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Is it possible to graph a European option's price as a function of say, its delta? I've been wondering this since, for example, for a call, the option price is given by $$Se^{-q*t}\Phi (d_1) - e^{-rt}*K\Phi (d_2)$$, and its delta is $$e^{-qt}\Phi (d_1)$$, with $S$ the stock price, $q$ the dividend yield, $t$ time to exercise, $d_1 = \frac{ln(S/K) + (r-q+\sigma^2/2)t}{\sigma \sqrt{t}}$ and $d_2 = d_1 - \sigma \sqrt{t}$, with $\sigma$ the volatility, it doesn't seem possible to analytically solve for the option's value as just a function of it's delta, or even, say, it's delta and it's stock.

Does anyone have any ideas about this? Is there any way to find the inverse function (graph the delta, gamma, etc. as a function of the option value)?

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"Is it possible to graph a European option's price as a function of say, its delta?" - yes, of course, every strike corresponds to certain delta, so you can numerically calculate it and plot. "Is there any way to find the inverse function" - there is no analytic solution, no. –  sashkello May 30 at 1:11

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