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Let C be the prime of a call in fi=unction of the price in term F, Strike K, volatilité $\sigma$ and maturity t: $C(F,K,\sigma,t,r) $ We assume that we know $\delta$

$\delta=\frac{\partial}{\partial F}C(F,K,\sigma,t,r)$

I would like to compute $\delta$ the variation of C in function of F in two cases :

1-If $\sigma=f(F,K)$

2-If $\sigma=g(\delta)$ Thanks everyone

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  • $\begingroup$ For your second question, the delta can only be solved from a differential equation. The first one is straightforward. $\endgroup$ – Gordon Feb 9 '16 at 17:57
  • $\begingroup$ Could you please explain more ! $\endgroup$ – Sino Feb 9 '16 at 18:11
  • $\begingroup$ What's the expression of C ? $\endgroup$ – Sino Feb 9 '16 at 19:52
  • $\begingroup$ Please edit your question. I do not know whether you want the formula for $C$ or anything else? $\endgroup$ – Gordon Feb 9 '16 at 21:30
  • $\begingroup$ For your second question, is you made up this or from a practical question, as I rarely see anything with an assumption that the volatility is a function of the delta. For FX, we can have some risk-reversal or butterfly quote, but the vol and the strikes can be correspondingly solved. That is, it makes more sense to assume that the vol to be a function of $F$ and $K$, while the second question does not make practical sense, though may be as a mathematical exercise. $\endgroup$ – Gordon Feb 9 '16 at 21:38

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