Inventory effects on the price dynamics of VSTOXX futures quantified via machine learning

Guterding, Daniel

doi:10.1016/j.jfds.2021.06.001

Cited by 4 publications

(3 citation statements)

References 47 publications

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“…Nevertheless, these models describe the whole dynamics of an underlying asset, instead of just the terminal density at a given point in time, which enables them to also price path-dependent options (Carr et al 2022;Guterding and Boenkost 2018;Tian et al 2014) and other exotic derivatives. (Guterding 2021;Zhu and Lian 2012).…”

Section: Introductionmentioning

confidence: 99%

Sparse Modeling Approach to the Arbitrage-Free Interpolation of Plain-Vanilla Option Prices and Implied Volatilities

Guterding

2023

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We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of the terminal density, we write these integral equations as a system of linear equations. We show that the kernel matrix of this system is, in general, ill-conditioned, so that it cannot be solved for the discretized density using a naive approach. Instead, we construct a sparse model for the kernel matrix using singular value decomposition (SVD), which allows us not only to systematically improve the condition number of the kernel matrix, but also determines the computational effort and accuracy of our method. In order to allow for the treatment of realistic inputs that may contain arbitrage, we reformulate the system of linear equations as an optimization problem, in which the SVD-transformed density minimizes the error between the input prices and the arbitrage-free prices generated by our method. To further stabilize the method in the presence of noisy input prices or arbitrage, we apply an L1-regularization to the SVD-transformed density. Our approach, which is inspired by recent progress in theoretical physics, offers a flexible and efficient framework for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, without the need to explicitly specify a stochastic process, expansion basis functions or any other kind of model. We demonstrate the capabilities of our method in a number of artificial and realistic test cases.

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Section: Introductionmentioning

confidence: 99%

Sparse Modeling Approach to the Arbitrage-Free Interpolation of Plain-Vanilla Option Prices and Implied Volatilities

Guterding

2023

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“…Nevertheless, these models describe the whole dynamics of an underlying asset instead of just the terminal density at a given point in time, which enables them to price also path-dependent options [16][17][18] and other exotic derivatives. 19,20 Inspired by recent progress on inverse problems in theoretical physics 21 , we present a new method that uses the singular value decomposition (SVD) and L 1regularization to obtain a sparse model, i.e. one containing only few non-zero parameters, of the relation between plain-vanilla European option prices and the terminal density of the underlying asset.…”

Section: Introductionmentioning

confidence: 99%

Sparse modeling approach to the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities

Guterding¹

2022

Preprint

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We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of the terminal density, we write these integral equations as a system of linear equations. We show that the kernel matrix of this system is in general ill-conditioned, so that it can not be solved for the discretized density using a naive approach. Instead, we construct a sparse model for the kernel matrix using the singular value decomposition (SVD), which allows us not only to systematically improve the condition number of the kernel matrix, but also determines the computational effort and accuracy of our method. In order to allow for the treatment of realistic inputs that may contain arbitrage, we reformulate the system of linear equations as an optimization problem, in which the SVD-transformed density minimizes the error between the input prices and the arbitrage-free prices generated by our method. To further stabilize the method in the presence of noisy input prices or arbitrage, we apply an L1-regularization to the SVD-transformed density. Our approach, which is inspired by recent progress in theoretical physics, offers a flexible and efficient framework for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, without the need to explicitly specify a stochastic process, expansion basis functions or any other kind of model. We demonstrate the capabilities of our method on a number of artificial and realistic test cases.

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“…Индекс считается единственным наиболее влиятельным предиктором доходности акций на следующий день [3]. Для моделирования VIX учитываются скачки цен инвестиционных активов, их волатильность и позиции трейдеров на фьючерсном рынке VIX, используется модель типа Хестона, представляющая собой хорошую основу для воссоздания ценообразования фьючерсов VIX [4]. При изучении волатильности фондового рынка Соединенных Штатов с помощью CBOE Volatility Index обнаруживается, что существуют периоды как высокой, так и низкой волатильности данного рынка, что характерно соответственно для кризисов и подъемов экономики страны [5].…”

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The Duration of the Impact of the “Investor Fear Index” on the Russian Stock Market

Tenkovskaya

2024

EPB

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In the process of investing during the period of expectation of a new global economic crisis, it is important to sell existing shares on time. In this regard, the topic of research on the impact of the “investor fear index” on the Russian stock market is relevant. The purpose of the research is to establish the duration of the impact of the CBOE Volatility Index (VIX) on the American and Russian stock markets. To achieve this goal, the following tasks have been solved: theoretical issues of the VIX relationship with stock markets, global economic crises, risk-free assets, monetary incentives have been considered; an appropriate research methodology has been selected; economic and mathematical models have been built reflecting the relationship of the stock markets of the United States and Russia with the “investor fear index”. The results of the study work showed that after the impact of high values of the “investor fear index”, signaling the onset of a new global economic crisis, the Russian stock market will recover and grow within twelve years, the price of shares of Sberbank PJSC — within seven years, the price of shares of Gazprom PJSC — within four years. The results of tainted have practical importance for long-term investors.

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Inventory effects on the price dynamics of VSTOXX futures quantified via machine learning

Cited by 4 publications

References 47 publications

Sparse Modeling Approach to the Arbitrage-Free Interpolation of Plain-Vanilla Option Prices and Implied Volatilities

Sparse Modeling Approach to the Arbitrage-Free Interpolation of Plain-Vanilla Option Prices and Implied Volatilities

Sparse modeling approach to the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities

The Duration of the Impact of the “Investor Fear Index” on the Russian Stock Market

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