Related papers: Calibration of Local Volatility Models with Stocha…
We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results…
In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial…
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the…
We provide a survey of recent results on model calibration by Optimal Transport. We present the general framework and then discuss the calibration of local, and local-stochastic, volatility models to European options, the joint VIX/SPX…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al.…
We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new…
Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually…
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers…
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…
We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear…
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston…
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…
This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the…
The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the…
In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian…
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…
Motivated by recent developments in the calibration of stochastic volatility models (SVMs for short), we study continuous-time formulations of martingale optimal transport and martingale Schr\"odinger bridge problems. We establish duality…
This paper deals with the exact calibration of semidiscretized stochastic local volatility (SLV) models to their underlying semidiscretized local volatility (LV) models. Under an SLV model, it is common to approximate the fair value of…
Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is…