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1 Sock Volailiy Models and he Pricing of Warrans Hong & Li 005 Absrac This paper used a lo of popular volailiy models o sudy he dynamic behavior of underlying sock and hen used Hong & Lee (005) nonparameric specificaion es o compare he model specificaion errors of differen models. Based on he resul of volailiy esimaiesimaion, we used he Mane-Carlo simulaions o price Baogang warran, Chinese firs Warran afer he reform of sock marke, and compare he pricing resuls of differen models. The pricing resuls showed ha Baogang Warran is seriously overpriced. There is a srong manipulaion in he marke. We sudied some possible insiuional reasons for such manipulaion and proposed some policy suggesions in he end. Key Words: Warrans Pricing, Jump, Disribuion, Specificaion Tes
2 Black & Scholes (973) (Duan, 995) volailiy cluseringleverage effec Engle (98) ARCH Bollerslev (986) ARCHGARCH Engle, Lilien & Robbins (987) ARCH-MNelson(99), Zakoian (994) EGARCHTGARCH() IPO (Ball & Torous (983), Vlaar & Palm (993), Das (00)) (Jump) 3 (GED) (00) (994), (998), (998), (999), (000) Galai & Schneller (978), Schulz & Trauman (989,994) Corunhy & Galai (99) GARCH Hong & Li (005) Hong & Li005
3 GARCH GARCH EWMA TGARCH GARCH-M 3 GARCH TGARCH GARCH-M 4 GARCH- TGARCH- GARCH-M- µ ( r, θ ) σ ( r, θ ) (a) µ σ GARCH µ EWMA µ TGARCH µ EGARCH µ (b) GARCH h ln h h h h h = α + αξ + β h = λξ + ( λ) h h h = α + ( α + ϕd ) ξ + β h = α + α ξ / h + βξ / h + β ln h GARCH-M GARCH TGARCH GARCH µ δ + h µ + Jdq J ~ N( ϑ, γ ) (c) (Jump) dq ~... i i d B() q µ + Jdq J ~ N( ϑ, γ ) dq ~ i.. i d. B( q ) µ + δ h + Jdq J ~ N( ϑ, γ ) h h h h = α + αξ + β h = α + αξ + β h h h = α + ( α + ϕd ) ξ + β h h h = α + αξ + β h dq ~... i i d B() q (d)
4 GARCH µ TGARCH µ h h = α + αξ + β h h h = α + ( α + ϕd ) ξ + β h GARCH-M µ δ + h h h = α + αξ + β h r = µ ( r, θ) + ξ θ ξ σ( r, θ) z (a), (b), (c) z ~... iid N(0,) (d) z ~ ( v) = v+ z Γ ( )( + ) v () = v v Γ vπ v+ Hong & Li (005) Hong & Li (005) { r } P 0 ( x, y, s) r s y x θ 0 θ { p( x, ys,, θ ) = P( x, ys, )} 0 0 { r } n τ τ = Z ( θ ) r τ ( τ ) Z ( θ) = px (, τ x,( τ ), θ) dx τ =,, n τ θ 0 θ { p( x, ys,, 0) P0( x, ys, )} θ = { Z ( 0)} n τ = Zτ θ τ= iid.. U(0,) Hong and Li (005) U (0,) { Zτ, Zτ j } g j ( z, z) gˆ j ( z, z) g j ( z, z) gˆ j ( z, z) n ˆ ˆ j = h τ h τ j τ = j+ gˆ ( z, z ) ( n j) K ( z, Z ) K ( z, Z )
5 x y h k( )/ k( u) du, x [0, h] h ( x/ h) x y Kh( x, y) = h k( ), x [ h, h] h ( x) / h x y h k( )/ k( u) du, x [ h,] h k() i [,] k( u) du =, uk( u) du = 0 ukudu ( ) ( u ) < 5 ku ( ) = ( u) X I 6 n i ( u ) i= I Z ˆ Z ( ˆ ) τ = τ θ ˆ /6 θ θ 0 h= SˆZ n S ˆZ { Z } n τ τ = gˆ j ( z, z) M ˆ ( j) M ˆ ( j) Q ˆ( j) Mˆ j g z z dzdz ( ) = [ ˆ j (, ) ] 0 0 Qˆ ( j) = [( n j) hmˆ ( j) A ]/ V 0 / h 0 b 0 h = + 0 b 0 = [ [ ( + ) ( ) ] ] A ( h ) k ( u) du k ( u) dudb V k u v k v dv du Hong & Li (005) ˆ ( ) d Q j N (0,) { Z ( 0)} n τ = Zτ θ τ= iid.. U (0,) ˆ( p Q j)
6 MLE BHHH GUASS6.0, GARCH GARCH GARCH-M TGARCH GARCH EWMA EGARCH GARCH % GARCH GARCH GARCH 3 GARCH Hong & Li (005) 3 3 Q ˆ( j ) j= j=5 j=0 j= j=5 j= GARCH-Jump GARCH TGARCH-Jump EWMA GARCH-M-Jump TGARCH GARCH EGARCH TGARCH GARCH-M GARCH-M
7 Q ˆ( j ) GARCH Q ˆ( j ) GARCH EWMA Q ˆ( j ) GARCH EWMA GARCH Q ˆ( j ) GARCH TGARCH GARCH-M Q ˆ( j ) GARCH- TGARCH- GARCH-M- 4 4 Galai & Schneller (978), Schulz & Trauman (989,994) Corunhy & Galai (99) max(0, S X) S 0 = X=4.5 r f =0.05 (005 8 ) T= T _GARCH_jump 0.475
8 _GARCH _GARCH_M_jump _GARCH_EWMA _TGARCH_jump _GARCH_M _GARCH_ _EGARCH _GARCH_M_ _TGARCH _TGARCH_ ( 4 ) GARCH EWMA % 4.5% 0.%, 5 5 r f =.3% r f =.7% r f =.3% r f =.7% _GARCH_jump
9 _GARCH _GARCH_M_jump _GARCH_EWMA _TGARCH_jump _GARCH_M _GARCH_ _EGARCH _GARCH_M_ _TGARCH _TGARCH_ S*=3.9 S*=4. S*=3.9 S*= _GARCH_jump _GARCH _GARCH_M_jump _GARCH_EWMA _TGARCH_jump _GARCH_M _GARCH_ _EGARCH _GARCH_M_ _TGARCH _TGARCH_
