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arXiv · 1907.07305

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

Peter Carr·Andrey Itkin·Sasha Stoikov
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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.

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Peter Carr, Andrey Itkin, Sasha Stoikov. 2019-07-17. A model-free backward and forward nonlinear PDEs for implied volatility. https://arxiv.org/abs/1907.07305

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