Option valuation and hedging in markets with a crunch

El-Khatib, Youssef; Hatemi‐J, Abdulnasser

doi:10.1108/jes-04-2016-0083

Cited by 14 publications

(6 citation statements)

References 15 publications

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“…It can be seen as a generalization of the models considered in El-Khatib and Hatemi-J (2017) on the valuation of options during the crisis and in El-Khatib and Hatemi-J (2019) , and El-Khatib and Hatemi-J (2022) where the authors investigated options pricing in illiquid and high volatile situations. The SDE (3.1) expands the previous models by adding regime switching which permits to vary the parameters according to different economic situations.…”

Section: Model Formulationmentioning

confidence: 99%

On a regime switching illiquid high volatile prediction model for cryptocurrencies

El-Khatib

Hatemi‐J

2023

JES

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PurposeThe current paper proposes a prediction model for a cryptocurrency that encompasses three properties observed in the markets for cryptocurrencies—namely high volatility, illiquidity, and regime shifts. As far as the authors’ knowledge extends, this paper is the first attempt to introduce a stochastic differential equation (SDE) for pricing cryptocurrencies while explicitly integrating the mentioned three significant stylized facts.Design/methodology/approachCryptocurrencies are increasingly utilized by investors and financial institutions worldwide as an alternative means of exchange. To the authors’ best knowledge, there is no SDE in the literature that can be used for representing and evaluating the data-generating process for the price of a cryptocurrency.FindingsBy using Ito calculus, the authors provide a solution for the suggested SDE along with mathematical proof. Numerical simulations are performed and compared to the real data, which seems to capture the dynamics of the price path of two main cryptocurrencies in the real markets.Originality/valueThe stochastic differential model that is introduced and solved in this article is expected to be useful for the pricing of cryptocurrencies in situations of high volatility combined with structural changes and illiquidity. These attributes are apparent in the real markets for cryptocurrencies; therefore, accounting explicitly for these underlying characteristics is a necessary condition for accurate evaluation of cryptocurrencies.

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Section: Model Formulationmentioning

confidence: 99%

On a regime switching illiquid high volatile prediction model for cryptocurrencies

El-Khatib

Hatemi‐J

2023

JES

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“…We suppose that the solutions of stochastic corona model (1) exists in the interval

. To solve the first and second equations of model (1) , as in [35] we consider the process

defined by the SDE

01

where

and

are two stochastic processes satisfying the required conditions to insure a solution of (31) as follows

…”

Section: Existence and Uniqueness Analysismentioning

confidence: 99%

Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model

2021

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In this article we propose a stochastic model to discuss the dynamics of novel corona virus disease. We formulate the model to study the long run behavior in varying population environment. For this purposes we divided the total human population into three epidemiological compartments: the susceptible, covid-19 infected, recovered and recovered along with one class of reservoir. The existence and uniqueness of the newly formulated model will be studied to show the well-possedness of the model. Moreover, we investigate the extinction analysis as well as the persistence analysis to find the disease extinction and disease persistence conditions. At the end we perform simulation to justify the investigation of analytical work with the help of graphical representations.

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“…Let us assume that the solutions of system (1) exist in +¥ 0, [ ). Following the same methodology as in [22], each SDE in our stochastic corona model (1) is associated to a geometric Brownian motion. In fact, we consider the 4 processes x…”

Section: {( ) }mentioning

confidence: 99%

“…Following [22], we find the solutions of the processes of model (1) by assuming that each solution can be written as product of a stochastic process times its corresponding geometric Brownian motion. For instance, we suggest that…”

Section: {( ) }mentioning

confidence: 99%

Modeling the dynamics of the SARS-CoV-2 virus in a population with asymptomatic and symptomatic infected individuals and vaccination

et al. 2021

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The SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics. The pandemic has spread worldwide through human interactions. Since the nature of the disease differs everywhere and it has a stochastic effect, we therefore develop a stochastic mathematical model to investigate its temporal dynamics. Asymptomatic individuals have a major effect on the spreading dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups. Multiple vaccinations have commenced across the globe. In this study, we assume that the vaccine confers permanent immunity. Moreover, due to the unpredictable characteristics of the disease random fluctuations are assumed in every population group. Using this model we show the existence and uniqueness of positive solutions to the proposed problem. We also discuss the disease extinction and persistence in the model to depict how contagious diseases can be eliminated from the community. We use the real data of SARS-CoV-2 virus, reported in Oman from the 1st January 2021 to 23rd May 2021 to parameterize the model. We then perform large-scale computational analysis to show the numerical simulation and verify the analytical findings.

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Option valuation and hedging in markets with a crunch

Cited by 14 publications

References 15 publications

On a regime switching illiquid high volatile prediction model for cryptocurrencies

On a regime switching illiquid high volatile prediction model for cryptocurrencies

Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model

Modeling the dynamics of the SARS-CoV-2 virus in a population with asymptomatic and symptomatic infected individuals and vaccination

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