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5

You can find an exact algorithm with a step-by-step explanation here: https://www.dropbox.com/s/t4fq067kzx26mhw/project_paper.pdf As you can see from the URL it is an archived document because the original site is unfortunately long gone and the tool referenced in the paper with it :-( But it should be helpful anyway to understand what is going on. Notice ...

3

Assume $p_i(x)$ is a payoff of one particular option. You can try to reproduce the diagram using a bunch of options with strikes on the breakpoints (underlying is useless, because its payoff can always be modelled by buy&sell of a certain call and put). Then you can create a system of k equations with n unknowns (number of each kind of option). All other ...

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