Related papers: Stationary Heston model: Calibration and Pricing o…

We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…

We extend upon the saddle-point equation presented in [1] to derive large-time model-implied volatility smiles, providing its theoretical foundation and studying its applications in classical models. As long as characteristic function…

In this paper, we consider option pricing in a framework of the fractional Heston-type model with $H>1/2$. As it is impossible to obtain an explicit formula for the expectation $\mathbb E f(S_T)$ in this case, where $S_T$ is the asset price…

In this paper an improved Cuckoo Search Algorithm is developed to allow for an efficient and robust calibration of the Heston option pricing model for American options. Calibration of stochastic volatility models like the Heston is…

We prove existence and uniqueness of stochastic representations for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our article focuses on the…

This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…

In this paper, we present a reduced basis method for pricing European and American options based on the Black-Scholes and Heston model. To tackle each model numerically, we formulate the problem in terms of a time dependent variational…

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…

The VSTOXX index tracks the expected 30-day volatility of the EURO STOXX 50 equity index. Futures on the VSTOXX index can, therefore, be used to hedge against economic uncertainty. We investigate the effect of trader inventory on the price…

We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on…

In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula.…

It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…

Given the promising results on joint modeling of SPX/VIX smiles of the recently introduced quadratic rough Heston model, we consider a multi-asset market making problem on SPX and its derivatives, e.g. VIX futures, SPX and VIX options. The…

We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…

This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To…

In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from…

We present an analytic approach to solve a degenerate parabolic problem associated to the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We…

Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…

We present a novel approach for parameter calibration of the Heston model for pricing an Asian put option, namely space mapping. Since few parameters of the Heston model can be directly extracted from real market data, calibration to real…

The Heston model is a well-known two-dimensional financial model. Because the Heston model contains implicit parameters that cannot be determined directly from real market data, calibrating the parameters to real market data is challenging.…