10 6 Hong & Li GARCH BS BS GARCH 3 4 [] Ball, C. A. and W. N. Torous, 983, A simplified jump process for common sock reurn, Journal of Financial and Quaniaive Analysis, 8, [] Black, F. and Scholes, M.,973, The pricing of opion and corporaion liabiliies, Journal of Poliical Economy, 8, [3] Bollerslev T, 986, Generalised auoregressive condiional eeroskedasicy, Journal of Economerics, 3, [4] Crouhy, M. and Galai, D., 99, "Warran valuaion and equiy volailiy", In: "Advances in Fuuresand Opions Research", F.J. Fabozzi (ed.), JAI Press Inc., page [5] Das, S. R., 00, The Surprise Elemen: Jumps in Ineres Raes, Journal of Ecnomerics, 06, [6] Duan, J.C.995, The GARCH opion pricing model, Mahemaical Finance, 5, 3-3 [7] Engle, R F, 98, Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion. Economerica, 50, [8] Engle, R. F., Lilien, D. M. and R. P. Robins, 987, Esimaing ime-varying premia in he erm srucure: he ARCH-M model, Economerica, 55, [9] Galai, D. and Schneller, M.I., 978, "Pricing of warrans and he value of he firm", The Journal of Finance, page [0] Hong, Y. and H. Li., 005, Nonparameric Specificaion Tesing for Coninuous-Time
11 Models Wih Applicaions o Ineres Rae Term Srucures, Review of Financial Sudies, 8, [] Nelson, D. B, 99, "Condiional Heeroskedasiciy in Asse Reurns: A New Approach." Economerica, 59, [] Schulz, G.U. and Traumann, S., 989, "Valuaion of warrans - heory and empirical ess for warrans wrien on German socks", Working Paper, Universiy of Sugar (Germany), Ocober 989. [3]Schulz, G.U. and Traumann, S.,994, "Robusness of opion-like warran valuaion", Journal of Banking and Finance, page [4] Vlaar, P. and F. Palm, 993, The Message in Weekly Exchange Raes in he European Moneary Sysem: Mean Reversion, Condiional Heeroskedasiciy, and Jumps, Journal of Business and Economic Saisics,, [5] Zakoian, J-M, 994, Threshold Heeroscedasic Models, Journal of Economic Dynamics and Conrol, 8, [6] 998 [7] 999-GARCH 4 [8] 998 (ARCH) 4 [9] [0] 00GARCH 6 [] 000 ARMA-ARCH-M 5
12
13 GARCH EWMA TGARCH EGARCH GARCH-M GARCH Jump TGARCH Jump GARCH-M Jump GARCH TGARCH GARCH-M µ 9.50E E E E E E03 ** -6.89E E04 ** -.09E E04-5.3E04 -.3E03 σ 0.07 *** α 4.0E-05 *** 4.4E-05 *** -8.90E-06 *** 4.4E-05 *** 7.0E E E E-06 ** 6.60E-06 ** 6.80E-06** α 0.8 *** 0.7 *** 0. *** 0. *** 0.07 *** 0.05 ** 0.07 *** 0.05 *** 0.05 *** 0.06*** β 0.70 *** 0.70 *** *** 0.83 *** 0.84 *** 0.83 *** 0.8 *** 0.8 *** 0.8*** ϕ β 0.89 *** λ *** δ 0.3 ** ϑ 6.40E E E03 γ 0.03 *** 0.03 *** 0.03 *** c 0.3 *** 0.3 *** 0.3 *** ν 3.07 *** 3.09 *** 3.06 *** Log *** ** 5
004 6 volailiy Hull Whie(987) vega( kappa) innovaion erm Poerba Summers(986) French, Schwer Sambaugh(987) Bollerslev, Engle Wooldridge (988) Bailie De
004 6-3 CARR(Condiional Auo-Regression Range) CARR GARCH CARR GARCH Chou(00) S P500 CARR CARR GARCH 004 6 volailiy Hull Whie(987) vega( kappa) innovaion erm Poerba Summers(986) French, Schwer Sambaugh(987)
《金融评论》投稿 封面
The Choice of he Inermediae Targe of Moneary Policy in China 968 993 5 0073 85957073683550599 [email protected] MM 994Q-008Q4 VECM M M GDPCPI M M M 007 VECM JEL E5C3E58 The Choice of he Inermediae Targe
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Black & choles Hull & Whie GARCH GARCH EGARCH EGARCH EGARCH GARCH EGARCH EGARCH GARCH GARCHEGARCH I Absrac ubprime morgage leads he financial sysem o be assauled grealy, and cause he global financial sunami.
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Muual Funds Performance Persisence and Classificaion Schemes β Ching-Jun Hsu, Chih-Chien Chiang, Deparmen of Financial Managemen, Nan-Hua Universiy ABSTRACT Muual funds performance persisence is a very
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