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Related papers: VIX options in the SABR model

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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 model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…

Mathematical Physics · Physics 2008-12-10 Przemyslaw Repetowicz , Peter Richmond

This paper shows how to recover a stochastic volatility model (SVM) from a market model of the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore are better suited for pricing…

Pricing of Securities · Quantitative Finance 2022-03-16 Andrew Papanicolaou

We apply vector quantisation within mixed one- and two-factor Bergomi models to implement a fast and efficient approach for option pricing in these models. This allows us to calibrate such models to market data of VIX futures and options.…

Pricing of Securities · Quantitative Finance 2025-07-01 Nelson Kyakutwika , Mesias Alfeus , Erik Schlögl

We introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping…

Pricing of Securities · Quantitative Finance 2015-02-23 Lorenz Schneider , Bertrand Tavin

We suggest an intermediate currency approach that allows us to price options on all FX markets simultaneously under the same risk-neutral measure which ensures consistency of FX option prices across all markets. In particular, it is…

Mathematical Finance · Quantitative Finance 2021-02-16 S. Maurer , T. E. Sharp , M. V. Tretyakov

In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our…

Statistical Finance · Quantitative Finance 2009-11-06 Aleksandar Mijatovic , Paul Schneider

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…

Computational Finance · Quantitative Finance 2010-03-10 Guoping Xu , Harry Zheng

We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple…

Computational Finance · Quantitative Finance 2016-02-16 Vinicius Albani , Uri M. Ascher , Jorge P. Zubelli

In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…

Mathematical Finance · Quantitative Finance 2017-12-08 Anatoliy Swishchuk , Zijia Wang

We present an Hilbert space formulation for a set of implied volatility models introduced in \cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price…

Computational Finance · Quantitative Finance 2008-12-10 A. Brace , G. Fabbri , B. Goldys

We propose a general, very fast method to quickly approximate the solution of a parabolic Partial Differential Equation (PDEs) with explicit formulas. Our method also provides equaly fast approximations of the derivatives of the solution,…

Computational Finance · Quantitative Finance 2018-12-27 Olesya Grishchenko , Xiao Han , Victor Nistor

We study the Heston model for pricing European options on stocks with stochastic volatility. This is a Black\--Scholes\--type equation whose spatial domain for the logarithmic stock price $x\in \RR$ and the variance $v\in (0,\infty)$ is the…

Analysis of PDEs · Mathematics 2017-11-15 Bénédicte Alziary , Peter Takáč

The SABR model is a benchmark stochastic volatility model in interest rate markets, which has received much attention in the past decade. Its popularity arose from a tractable asymptotic expansion for implied volatility, derived by heat…

Mathematical Finance · Quantitative Finance 2017-07-27 Leif Doering , Blanka Horvath , Josef Teichmann

The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge," the VIX is a measure of the…

Physics and Society · Physics 2009-11-13 Stephen D. H. Hsu , Brian M. Murray

Options with maturities below one week, hereafter "ultra-short-term" options, have seen a sharp increase in trading activity in recent years. Yet, these instruments are difficult to price jointly using classical pricing models due to the…

Mathematical Finance · Quantitative Finance 2026-04-01 Federico M. Bandi , Nicola Fusari , Guido Gazzani , Roberto Renò

In this paper, we consider three stochastic-volatility models, each characterized by distinct dynamics of instantaneous volatility: (1) a CIR process for squared volatility (i.e., the classical Heston model); (2) a mean-reverting lognormal…

Pricing of Securities · Quantitative Finance 2025-10-14 V. Perederiy

We regard options on VIX and Realised Variance as solutions to path-dependent partial differential equations (PDEs) in a continuous stochastic volatility model. The modeling assumption specifies that the instantaneous variance is a $C^3$…

Probability · Mathematics 2025-07-22 Alexandre Pannier

In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston…

Pricing of Securities · Quantitative Finance 2019-06-18 Raul Merino , Jan Pospíšil , Tomáš Sobotka , Josep Vives

In this paper, we price European Call three different option pricing models, where the volatility is dynamically changing i.e. non constant. In stochastic volatility (SV) models for option pricing a closed form approximation technique is…

Pricing of Securities · Quantitative Finance 2023-09-19 Natasha Latif , Shafqat Ali Shad , Muhammad Usman , Chandan Kumar , Bahman B Motii , MD Mahfuzer Rahman , Khuram Shafi , Zahra Idrees