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Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…

Computational Finance · Quantitative Finance 2026-05-15 Julia Sun , Zheyu Jin , Jiawei Zhang , Jeffrey D. Varner

In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the…

Mathematical Finance · Quantitative Finance 2025-04-15 Elisa Alòs , Eulalia Nualart , Makar Pravosud

In the present work, a novel second-order approximation for ATM option prices is derived for a large class of exponential L\'{e}vy models with or without Brownian component. The results hereafter shed new light on the connection between…

Pricing of Securities · Quantitative Finance 2014-04-08 José E. Figueroa-López , Ruoting Gong , Christian Houdré

We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the…

Methodology · Statistics 2026-03-03 Qiang Liu , Zhi Liu , Wang Zhou

The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log…

Computational Finance · Quantitative Finance 2024-10-03 Jimin Lin , Guixin Liu

In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier,…

Pricing of Securities · Quantitative Finance 2024-02-13 Andrey Itkin

Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we integrate price--volatility co-jumps and volatility short-term dependency into a coherent…

Pricing of Securities · Quantitative Finance 2025-06-17 Boyi Li , Weixuan Xia

Pure-jump L\'evy processes are popular classes of stochastic processes which have found many applications in finance, statistics or machine learning. In this paper, we propose a novel family of self-decomposable L\'evy processes where one…

Methodology · Statistics 2025-02-06 Fadhel Ayed , Juho Lee , François Caron

We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of…

Machine Learning · Statistics 2017-01-09 P. Dellaportas , A. Plataniotis , M. K. Titsias

We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…

Pricing of Securities · Quantitative Finance 2023-05-19 Qian Li , Li Wang

L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an…

Statistics Theory · Mathematics 2013-02-22 L. Gerencsér , M. Mánfay

Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the…

Statistical Finance · Quantitative Finance 2020-09-22 Fearghal Kearney , Han Lin Shang , Lisa Sheenan

This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…

Probability · Mathematics 2025-09-01 Zbigniew Palmowski , Paweł Stȩpniak

We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent…

Mathematical Finance · Quantitative Finance 2020-02-25 Len Patrick Dominic M. Garces , Gerald H. L. Cheang

In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…

Pricing of Securities · Quantitative Finance 2012-06-12 Lorenzo Torricelli

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…

Machine Learning · Computer Science 2022-11-04 Luxuan Yang , Ting Gao , Yubin Lu , Jinqiao Duan , Tao Liu

The Constant Elasticity of Variance (CEV) model is mathematically presented and then used in a Credit-Equity hybrid framework. Next, we propose extensions to the CEV model with default: firstly by adding a stochastic volatility diffusion…

Probability · Mathematics 2007-05-23 Marc Atlan , Boris Leblanc

Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black-Scholes model is appealing because of…

Pricing of Securities · Quantitative Finance 2016-10-04 Runhuan Feng , Alexey Kuznetsov , Fenghao Yang

We consider the Euler scheme for stochastic differential equations with jumps, whose intensity might be infinite and the jump structure may depend on the position. This general type of SDE is explicitly given for Feller processes and a…

Probability · Mathematics 2020-04-17 Björn Böttcher , Alexander Schnurr

This paper focuses on the pricing of the variance swap in an incomplete market where the stochastic interest rate and the price of the stock are respectively driven by Cox-Ingersoll-Ross model and Heston model with simultaneous L\'{e}vy…

Pricing of Securities · Quantitative Finance 2018-03-15 Ben-zhang Yang , Jia Yue , Nan-jing Huang