In the past years, there has been an extensive investigation of the class of stochastic volatility models for the …-Scholes economy and accounting for discrepancies between observation and predictions in the simple log-normal, constant-volatility … model. In this paper, we study the structure of an options market with a stochastic volatility that will eventually vanish …

We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which … accuracy of our method. In order to allow for the treatment of realistic inputs that may contain arbitrage, we reformulate the … input prices and the arbitrage-free prices generated by our method. To further stabilize the method in the presence of noisy …

In this paper, we introduce a 3D finite dimensional Gaussian process (GP) regression approach for learning arbitrage … is proven to be arbitrage-free along the strike direction (butterfly and call-spread arbitrages are precluded on the … entire 3D input domain). The cube is free from static arbitrage along the tenor and maturity directions if swaption prices …