Written by Hans Buehler, JP Morgan Chase, London; Technical University of Berlin- Institut fur Mathematik, and Evgeny Ryskin, JP Morgan Chase. Hans and Evgency will both be presenting at the session "Discrete Local Volatility & Applications" at Global Derivatives 2017.
We construct a state-and-time discrete martingale which is calibrated globally to a set of given input option prices which may exhibit arbitrage. We also provide a method to take small steps, fully consistent with the transition kernels of the large steps.
The method's robustness vs. arbitrage violations in the input surface makes our approach particularly suited for computations in stressed scenarios. Indeed, our method of finding a globally closest arbitrage-free surface under constraints on implied and local volatility is useful in its own right.
We demonstrate the power of our approach by showing its application to affine dividends calibrated to option prices given by proportional dividends, availability of Likelihood Greeks, and to mean-reverting assets such as VIX. We also comment on how to introduce jumps into our processes.
Find the full paper here.