Computation of the unknown volatility from integral option price observations in jump–diffusion models

Georgiev, Slavi G.; Vulkov, Lubin G.

doi:10.1016/j.matcom.2021.05.008

Cited by 11 publications

(3 citation statements)

References 21 publications

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“…Efficient Monte Carlo (MC and quasi-Monte Carlo (QMC) methods [31][32][33] play a crucial role in conducting SA for large-scale computer models, ensuring optimal utilization of computational resources. These methods prove particularly valuable for analyzing intricate models characterized by a multitude of input parameters, as they can handle substantial volumes of data and yield rapid and accurate outcomes.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Unveiling the Power of Stochastic Methods: Advancements in Air Pollution Sensitivity Analysis of the Digital Twin

Todorov

Dimov

2023

Atmosphere

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Thorough examination of various aspects related to the distribution of air pollutants in a specific region and the factors contributing to high concentrations is essential, as these elevated levels can be detrimental. To accomplish this, the development and improvement of a digital twin that encompasses all relevant physical processes in the atmosphere is necessary. This tool, known as DIGITAL AIR, has been created, and it is now necessary to extend it with precise sensitivity analysis. DIGITAL AIR is gaining popularity due to its effectiveness in addressing complex problems that arise in intricate environments; this motivates our further investigations. In this paper, we focus on the preparation and further investigation of DIGITAL AIR through sensitivity analysis with improved stochastic approaches for investigating high-level air pollutants. We discuss and test the utilization of this digital tool in tackling the issue. The unified Danish Eulerian model (UNI-DEM) plays a crucial role within DIGITAL AIR. This mathematical model, UNI-DEM, is highly versatile and can be applied to various studies concerning the adverse effects caused by elevated air pollution levels.

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Section: Sensitivity Analysismentioning

confidence: 99%

Unveiling the Power of Stochastic Methods: Advancements in Air Pollution Sensitivity Analysis of the Digital Twin

Todorov

Dimov

2023

Atmosphere

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“…Regarding the pros and cons of the two latter solutions, one may refer to . Furthermore, Georgiev & Vulkov (2021) proposed a robust algorithm determining time-dependent volatility, whereas Tae-Kyoung et al ( 2022) constructed a network for estimating the Black-Scholes implied volatilities through large-scale online learning. Last but not least, in case of turbulent markets the reader may refer to the analytical approximation of the critical stock price as well as of the implied volatility by Bufalo & Orlando (2022).…”

Section: Literature Reviewmentioning

confidence: 99%

A generalized derivation of the Black-Scholes implied volatility through hyperbolic tangents

Mininni¹,

Orlando²,

Tagliatela³

2022

Argumenta Oeconomica

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This article extends the previous research on the notion of a standardized call function and how to obtain an approximate model of the Black-Scholes formula via the hyperbolic tangent. Although the Black-Scholes approach is outdated and suffers from many limitations, it is still widely used to derive the implied volatility of options. This is particularly important for traders because it represents the risk of the underlying, and is the main factor in the option price. The approximation error of the suggested solution was estimated and the results compared with the most common methods available in the literature. A new formula was provided to correct some cases of underestimation of implied volatility. Graphic evidence, stress tests and Monte Carlo analysis confirm the quality of the results obtained. Finally, further literature is provided as to why implied volatility is used in decision making.

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“…Also, existing studies have suggested the importance of explicitly allowing for jumps, or discontinuities, in the estimation of specific stochastic volatility models (Andersen et al, 2002; Chan & Maheu, 2002; Eraker, 2004; Georgiev & Vulkov, 2021; Laurent & Shi, 2020). Based on the continuous‐time jump diffusion process, Andersen et al (2007) distinguish the jump from non‐jump movements in volatility and find that the volatility jump component is both highly important and distinctly less persistent than the continuous component.…”

Section: Introductionmentioning

confidence: 99%

Which implied volatilities contain more information? Evidence from China

Wang

2023

Int. J Fin Econ

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This paper aims to examine the information capacity of implied volatility (IV) estimated with model‐based and model‐free methods. Among the model‐free approaches, we further divide them into direct estimation (DE) and indirect estimation (INDE) approaches according to the computational process. We study the predictability of different implied volatilities on realized volatility over various forecasting horizons based on the Chinese option data. The out‐of‐sample results indicate that all the IVs contain the information transmitted by option market, and have predictive ability on the realized volatility. Using three different loss functions, we find that the implied volatilities estimated with DE approach contain more information. When considering different market scenarios, we find model‐based implied volatility performs best during the stable period and the DE approach always works well no matter the investor sentiment is normal or abnormal. Moreover, we also discuss the predictability of implied volatility on crash risk. Our results remain robust by using alternative realized volatility and alternative rolling windows.

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Computation of the unknown volatility from integral option price observations in jump–diffusion models

Cited by 11 publications

References 21 publications

Unveiling the Power of Stochastic Methods: Advancements in Air Pollution Sensitivity Analysis of the Digital Twin

Unveiling the Power of Stochastic Methods: Advancements in Air Pollution Sensitivity Analysis of the Digital Twin

A generalized derivation of the Black-Scholes implied volatility through hyperbolic tangents

Which implied volatilities contain more information? Evidence from China

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