k(1+r) -n [a; n, p] j= a j n j (1 p) [a; n, p]n p a B-S T n n=t/ 0 n n=t r* T (1+r*) T -1 r T n T (1+r ) n -1 (1+r ) n =(1+r*) T. r T e r =1+r* r=log(1+r*) 1+r =e r (1+r ) n =e rn =e rt =(1+r*) T C=S[a; n, p*]-k(1+r ) -n [a; n, p] n =S[a; n, p*]-ke -rt [a; n, p] n B-S ] n j ]

31 C=SN( 1 )-Ke -rt N( 2 ) N( ) = = 1 S [log T K T + (r+ n 2 ) T] 2 [a; n, p*]n( 1 ) [a; n, p]n( 2 ) B-S [a; n, p] [a; n, p]=p(ja)1-[a; n, p]=p(ja-1) j n p 1 1-p 0j E(j)=npVar(j)=np(1-p) j E(j) a1 E(j) P(j a1) = P( ) = P( Var(j) Var(j) j np np(1 p) n j np a 1 np a1 np P( ) N( ) np(1 p) np(1 p) np(1 p) a1 np ) np(1 p) j np a1 np a1 np [a; n, p]=1- P( ) N( ) np(1 p) np(1 p) np(1 p) n a1 np 2 np(1 p) [a; n, p]n( 2 ) a log[k/(s n )]/log(u/)

32 a-1= log[k/(s n )]/log(u/)-ε =[log(k/s)-nlog-εlog(u/)]/log(u/) 0<ε<1 2 p)[log(u/)] np(1 nplog(u/) εlog(u/) nlog log(k/s) p) np(1 np 1 a = rt/n T/n rt/n r e, e e u + + = = = >0 u=u=e 2r =(1+r ) 2 e, e u = = u=u=1 u u>1+r> B-S u r r r r e e e e u ) r (1 p + = + = '

33 1 e 1 1 e 1 e 2 + = = r r p( ) f(x) f(x)=f(0)+f (0)x p(0)=1/2 2 1) (e e ) p ( + = p (0)=-/4 n p u n ) 2 / logr ( p logr 2logr 2 1 p

34 u log(u/) = 2 n 0log(u/)0 log = r n 0 l og(k/s) nlog εlog(u/) nplog(u/) 1 log(k/s) n(r ) n( ) K K log (r ) n = log (r )T S 2 S np(1 p)[log(u/)] n( )( + )( = n n = T T T 4 4 n 2 a1 np log(k/s) (r / 2) T = np(1 p) T [a; n, p]n( 2 ) p*=pu/(1+r ) e 1 p* = pe = + e [a; n, p*]n( 1 ) B-S 4 2 ) 2

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26 D00 27 D02 28 D03 29 D05 30 D06 31 D10 32 D12 33 D13 34 D14 35 D16 36 D17 37 D18, 38 D19 39 D20 40 D21 41 D22 42 D23 43 D24 44 D25 45 D26 46 D27 47 2 (600 ) 1 A03 2 A18 3 A23 4 A38 5 A39 6 A41 7 A59 [ ] 8 B15 9 B16 10 B17 11 B18 12 B19 13 B30 14 B37 15 C47 16 C50 17 C53 18 C54 19 C56 20 C60 21 C62 22 C64 ( ) 23 C65 24 C66 25 C71 16 26 D00 27 D02 28