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We introduce a multi-factor stochastic volatility model based on the CIR/Heston volatility process that incorporates seasonality and the Samuelson effect. First, we give conditions on the seasonal term under which the corresponding…

Pricing of Securities · Quantitative Finance 2015-06-22 Lorenz Schneider , Bertrand Tavin

This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model,…

Pricing of Securities · Quantitative Finance 2015-03-18 Ricardo Crisostomo

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes…

Computational Finance · Quantitative Finance 2010-04-14 Masaaki Fukasawa

We consider the fractional Heston model originally proposed by Comte, Coutin and Renault. Inspired by recent ground-breaking work on rough volatility, which showed that models with volatility driven by fractional Brownian motion with short…

Mathematical Finance · Quantitative Finance 2017-08-10 Hamza Guennoun , Antoine Jacquier , Patrick Roome , Fangwei Shi

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…

Mathematical Finance · Quantitative Finance 2015-03-30 Raul Merino , Josep Vives

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing…

Mathematical Finance · Quantitative Finance 2015-12-15 José E. Figueroa-López , Sveinn Ólafsson

We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options.…

Pricing of Securities · Quantitative Finance 2016-04-06 Peter Friz , Stefan Gerhold , Arpad Pinter

We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models…

Pricing of Securities · Quantitative Finance 2015-03-20 Alvise De Col , Alessandro Gnoatto , Martino Grasselli

In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility…

Mathematical Finance · Quantitative Finance 2024-03-05 Elisa Alòs , Eulalia Nualart , Makar Pravosud

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.…

Computational Finance · Quantitative Finance 2021-03-10 Javier de Frutos , Victor Gaton

In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochastic…

Mathematical Finance · Quantitative Finance 2025-02-20 Elisa Alòs , Eulalia Nualart , Makar Pravosud

We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical…

Mathematical Finance · Quantitative Finance 2021-06-09 Matthew Lorig , Natchanon Suaysom

In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries…

Mathematical Finance · Quantitative Finance 2016-12-14 Michael R. Tehranchi

We consider a model of stochastic volatility which combines features of the multiplicative model for large volatilities and of the Heston model for small volatilities. The steady-state distribution in this model is a Beta Prime and is…

Mathematical Finance · Quantitative Finance 2024-04-15 M. Dashti Moghaddam , R. A. Serota

We consider the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant…

Pricing of Securities · Quantitative Finance 2013-11-26 Archil Gulisashvili

In a model driven by a multi-dimensional local diffusion, we study the behavior of implied volatility {\sigma} and its derivatives with respect to log-strike k and maturity T near expiry and at the money. We recover explicit limits of these…

Probability · Mathematics 2016-10-06 Stefano Pagliarani , Andrea Pascucci

The double Heston model is one of the most popular option pricing models in financial theory. It is applied to several issues such that risk management and volatility surface calibration. This paper deals with the problem of global…

Statistics Theory · Mathematics 2025-01-29 Mohamed Ben Alaya , Houssem Dahbi , Hamdi Fathallah

The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square…

Analysis of PDEs · Mathematics 2011-09-07 Panagiota Daskalopoulos , Paul M. N. Feehan

We study here the large-time behaviour of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the…

Pricing of Securities · Quantitative Finance 2012-03-23 Antoine Jacquier , Aleksandar Mijatovic

This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and…

Computational Finance · Quantitative Finance 2024-10-22 Zheng Cao , Xinhao Lin