How to calculate implied correlation via observed market price (Margrabe option)












2












$begingroup$


I can't seem to figure out how to do the following:



Compute the implied correlation $ρ_{imp}$ by using the observed market price $M_{quote}$ of a Margrabe option, and solving the non-linear equation shown below:



$$M_{quote} = e^{−(q_0T)*S_0(0)*N(d+)}−e^{(−q_1T)*S_1(0)*N(d−)}$$



Where:



$d± = [log(S_0(0)/S_1(0))+(q_1 − q_0 ±σ^2/2)T]/ σ√T$



(note that d− = d+ − σT),



and



$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_{imp}σ_0 σ_1)]$






black-scholes correlation european-options implied nonlinear






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    2












    $begingroup$


    I can't seem to figure out how to do the following:



    Compute the implied correlation $ρ_{imp}$ by using the observed market price $M_{quote}$ of a Margrabe option, and solving the non-linear equation shown below:



    $$M_{quote} = e^{−(q_0T)*S_0(0)*N(d+)}−e^{(−q_1T)*S_1(0)*N(d−)}$$



    Where:



    $d± = [log(S_0(0)/S_1(0))+(q_1 − q_0 ±σ^2/2)T]/ σ√T$



    (note that d− = d+ − σT),



    and



    $σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_{imp}σ_0 σ_1)]$






    black-scholes correlation european-options implied nonlinear






    share









    New contributor




    Tara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      2












      2








      2





      $begingroup$


      I can't seem to figure out how to do the following:



      Compute the implied correlation $ρ_{imp}$ by using the observed market price $M_{quote}$ of a Margrabe option, and solving the non-linear equation shown below:



      $$M_{quote} = e^{−(q_0T)*S_0(0)*N(d+)}−e^{(−q_1T)*S_1(0)*N(d−)}$$



      Where:



      $d± = [log(S_0(0)/S_1(0))+(q_1 − q_0 ±σ^2/2)T]/ σ√T$



      (note that d− = d+ − σT),



      and



      $σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_{imp}σ_0 σ_1)]$






      black-scholes correlation european-options implied nonlinear






      share









      New contributor




      Tara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I can't seem to figure out how to do the following:



      Compute the implied correlation $ρ_{imp}$ by using the observed market price $M_{quote}$ of a Margrabe option, and solving the non-linear equation shown below:



      $$M_{quote} = e^{−(q_0T)*S_0(0)*N(d+)}−e^{(−q_1T)*S_1(0)*N(d−)}$$



      Where:



      $d± = [log(S_0(0)/S_1(0))+(q_1 − q_0 ±σ^2/2)T]/ σ√T$



      (note that d− = d+ − σT),



      and



      $σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_{imp}σ_0 σ_1)]$






      black-scholes correlation european-options implied nonlinear




      black-scholes correlation european-options implied nonlinear





      share









      New contributor




      Tara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.










      share









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      Tara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      edited 3 hours ago









      Alex C

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      6,62611123






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      asked 4 hours ago









      TaraTara

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      114




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      New contributor





      Tara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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          We know that $-1lerho_{imp}le 1$ so perhaps the simplest approach is to try the possible values $rho_{imp}={-1,-0.9,-0.8,cdots,0.8,0.9,+1}$, to calculate resulting $sigma$ values, d± values, and $M_{quote}$ values, then see which of these is closest to the observed market price. If desired you can then search a finer grid between two adjacent assumed correlations to pin it down more precisely. It is a manual but relatively simple method.






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            $begingroup$

            We know that $-1lerho_{imp}le 1$ so perhaps the simplest approach is to try the possible values $rho_{imp}={-1,-0.9,-0.8,cdots,0.8,0.9,+1}$, to calculate resulting $sigma$ values, d± values, and $M_{quote}$ values, then see which of these is closest to the observed market price. If desired you can then search a finer grid between two adjacent assumed correlations to pin it down more precisely. It is a manual but relatively simple method.






            share|improve this answer









            $endgroup$


















              1












              $begingroup$

              We know that $-1lerho_{imp}le 1$ so perhaps the simplest approach is to try the possible values $rho_{imp}={-1,-0.9,-0.8,cdots,0.8,0.9,+1}$, to calculate resulting $sigma$ values, d± values, and $M_{quote}$ values, then see which of these is closest to the observed market price. If desired you can then search a finer grid between two adjacent assumed correlations to pin it down more precisely. It is a manual but relatively simple method.






              share|improve this answer









              $endgroup$
















                1












                1








                1





                $begingroup$

                We know that $-1lerho_{imp}le 1$ so perhaps the simplest approach is to try the possible values $rho_{imp}={-1,-0.9,-0.8,cdots,0.8,0.9,+1}$, to calculate resulting $sigma$ values, d± values, and $M_{quote}$ values, then see which of these is closest to the observed market price. If desired you can then search a finer grid between two adjacent assumed correlations to pin it down more precisely. It is a manual but relatively simple method.






                share|improve this answer









                $endgroup$



                We know that $-1lerho_{imp}le 1$ so perhaps the simplest approach is to try the possible values $rho_{imp}={-1,-0.9,-0.8,cdots,0.8,0.9,+1}$, to calculate resulting $sigma$ values, d± values, and $M_{quote}$ values, then see which of these is closest to the observed market price. If desired you can then search a finer grid between two adjacent assumed correlations to pin it down more precisely. It is a manual but relatively simple method.







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 3 hours ago









                Alex CAlex C

                6,62611123




                6,62611123






















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