An explicit piecewise-constant-curvature construction with power-law tails converts discrete arbitrage-free call prices into full risk-neutral marginal laws that exactly reprice inputs and are free of butterfly and calendar arbitrage.
Building arbitrage-free implied volatility: Sinkhorn's algorithm and variants
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abstract
We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently used to solve efficiently (martingale) optimal transport problems.
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Arbitrage-Free Multi-Maturity Risk-Neutral Marginals
An explicit piecewise-constant-curvature construction with power-law tails converts discrete arbitrage-free call prices into full risk-neutral marginal laws that exactly reprice inputs and are free of butterfly and calendar arbitrage.