How to calculate implied correlation via observed market price (Margrabe option)
$begingroup$
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
edited 3 hours ago
Alex C
6,62611123
asked 4 hours ago
TaraTara
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$begingroup$
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
edited 3 hours ago
Alex C
6,62611123
asked 4 hours ago
TaraTara
114
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.
$endgroup$
add a comment |
$begingroup$
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
edited 3 hours ago
Alex C
6,62611123
asked 4 hours ago
TaraTara
114
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
edited 3 hours ago
Alex C
6,62611123
asked 4 hours ago
TaraTara
114
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.
edited 3 hours ago
Alex C
6,62611123
asked 4 hours ago
TaraTara
114
New contributor
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
6,62611123
edited 3 hours ago
Alex C
6,62611123
edited 3 hours ago
Alex C
6,62611123
6,62611123
asked 4 hours ago
TaraTara
114
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.
asked 4 hours ago
TaraTara
114
asked 4 hours ago
TaraTara
114
114
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.
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.
Tara is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
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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.
answered 3 hours ago
Alex CAlex C
6,62611123
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
answered 3 hours ago
Alex CAlex C
6,62611123
$endgroup$
add a comment |
$begingroup$
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.
answered 3 hours ago
Alex CAlex C
6,62611123
$endgroup$
add a comment |
$begingroup$
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.
answered 3 hours ago
Alex CAlex C
6,62611123
$endgroup$
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.
answered 3 hours ago
Alex CAlex C
6,62611123
answered 3 hours ago
Alex CAlex C
6,62611123
answered 3 hours ago
Alex CAlex C
6,62611123
answered 3 hours ago
Alex CAlex C
6,62611123
6,62611123
add a comment |
add a comment |
Tara is a new contributor. Be nice, and check out our Code of Conduct.
Tara is a new contributor. Be nice, and check out our Code of Conduct.
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