Leverage Certificates
description
Transcript of Leverage Certificates
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Leverage Certificates-A Case of Innovative Financial Engineering
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介紹何謂 Leverage Certificates(LC) 。 對 LC 評價並分析發行 LC 的報酬率。 利用統計方法檢定這些結構型商品是否錯誤定價
(mispricing)
摘要
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結構型商品 (Structured Notes) 又稱連動式債券,其係透過財務工程技術,針對投資者對於市場之不同預期,以拆解或組合衍生性金融商品 ( 股票、一籃子股票、指數、一籃子指數、利率、貨幣、基金、商品及信用等 ) 搭配零息票券的方式去組合成各種報酬型態的商品。
結構型商品
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Leverage Certificates(LC)
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FV :面額總值 I_0 :標的物在時間 t=0 時的價值 I_T :標的物在時間 t=T 時的價值 拿不到 Dividend
LC在時間 T的價值 (V_T)
0
0
0
1 2 ( 1).....( 1)
.....( 2)
601 .....( 3)1000
60 .....( 4)1000
T
T
T
T
I ScenarioI
I ScenarioIV FV
Scenario
I ScenarioI
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設定:◦ FV =1000◦ I_0=1000◦ I_ko=1400
Example
1400
1000
Time
I
T
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Scenario 10
(1 2 ( 1))TT
IV FVI
1400
1000
Time
I
T
1000 (1 2 ( 1))1000
2 1000 , 1000 1400
TT
T T
IV
I if I
1000
TV
TI1000 1400
1800
LC 在時間 T 的價值(V_T)
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Scenario 20
TT
IV FVI
1400
1000
Time
I
T
10001000
, 0 1000
TT
T T
IV
I if I
1000
TV
TI1000
LC 在時間 T 的價值(V_T)
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Scenario 3 60(1 )1000TV FV
1400
1000
Time
I
T601000 (1 )
1000 1060 , 1000
T
T
V
if I
1000
TV
TI1000
1060
LC 在時間 T 的價值(V_T)
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Scenario 40
60( )1000
TT
IV FVI
1400
1000
Time
I
T601000 ( )
1000 1000 60 , 0< 1000
TT
T T
IV
I if I
60
TV
TI1000
1060
LC 在時間 T 的價值(V_T)
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Scenario1+2 & 3+4
1000
TV
TI1000 1400
1800
LC 在時間 T 的價值(V_T)
1000
TV
TI1000
1060
LC 在時間 T 的價值(V_T)
60
標的物未觸及 I_ko情形下 標的物觸及 I_ko 情形下
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統整
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拆解&複製
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00
1000[ max(0; )]T T TV I I II
(1)Long shares of the underlying asset
(2)Short zero coupon bonds. FV= cash dividend of (1) ; T=ex-dividend date
(3)Long shares of call options on the underlying asset. X=
By put-call parity :
=> (4)Long one zero coupon bond. FV=1000
(5)Short shares of put options on the underlying asset. X=
(6)Long 2* shares of call options on the underlying asset. X=
0
1000I
0
1000I 0I
rTS Xe C P
00
1000(1) (2) ( )rTI e C PI
0
1000I 0I
0
1000I 0I
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(1)Long one zero coupon bond. FV=1000
(2)Short shares of put options on the underlying asset. X=
(3)Long one zero coupon bond. FV=60
00
10001000 max(0; ) 60T TV I II
0
1000I 0I
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00
1000[ max(0; )]T T TV I I II
00
10001000 max(0; ) 60T TV I II
(1)Long one zero coupon bond. FV=1000
(2)Short shares of put options on the underlying asset.
(3)Long 2* shares of call options on the underlying asset.
(1)Long one zero coupon bond. FV=1000
(2)Short shares of put options on the underlying asset.
(3)Long one zero coupon bond. FV=60
0
1000I 0
1000I
0
1000I
Þ
(3) Long 2* shares of up-and-out call options on the underlying asset. X= ; barrier=
(4) Long 60 up-and-in cash-or-nothing option. X= ; barrier=
0
1000I
0I koI
0I koI
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評價0 0
0
0
1000 1000 cos (1000) 2
(1000) 1000 ( )
( , )
( 60,
uo ui
uo ko
ui
k
LC t PV P C CNI I
PVP Put option X IC up and out call option X I barrier ICN up and in cash or nothing option
cash barrier I
的折現值的價格
的價格的價格
)o
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Profit & Profitability
0( ) ( )profit B issue price TC
Pr 100%ofitabilityTC
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2004 年 6 月 14 日, CSFB 發行 LC ,部分契約如下: 依前面的評價方式求算出: Profit=1000-862.04=137.96 Profitability=137.96/862.04=16.0%
實例
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實證結果&統計分析
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實證結果&統計分析
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實證結果&統計分析
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實證結果&統計分析
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實證結果&統計分析
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介紹何謂 LC 並評價。 以統計方法分析結構型商品的 mispricing 問題 本篇 paper 所使用的評價方法,可望用於評價其它的結構型商品。
總結