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?
If Manufacturer spice model and Datasheet give different values which should I use?
A Journey Through Space and Time
Schwarzchild Radius of the Universe
How can the DM most effectively choose 1 out of an odd number of players to be targeted by an attack or effect?
Why was the small council so happy for Tyrion to become the Master of Coin?
Prevent a directory in /tmp from being deleted
Could a US political party gain complete control over the government by removing checks & balances?
How old can references or sources in a thesis be?
What is the command to reset a PC without deleting any files
Is Social Media Science Fiction?
Motorized valve interfering with button?
N.B. ligature in Latex
How can bays and straits be determined in a procedurally generated map?
Why are 150k or 200k jobs considered good when there are 300k+ births a month?
A function which translates a sentence to title-case
Email Account under attack (really) - anything I can do?
whey we use polarized capacitor?
My colleague's body is amazing
I probably found a bug with the sudo apt install function
What would the Romans have called "sorcery"?
Japan - Plan around max visa duration
What defenses are there against being summoned by the Gate spell?
Why is this code 6.5x slower with optimizations enabled?
Can a German sentence have two subjects?
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
$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_impσ_0 σ_1)]$
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
$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_impσ_0 σ_1)]$
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
$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_impσ_0 σ_1)]$
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
$σ = sqrt[σ^2_0 + σ^2_1 − 2ρ_impσ_0 σ_1)]$
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.
Check out our Code of Conduct.
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
1
active
oldest
votes
$begingroup$
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.
answered 3 hours ago
Alex CAlex C
6,62611123
$endgroup$
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 $-1lerho_imple 1$ 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.
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.
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.
answered 3 hours ago
Alex CAlex C
6,62611123
$endgroup$
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.
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.
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
