Related papers: Efficient option pricing in the rough Heston model…
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…
We study the weak convergence rate in the discretization of rough volatility models. After showing a lower bound $2H$ under a general model, where $H$ is the Hurst index of the volatility process, we give a sharper bound $H + 1/2$ under a…
We examine the empirical performance of some parametric and nonparametric estimators of prices of options with a fixed time to maturity, focusing on variance-gamma and Heston models on one side, and on expansions in Hermite functions on the…
We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value.…
We provide explicit approximation formulas for VIX futures and options in forward variance models, with particular emphasis on the family of so-called Bergomi models: the one-factor Bergomi model [Bergomi, Smile dynamics II, Risk, 2005],…
This paper deals with the numerical solution of the Heston partial differential equation that plays an important role in financial option pricing, Heston (1993, Rev. Finan. Stud. 6). A feature of this time-dependent, two-dimensional…
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter smaller than half, and have attracted much attention since a seminal…
We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an oracle access to a stochastic estimate of the Hessian matrix. The oracle model includes…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…
We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…
We investigate the statistical evidence for the use of `rough' fractional processes with Hurst exponent $H< 0.5$ for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for…