This paper discusses the generalized Black-Scholes-Merton model, where the volatility coefficient, the drift … that the volatility, the drift, and the interest rate depend on a gamma or inverse-gamma random variable. This model …

subsequent local volatility surface is never considered. In this article, we develop a deep learning approach for interpolation … performance. A novel component is the use of the Dupire formula to enforce bounds on the local volatility associated with option …

stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical …

We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in … particular the ad hoc interpolation of the volatility surface. To achieve this, we parametrize the leverage function by a family … be seen in the context of neural SDEs and (causal) generative adversarial networks: we generate volatility surfaces by …

This paper studies the effect of variance swap in hedging volatility risk under the mean-variance criterion. We … consider two mean-variance portfolio selection problems under Heston's stochastic volatility model. In the first problem, the … variance swap can be used to hedge against the volatility risk. In the second problem, only the bank account and the stock can …

this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with … volatility model with a Vasicek interest rate model. …

implied volatility and compare the spline collocation results with those obtained through arbitrage-free interpolation …