財務統計.doc

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1 . (ucerai) (asse) (predicable) (risk) (derivaives) (o arbirage) (risk eural probabiliy) (discoued prices) (marigale) (sochasic calculus) ( (opio)) 5 (reur) (radom walk) 3 (efficie marke) 4 (Europea opio) ( ) 5. 3 Cowles (933), Workig (934),Cowles Joes (937) R l,,, (.) (rhyhms) (cycles) (reds) 5 Kedall (953) (Royal aisical ociey) Kedall ( )

2 he demo of chace drew a radom umber ad added i o he curre price o deermie he ex price R l (radom walk) Bachelier (9) ( ) ( ) ( ) ( ),,Λ k ( ) k + ζ + ζ + Λ + ζ k, (.) ( ζ ) i σ, σ E ( ) ( ) ( k ), Var( k ) σ ( k ). (.3) k, >, Bachelier (.) ( ), ( ) lim ( ) W, EW, EW + σ, (.4) W W ), ( W ) (sadard Browia ( moio) Wieer ( B&T TOP3 ) (upredicable) i i i+ i+ i i + Ri l Ri (.5) i i ((.5) l( x) x )..3 (oise) i

4 .3 ( ).4 ( φ ( x) e π x / Ri R ) R M R R i, M R ( Ri M M i M i R), (.6) Reur.4 4

5 i Ri l mea + sadard deviaio φ (.7) i µ k + σ kφ. (.3)(.4) k, W W ), ( e ( µ σ ) + σw, (.8), amuelso(965) ( ) (geomeric Browia moio) (.8).5 (.8) K ( ) : (a) (b) (c) 5

6 (a)(b)(c) (efficie marke) (a) (b) K % ( (3.) µ > ) Bachelier (iformaio) Fama (l97) * V < s { V } a.s. (3.) E * s s {, [, T]} 6

7 (iformaio flow) (3.l) {,, [, T]} (marigale) (i) ] [, T σ -(σ -field) (ii) s > (iii) - (iv) E( ) a.s. s > s s (iv) (iv) s > (3.) (iv) σ - ) E( (weak form) (semi-srog form) ( ) ) (srog form) ( l l + µ + ε, (3.) µ ε (i) { ε, } E ε, Var( ε ) σ (ii) { ε, } ( ) (iii) { ε, } s Cov ( ε, ) ε s (ii) (i) ( ) 7

8 3. (Markov process) (3.) (a) (b) (a),, 3, Λ, P{ + < x (,, Λ, ) A, a} P{ + < x a} (3.3) a R A R (3.3),, Λ (Markov process), (a) 3.3,, Λ ζ ζ (marigale differece) E( ζ ) a.s. ζ i i ζ, (3.4) ζ g(,, Λ, ),, Λ, Y g, Λ, ) ζ. (3.5) ( E( Y ) E( g ζ ) g E( ζ ), a.s. (3.6) Y i Z Y i, (3.7) Z ζ g ) Y g ζ g ( Z ( ( g g, Λ, ) ) g 8

9 ( )? T T { T } T (soppig ime) * T ; (3.8) * T > T. T * T,,Λ T < Λ, { T } < T ** T ** Λ T,, T ** T 3.4 A. B. (cosa) C. D. A +τ +τ E( + τ J ) J E ( + τ J ) > a.s. ) E( + τ J (buy ad hold) (K ) 9

10 (filer rule) 3% ( ) 3% K A A B R + τ ( + τ ) / {,, Λ, } R, R, Λ, R } { E( R+ τ, Λ, ) E( R+ τ R, Λ, R ) + τ R,, R ) α + H : β. (3.9) E( R Λ βr. (3.) (3.9)(3.) (auoregressive model) C D 4. ( (call opio)) ( (pu opio)) 973Blackcholes(973)Mero(973) (closed-form soluios) Black choles Mero (uderlyig asse) (raioal price) ( ) (.8) d µ d + σ dw, (4.)

11 µ σ (volailiy) W ) V ( (/) x (/) σ T+ σ x rt e V ( C) [( e T + e K) ] dx, (4.) π K T r (4.) V C rt ( C) Φ( d+ ) Ke Φ( d ), (4.3) log( / K) + ( r ± σ ) T Φ d ± σ T rt (call-pu pariy)v ( C) V ( P) Ke, V ( ), P V rt ( P) Ke Φ( d ) Φ( d + ), (4.4) Black-choles T T V d ± (log( / K) + ( r ± σ )( T )) / σ r( T ) V ( C) Φ( d ) Ke ( d ), (4.5) + Φ T (4.3) V ( C ), K,T,r σ d ± Φ( d ± ) V ( C) r( T ) Ke (forward corac) (cerai) T K s ( ) T r( T ) ( ) > K d +, e ± ± V ( C) K < K, d,( C),T, V ( C) ( K ) + V Black-choles (4.3) µ µ Black-choles (PDE) µ µ (biomial arbirage) ( ) Black-choles µ

12 Black-choles (derivaives) (derivaive) (4.) e σ ( µ ) + σ W. (4.6) l f f ( x) ( µ σ ) + σx x (4.6) µ σ (4.3), K,T r σ f (x) f f (x) σ ( ) µ 5. (a) ( ) (b) (derivaive) (derivaives) ( ) (dilemma) ( ) ( ) sochasic volailiy models, (G)ARCH models, jump diffusio models (quaiaive fiace) (America opio)( ) (exoic opios)( (Wall ree) ) ( ) (fiacial egieerig) 3 Hull () ( )

13 Pliska () ( ) hiryayev (999) Bachelier, L. (99). Théorie de la spéculaio. Aales de l'ecole Normale upérieure, 7, -86. Black, F. ad choles, M. (973). The pricig of opios ad corporae liabiliies. Joural of Poliical Ecoomy, 8, Cowles, A. (933). Ca sock marke forecasers forecas? Ecoomerica,, Cowles, A. ad Joh, H. E. (937). ome a poseriori probabiliies i sock marke acio. Ecoomerica, 5, Fama, E. F. (97). Efficie capial marke: A review of hisory ad empirical work. Joural of Fiace, 5, Hull, J. (). Opios, Fuures, ad Oher ecuriies. 4 h ed. Preice Hall, New Jersey. Kedall, M. G. (953). The aalysis of ecoomic ime-series. Par. Prices. Joural of he Royal aisical ociey, 96, -5. Mero, R. C. (973). Theory of raioal opio pricig. Bell Joural of Ecoomics ad Maageme ciece, 4, Pliska,. R. (). Iroducio o Mahemaical Fiace: Discree Time Model. Blackwell, Grea Briai. amuelso, P. A. (965). Proof ha propery aicipaed prices flucuae radomly. Idusrial Maageme Review, 6, hiryayev, A. N. (999). Esseials of ochasic Fiace: Facs, Models, Theory. World cieific, igapore. Workig, H. (934). A radom-differece series for use i he aalysis of ime series. Joural of he America aisical Associaio, 9, -4. 3

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