A model-free backward and forward nonlinear PDEs for implied volatility

Peter Carr, Andrey Itkin () and Sasha Stoikov

Papers from arXiv.org

Abstract: We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at a possibly random time is convex. We also discuss suitable initial and boundary conditions for those PDEs. Finally, we demonstrate how to solve them numerically by using an iterative finite-difference approach.

Date: 2019-07
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1907.07305

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