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

Implied Correlation using market quotesDoes Implied Volatility always exist?Implied Vol vs. Calibrated VolHow do they calculate stocks implied volatility?Pricing log-contract with Black-Scholes PDENotion of risk-less portfolio in derivation of Black-ScholesParametric estimation of risk-neutral density/implied distributionDrift rate vs. Riskless rate in the Black-Scholes modelImplied correlationIs American option price lower than European option price?

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 4 hours ago

Alex C

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asked 5 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 4 hours ago

Alex C

6,62611123

asked 5 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 4 hours ago

Alex C

6,62611123

asked 5 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 4 hours ago

Alex C

6,62611123

asked 5 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 4 hours ago

Alex C

6,62611123

asked 5 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 4 hours ago

Alex C

6,62611123

edited 4 hours ago

Alex C

6,62611123

asked 5 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 5 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

$endgroup$

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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