On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model

Ivanov, Roman

doi:10.3390/risks11060111

Cited by 5 publications

(3 citation statements)

References 60 publications

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“…In practical markets, however, investors incur trading costs, including bid-ask spreads, brokerage fees, and market impact, all of which influence option prices and trading strategies. The Black-Scholes model presumes a market without frictions, thus causing potential variances between theoretical and actual option prices [7].…”

Section: Challenges and Limitations Of The Black-scholes Modelmentioning

confidence: 99%

Evolution of option pricing models: From Black-Scholes to Heston and beyond

Hong

2024

TNS

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This essay explores the evolution of option pricing models, tracing their development from the foundational Black-Scholes model to more advanced frameworks such as the Heston model and beyond. Beginning with an introduction to option pricing theory, the essay discusses the origins of the Black-Scholes model and its assumptions, as well as the challenges and limitations it faces. It then examines the extension of the Black-Scholes model, so-called the Black-Scholes-Merton model. It incorporates dividends, and lays the groundwork for further research into options pricing and financial derivatives. Then various stochastic volatility models emerge, and the essay chooses the Heston model as a typical example for analysis, highlighting its advantages and applications in option pricing. Furthermore, the essay compares the Heston model with other option pricing models, including the SABR model and Bates model. At the end of the essay, recent advances and future directions in option pricing are introduced and discussed. Through this comprehensive exploration, readers can gain a deeper understanding of the evolution of option pricing models and their significance in modern finance.

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Section: Challenges and Limitations Of The Black-scholes Modelmentioning

confidence: 99%

Evolution of option pricing models: From Black-Scholes to Heston and beyond

Hong

2024

TNS

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“…For their properties and connections with other special functions, see Rathie and de Sena Monteiro Ozelim [27], Choi et al [28], and Srivastava [29]. We refer to Madan et al [30], Ano and Ivanov [31], and Ivanov [32] regarding the variance-gamma model, to Ivanov [33] regarding the skew Student's t model, and to Ano and Ivanov [31] and Ivanov and Temnov [10] regarding the NIG one. At the same time, modern research papers that analyze data from financial markets often recommend the simulation of index returns with GH distribution as well as the above-mentioned ones.…”

Section: Introductionmentioning

confidence: 99%

The Semi-Hyperbolic Distribution and Its Applications

Ivanov

2023

Stats

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This paper studies a subclass of the class of generalized hyperbolic distribution called the semi-hyperbolic distribution. We obtain analytical expressions for the cumulative distribution function and, specifically, their first and second lower partial moments. Using the received formulas, we compute the value at risk, the expected shortfall, and the semivariance in the semi-hyperbolic model of the financial market. The formulas depend on the values of generalized hypergeometric functions and modified Bessel functions of the second kind. The research illustrates the possibility of analysis of generalized hyperbolic models using the same methodology as is employed for the well-established variance-gamma model.

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“…We refer the reader to [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] for a detailed overview of the processes mentioned above. These are just a few examples of the stochastic processes commonly employed in insurance modeling.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Exact Controllability of Mean and Variance of an Insurance Policy

Rajaram

Ritchey

2023

Mathematics

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We explore the simultaneous exact controllability of mean and variance of an insurance policy by utilizing the benefit St and premium Pt as control inputs to manage the policy value tV and the variance 2σt of future losses. The goal is to determine whether there exist control inputs that can steer the mean and variance from a prescribed initial state at t=0 to a prescribed final state at t=T, where the initial–terminal pair of states (0V,TV) and (2σ0,2σT) represent the mean and variance of future losses at times t=0 and t=T, respectively. The mean tV and variance 2σt are governed by Thiele’s and Hattendorff’s differential equations in continuous time and recursive equations in discrete time. Our study focuses on solving the problem of exact controllability in both continuous and discrete time. We show that our result can be used to devise control inputs St,Pt in the interval [0,T] so that the mean and variance partially track a specified curve tV=a(t) and 2σt=b(t), respectively, i.e., at a fine sampling of points in the time interval [0,T].

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On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model

Cited by 5 publications

References 60 publications

Evolution of option pricing models: From Black-Scholes to Heston and beyond

Evolution of option pricing models: From Black-Scholes to Heston and beyond

The Semi-Hyperbolic Distribution and Its Applications

Simultaneous Exact Controllability of Mean and Variance of an Insurance Policy

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