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There are by now a lot of papers on discretizations of Heston. One objective of them being to avoid negativity. As has already been said, the Heston SDE has no negative solutions, but a crude discretization does give negative variance with positive probability. If you want to do small steps, then using a log-normal approximation or the QE approximation ...


1) JPY yield curve is currently upward sloping, not inverted... 2) Empirically, an upward sloping yield curve predicts recessions, not an inverted one. See this famous paper http://newyorkfed.org/research/current_issues/ci2-7.pdf

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