Just to clarify, BS is a canonical example, but all I need is a PDE linear in second spatial derivative. So to meet your requirement I need a linear parabolic PDE a la heat equation (ie the unknown and all its spatial derivatives are in first power + the first derivative of time). Then the second spatial derivative “smooths out” all local spikes and dips - as time goes by.
I believe local volatility models qualify too, as long as they are linear in second derivative .
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- katastrofa
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- Cuchulainn
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Re: Analytic formula for the CDF of Two Normal Distributions combined with T - Copula
Exactly. That's why I posted the thesis of Matt Robinson a few days back...Hmm - your calculation reminds me of Peter Carr’s “Deriving derivatives of derivative securities” paper, which is explicitly set in a Black-Scholes framework. I’ll try to muster some mental energy to work out at least one little example of my point tomorrow.
It's based on Cauchy Kowaleski theorem.
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Re: Analytic formula for the CDF of Two Normal Distributions combined with T - Copula
Still clear to me but have bearish' goalposts changed.This is 100% clear!At great risk of causing further confusion, the essence of the question is to identify conditions under which monotonicity and convexity of the terminal payoff function are inherited by the valuation function prior to maturity.
Very confucious.
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- katastrofa
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Re: Analytic formula for the CDF of Two Normal Distributions combined with T - Copula
Here’s what I’m talking about! Of course the physicists solved it (-:
https://math.arizona.edu/~friedlan/teach/456/max.pdf
Wikipedia (didn’t read that one carefully): https://en.m.wikipedia.org/wiki/Maximum_principle
https://math.arizona.edu/~friedlan/teach/456/max.pdf
Wikipedia (didn’t read that one carefully): https://en.m.wikipedia.org/wiki/Maximum_principle
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- Cuchulainn
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Re: Analytic formula for the CDF of Two Normal Distributions combined with T - Copula
Not really, but never mind.Here’s what I’m talking about! Of course the physicists solved it (-:
https://math.arizona.edu/~friedlan/teach/456/max.pdf
Wikipedia (didn’t read that one carefully): https://en.m.wikipedia.org/wiki/Maximum_principle
A full discussion is here
http://inis.jinr.ru/sl/vol2/Mathematics ... 08_435.pdf
Enjoy!
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- katastrofa
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