construct the whole implied volatility surface and use the explicit constructions of calibrated (jump-) diffusions, available in …

Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series … and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility … a semimartingale nor a Markov process, there is no unified method that not only applies to all rough volatility models …

, April 2020] and explain how to build a continuous-time stochastic volatility (SV) model which jointly and exactly calibrates … leads to "Dispersion-constrained martingale Schrödinger bridges'', a new type of Schrödinger bridges which are constrained … both the SPX and the instantaneous volatility. Numerical results on model-generated data illustrate the accuracy of the …

Grail of volatility modeling: build a model that jointly and exactly calibrates to the prices of S&P 500 (SPX) options, VIX … satisfy the martingality constraint on the SPX as well as the requirement that the VIX is the implied volatility of the 30-day … we call a dispersion-constrained martingale optimal transport problem, we establish a strong duality theorem and, as a …

Stochastic volatility models have grown in popularity in the past decade or two. However, for many stochastic … volatility models, the functional form of volatility along with the description of the diffusion process for volatility have been … improves and that a more general specification for the stock price and volatility processes may be necessary. This leads to an …

's stochastic volatility model, our method is shown to be extremely efficient and fairly accurate …

-of-the-money and long-maturity options. When applied to Heston's stochastic volatility model, our method is shown to be extremely …

of measure from the market measure to an equivalent martingale measure is introduced. The choice of parameters in the …