The Drivers of Cross Market Arbitrage Opportunities: Theory and Evidence for the European Bond Market

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Munich Personal RePEc Archive

The Drivers of Cross Market Arbitrage Opportunities: Theory and Evidence for the European Bond Market

Perlin, Marcelo and Dufour, Alfonso and Brooks, Chris

Reading University

June 2010

Online at https://mpra.ub.uni-muenchen.de/23381/

MPRA Paper No. 23381, posted 20 Jun 2010 04:28 UTC

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(25)

&&

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(26)

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(29)

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(30)

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(31)

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@ ! !

(

^" ^" ^" ^"

)

&'%() % = Φ α β+ ) % ⁻+φ'* % ⁻+γ+,- ⁻+θ %& .

(

@ !! /

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&'%() % ) %

'* %

+,-

%& .

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(34)

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(35)

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(36)

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':

! φ =%$ ! &

! %

&0%

%0 &0

= − − M " %"%N

- . M " %"%N / . %$ C$ _%0 = −_%

! %$ _&0 =% ! &$ /

&0% % &

%0 &0

& &

 

= − − + − M "%"&N

5 _%0 _&0

&0% % &

% %0 % & &0 %

& &

− − −

= − − + − − − M "%"'N

( / - − ₋ / / / !

" 5 /

− − M "%":N

5

% θν

− + + − − M "%";N

5 ₋_%

& θν % % θν

− + − + − + + − − M "%">N

" ₋ /

% θν

− − + − + − " 0 ! ? / /

(38)

';

% %

, ,

− θ ν−

− − −

= =

− =

∑

+

∑

M "%"*N

8 . M "%"'N

% %

&0% % &

% %0 % & &0 %

, θ ν, &

− −

− − − −

= =

=

∑

+

∑

− + − + − M "%"AN

(39)

'>

! _%0₋_%

%0−%= %0−&− %0−% M "&"%N

! _%0₋_& /

%0−%= %0−'− %0−&− %0−% M "&"&N

5 _%0₋_'

%0−%= %0−:− %0−'− %0−&− %0−% M "&"'N

2 / ! @% /

%

%0 % %0, %0

%

−

− −

=

= −

∑

M "&":N

3 . 0 _%0,

. B " 8 _%0 0 /

%

%0 %

%

λ ν⁻

− −

=

= −

∑

M "&";N

0 ! %0 ! @%

! ! ν ₋ 0 / λ"

(40)

'*

! " # $ ' )

( / ! 0 /

/

% %

, ,

− θ ν−

− −

= =

=

∑

+

∑

M "'"%N

( )

(

% &

)

^%

%

λ % λ ⁻ ν ₋

=

= − −

∑

M "'"&N

/

( )

0 M $NM $N

σ = − − M "'"'N

5 M "'"%N M "'"&N M "'"'N

$=,

( )

% % %

0 % &

, , %

N %

σ ⁻ ₋ θ ν⁻ ₋ λ λ ⁻ ν ₋

= = =

   

= 

∑

+

∑

   − −

∑

 M "'":N

D / ν " 0 !

%

,

−

∑

=

M "'":N ν /

B

(

−^ν −

)

=^, " ! !

( )

% %

0 % &

, %

N %

σ θ ν⁻ ₋ λ λ ⁻ ν ₋

= =

   

= 

∑

   − −

∑

 M "'";N

3 . M "'";N0 ! ! ! ! " (

! ! /

( )

% %

0 % &

% %

N %

σ θν θ ν⁻ ₋ λ λ ⁻ ν ₋

= =

   

=  +

∑

   − −

∑

 M "'">N

$=,

(41)

'A

D /0

(

^{ν ν}− −

)

=^,0 /

ν ₋ / ν − ≠ / . B -

"

( )

% %

0 % &

% %

N %

σ θ ν⁻ ₋ λ λ ⁻ν ₋

= =

   

= 

∑

   − −

∑

 M "'"*N

D /0

( )

^&− =^σ^& / ! M "'"*N0

( )

( ) ( )

^&

0 % % & % _ν

σ =θ λ − −λ − σ M "'"AN

(42)

'C

% " # & ' (

/ / !

0 !" /

(

^>^,

)

^{= −}^%

⁽

^{+ ≤ −} ^J

⁾

⁺

⁽

^{+ ≤} ^J

⁾

M ":"%N

3 ! 0 !

! L $ " /

( )

^% ^% _&

& &

% ! σ ₊

  − 

  

+ ≤ − = +

 

  

 

M ":"&N

5 M ":"&N M ":"%N /

(

^,

)

^% ^% ^% _& ^% ^% _&

& & & &

% ! % !

σ ₊ σ ₊

  −    

     

> = − + + +

   

     

   

M ":"'N

5 ! . ^{% !}

( )

^{− = −}^{% !}

( )

^/

( )

(

^&

)

, %

&

% ! σ ₊

 

 

> = +  

 

M ":":N

(

( ) ( ⁽ ⁾ ) ( ( ) ) ( ) ( )

& & & & &

% % & % % & % & %

ν ν

σ ₊ = σ +θ σ + λ − −λ σ ^ λ − −λ − + θ − ^

( )

(

^&⁻^% ^% ^&

)

= − + +

- M ":":N /

(

^,

)

^% ^& _,^ψ ^-

( )

^&

> = + π

∫

− M ":";N

(43)

:, (

( )

( ) ( ⁽ ⁾ ) ( ( ( ) ) ( ) ( ) )

%

% &

& & & &

% & % &

&

& _ν % _ν % % & %

ψ σ θ σ λ λ σ λ λ θ

− − + +

=  + + − − − − − + − 

The Drivers of Cross Market Arbitrage Opportunities: Theory and Evidence for the European Bond Market

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