Obtaining arbitrage-free foreign exchange implied volatility by variational inference

An ML-based algorithm that provides implied volatilities from bid-ask prices is proposed

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Yoshihiro Tawada proposes using variational inference – a technique widely used in machine learning – to obtain foreign exchange implied volatilities with nonlinear constraints for strike-order consistency and for no arbitrage. The algorithm gives reasonable implied volatilities within bid-ask spreads of at-the-money, risk reversal and butterfly volatilities

The simplest way to obtain a set of implied volatilities is by using the midpoint of bid and ask

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