How to calculate implied correlation via observed market price (Margrabe option)Implied Correlation using...
What is the offset in a seaplane's hull?
TGV timetables / schedules?
Draw simple lines in Inkscape
How to make payment on the internet without leaving a money trail?
Banach space and Hilbert space topology
Why is this code 6.5x slower with optimizations enabled?
How do we improve the relationship with a client software team that performs poorly and is becoming less collaborative?
What are these boxed doors outside store fronts in New York?
Is there a minimum number of transactions in a block?
The magic money tree problem
Is there a familial term for apples and pears?
Is it tax fraud for an individual to declare non-taxable revenue as taxable income? (US tax laws)
Extreme, but not acceptable situation and I can't start the work tomorrow morning
Why Is Death Allowed In the Matrix?
Is Social Media Science Fiction?
Copycat chess is back
I probably found a bug with the sudo apt install function
What defenses are there against being summoned by the Gate spell?
Could a US political party gain complete control over the government by removing checks & balances?
Is it possible to make sharp wind that can cut stuff from afar?
How is the claim "I am in New York only if I am in America" the same as "If I am in New York, then I am in America?
"which" command doesn't work / path of Safari?
My colleague's body is amazing
Email Account under attack (really) - anything I can do?
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?
$begingroup$
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
New contributor
$endgroup$
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
New contributor
$endgroup$
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
New contributor
$endgroup$
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
New contributor
New contributor
edited 3 hours ago
Alex C
6,62611123
6,62611123
New contributor
asked 5 hours ago
TaraTara
114
114
New contributor
New contributor
add a comment |
add a comment |
1 Answer
1
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.
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "204"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Tara is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f44977%2fhow-to-calculate-implied-correlation-via-observed-market-price-margrabe-option%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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.
$endgroup$
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.
$endgroup$
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.
$endgroup$
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
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.
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.
Thanks for contributing an answer to Quantitative Finance Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f44977%2fhow-to-calculate-implied-correlation-via-observed-market-price-margrabe-option%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown