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

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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

$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_impσ_0 σ_1)]$

black-scholes correlation european-options implied nonlinear

share

edited 3 hours ago

Alex C

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asked 4 hours ago

TaraTara

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$endgroup$

add a comment | 

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

$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_impσ_0 σ_1)]$

black-scholes correlation european-options implied nonlinear

share

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

$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_impσ_0 σ_1)]$

black-scholes correlation european-options implied nonlinear

share

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.

$endgroup$

share

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.

share

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

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.

asked 4 hours ago

TaraTara

114

1 Answer
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1

$begingroup$

We know that $-1lerho_imple 1$ 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

answered 3 hours ago

Alex CAlex C

6,62611123

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1

$begingroup$

We know that $-1lerho_imple 1$ 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

answered 3 hours ago

Alex CAlex C

6,62611123

$endgroup$

add a comment | 

1

$begingroup$

We know that $-1lerho_imple 1$ 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

answered 3 hours ago

Alex CAlex C

6,62611123

$endgroup$

add a comment | 

$begingroup$

We know that $-1lerho_imple 1$ 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

answered 3 hours ago

Alex CAlex C

6,62611123

$endgroup$

share|improve this answer

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