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I learned mathematical finance from Bjork's Arbitrage Theory in Continous Time, and never once did I encounter the "quadratic variation"-thingy with the angle brackets.
So now that I am reading Bergomi's book on Stochastic Volatility and I run into this monster on the first chapter, you can understand my confusion:
Please explain whats' going on here. What is an "average covariation"? I cannot find this on wikipedia. I found what a "quadratic covariation" is, but what does it mean intuitively, especially in this context?
In this context, Bergomi says that he wants to equate implied volatility the future realized volatility. Okay, so I get that the implied volatility is hat-sigma and realized volatility is sigma, and he is weighting them by the "dollar gamma" and then he takes an integral because he wants the average over the period [0, T]. Cool .... but why does he then end by taking those angle-brackets? Why not just equate the two integrals? Why is equating the "covariations" or whatever it is necessary here?
finance-mathematics
asked 10 hours ago
SarahKuchSarahKuch
161
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SarahKuch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
$begingroup$
I learned mathematical finance from Bjork's Arbitrage Theory in Continous Time, and never once did I encounter the "quadratic variation"-thingy with the angle brackets.
So now that I am reading Bergomi's book on Stochastic Volatility and I run into this monster on the first chapter, you can understand my confusion:
Please explain whats' going on here. What is an "average covariation"? I cannot find this on wikipedia. I found what a "quadratic covariation" is, but what does it mean intuitively, especially in this context?
In this context, Bergomi says that he wants to equate implied volatility the future realized volatility. Okay, so I get that the implied volatility is hat-sigma and realized volatility is sigma, and he is weighting them by the "dollar gamma" and then he takes an integral because he wants the average over the period [0, T]. Cool .... but why does he then end by taking those angle-brackets? Why not just equate the two integrals? Why is equating the "covariations" or whatever it is necessary here?
finance-mathematics
asked 10 hours ago
SarahKuchSarahKuch
161
New contributor
SarahKuch 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 learned mathematical finance from Bjork's Arbitrage Theory in Continous Time, and never once did I encounter the "quadratic variation"-thingy with the angle brackets.
So now that I am reading Bergomi's book on Stochastic Volatility and I run into this monster on the first chapter, you can understand my confusion:
Please explain whats' going on here. What is an "average covariation"? I cannot find this on wikipedia. I found what a "quadratic covariation" is, but what does it mean intuitively, especially in this context?
In this context, Bergomi says that he wants to equate implied volatility the future realized volatility. Okay, so I get that the implied volatility is hat-sigma and realized volatility is sigma, and he is weighting them by the "dollar gamma" and then he takes an integral because he wants the average over the period [0, T]. Cool .... but why does he then end by taking those angle-brackets? Why not just equate the two integrals? Why is equating the "covariations" or whatever it is necessary here?
finance-mathematics
asked 10 hours ago
SarahKuchSarahKuch
161
New contributor
SarahKuch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I learned mathematical finance from Bjork's Arbitrage Theory in Continous Time, and never once did I encounter the "quadratic variation"-thingy with the angle brackets.
So now that I am reading Bergomi's book on Stochastic Volatility and I run into this monster on the first chapter, you can understand my confusion:
Please explain whats' going on here. What is an "average covariation"? I cannot find this on wikipedia. I found what a "quadratic covariation" is, but what does it mean intuitively, especially in this context?
In this context, Bergomi says that he wants to equate implied volatility the future realized volatility. Okay, so I get that the implied volatility is hat-sigma and realized volatility is sigma, and he is weighting them by the "dollar gamma" and then he takes an integral because he wants the average over the period [0, T]. Cool .... but why does he then end by taking those angle-brackets? Why not just equate the two integrals? Why is equating the "covariations" or whatever it is necessary here?
finance-mathematics
finance-mathematics
asked 10 hours ago
SarahKuchSarahKuch
161
New contributor
SarahKuch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 hours ago
SarahKuchSarahKuch
161
New contributor
SarahKuch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 hours ago
SarahKuchSarahKuch
161
New contributor
SarahKuch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 10 hours ago
SarahKuchSarahKuch
161
asked 10 hours ago
SarahKuchSarahKuch
161
161
New contributor
SarahKuch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
SarahKuch 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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In physics (statistical physics), this angle bracket is used to represent average, for example, here is the notation from Van Kampen’s book:
And in stochastic calculus, the quadratic variation is usually represented by the same angle brackets. But like he noted the context should make clear which one is meant.
In the equation you have referenced, an average is meant. So the thing inside the brackets is the P&L of a path, and the angle brackets is then computing the average across the paths.
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
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$begingroup$
In physics (statistical physics), this angle bracket is used to represent average, for example, here is the notation from Van Kampen’s book:
And in stochastic calculus, the quadratic variation is usually represented by the same angle brackets. But like he noted the context should make clear which one is meant.
In the equation you have referenced, an average is meant. So the thing inside the brackets is the P&L of a path, and the angle brackets is then computing the average across the paths.
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
$endgroup$
add a comment |
$begingroup$
In physics (statistical physics), this angle bracket is used to represent average, for example, here is the notation from Van Kampen’s book:
And in stochastic calculus, the quadratic variation is usually represented by the same angle brackets. But like he noted the context should make clear which one is meant.
In the equation you have referenced, an average is meant. So the thing inside the brackets is the P&L of a path, and the angle brackets is then computing the average across the paths.
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
$endgroup$
add a comment |
$begingroup$
In physics (statistical physics), this angle bracket is used to represent average, for example, here is the notation from Van Kampen’s book:
And in stochastic calculus, the quadratic variation is usually represented by the same angle brackets. But like he noted the context should make clear which one is meant.
In the equation you have referenced, an average is meant. So the thing inside the brackets is the P&L of a path, and the angle brackets is then computing the average across the paths.
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
$endgroup$
In physics (statistical physics), this angle bracket is used to represent average, for example, here is the notation from Van Kampen’s book:
And in stochastic calculus, the quadratic variation is usually represented by the same angle brackets. But like he noted the context should make clear which one is meant.
In the equation you have referenced, an average is meant. So the thing inside the brackets is the P&L of a path, and the angle brackets is then computing the average across the paths.
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
edited 9 hours ago
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
answered 10 hours ago
Magic is in the chainMagic is in the chain
1,69936
1,69936
add a comment |
add a comment |
SarahKuch is a new contributor. Be nice, and check out our Code of Conduct.
SarahKuch is a new contributor. Be nice, and check out our Code of Conduct.
SarahKuch is a new contributor. Be nice, and check out our Code of Conduct.
SarahKuch is a new contributor. Be nice, and check out our Code of Conduct.
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