Related papers: Mean-Reverting SABR Models: Closed-form Surfaces a…
We introduce a fast and flexible Machine Learning (ML) framework for pricing derivative products whose valuation depends on volatility surfaces. By parameterizing volatility surfaces with the 5-parameter stochastic volatility inspired (SVI)…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…
In this paper, a new way to integrate volatility information for estimating value at risk (VaR) and conditional value at risk (CVaR) of a portfolio is suggested. The new method is developed from the perspective of Bayesian statistics and it…
We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…
We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough…
In industrial applications it is quite common to use stochastic volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a…
We consider Heston's (1993) stochastic volatility model for valuation of European options to which (semi) closed form solutions are available and are given in terms of characteristic functions. We prove that the class of scale-parameter…
We treat implied volatility surface (IVS) reconstruction as a learning problem guided by two principles. First, we adopt a meta-learning view that trains across trading days to learn a procedure that maps sparse option quotes to a full IVS…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture…
Cox-Ingersoll-Ross (CIR) processes are widely used in financial modeling such as in the Heston model for the approximative pricing of financial derivatives. Moreover, CIR processes are mathematically interesting due to the irregular square…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
In this paper, we study a family of stochastic volatility processes; this family features a mean reversion term for the volatility and a double CEV-like exponent that generalizes SABR and Heston's models. We derive approximated closed form…
In this paper similar to [P. Carr, A. Itkin, 2019] we construct another Markovian approximation of the rough Heston-like volatility model - the ADO-Heston model. The characteristic function (CF) of the model is derived under both…
We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself.…
It is well documented from various empirical studies that the volatility process of an asset price dynamics is stochastic. This phenomenon called for a new approach to describing the random evolution of volatility through time with…
For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR)…
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 present a detailed analysis of \emph{observable} moments based parameter estimators for the Heston SDEs jointly driving the rate of returns $R_t$ and the squared volatilities $V_t$. Since volatilities are not directly observable, our…