The sub-fractional CEV model

Araneda, Axel A.; Bertschinger, Nils

doi:10.1016/j.physa.2021.125974

Cited by 12 publications

(15 citation statements)

References 22 publications

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“…with the initial condition r 0 > 0, where κ(t), θ(t) and σ(t) are smooth and bounded time-dependent parameter functions and W t is a standard Brownian motion, which has asymmetric sample paths, under a probability space (Ω, F , P ) with filtration {F t } t≥0 . In this study, we only focus on the case that β < 1 in the SDE (1). Let := 2 − 2β.…”

Section: Ind-cev Processmentioning

confidence: 99%

“…The stochastic differential equation (SDE) has been used to model various phenomena and investigate their properties, such as the moments, variance and conditional moments, which are beneficial for estimating parameters that play significant roles in several practical applications. For example, financial derivative prices, such as moment swaps, can be obtained by calculating the conditional moments of their payoffs under the risk neutral measure; see for more concrete studies Araneda et al [1], Cao et al [2], He and Zhu [3] and Nonsoong et al [4]. Actually, such moments can be directly computed by employing SDE's transition probability density function (PDF).…”

Section: Introductionmentioning

confidence: 99%

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Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

2022

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The stochastic differential equation (SDE) has been used to model various phenomena and investigate their properties. Conditional moments of stochastic processes can be used to price financial derivatives whose payoffs depend on conditional moments of underlying assets. In general, the transition probability density function (PDF) of a stochastic process is often unavailable in closed form. Thus, the conditional moments, which can be directly computed by applying the transition PDFs, may be unavailable in closed form. In this work, we studied an inhomogeneous nonlinear drift constant elasticity of variance (IND-CEV) process, which is a class of diffusions that have time-dependent parameter functions; therefore, their sample paths are asymmetric. The closed-form formulas for conditional moments of the IND-CEV process were derived without having a condition on eigenfunctions or the transition PDF. The analytical results were examined through Monte Carlo simulations.

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Section: Ind-cev Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

2022

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“…Although the fractional Brownian motion model can greatly describe the process of asset price changes in financial markets, it allows the existence of arbitrage opportunities [6] [7]. In order to solve the arbitrage problem in the financial market, a large number of scholars have proposed modified fractional Brownian motion models to describe the price changes in the financial market [8] [9] [10].…”

Section: Introductionmentioning

confidence: 99%

Asset Pricing and Simulation Analysis Based on the New Mixture Gaussian Processes

Peng

2023

JAMP

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European compound option pricing model is established by using the mixed bifractional Brownian motion. Firstly, using the principle of risk-neutral pricing, the European option pricing formulas and the parity formulas are obtained. Secondly, with the Delta hedging strategy, the corresponding compound option pricing formulas and the parity formulas are got. Finally, using the daily closing price data of "Lingang B shares" and "Yitai B shares" respectively, the results show that the mixed model is closer to the true value than the previous model.

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“…Cheng and Xu considered the pricing of vulnerable options under a mixed FBM model with jumps [9]. By introducing an FBM to the constant elasticity of variance (CEV) model, Araneda and Bertschinger proposed a sub-fractional CEV model and considered the pricing of options underneath [3]. Han et al raised a stochastic volatility model driven by both an FBM and a standard Brownian motion (BM), and obtained an analytical solution for the European option price [12].…”

Section: Introductionmentioning

confidence: 99%

An Imex-Based Approach for the Pricing of Equity Warrants Under Fractional Brownian Motion Models

CHEN,

JIANG

2022

ANZIAM J.

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In this paper, the pricing of equity warrants under a class of fractional Brownian motion models is investigated numerically. By establishing a new nonlinear partial differential equation (PDE) system governing the price in terms of the observable stock price, we solve the pricing system effectively by a robust implicit-explicit numerical method. This is fundamentally different from the documented methods, which first solve the price with respect to the firm value analytically, by assuming that the volatility of the firm is constant, and then compute the price with respect to the stock price and estimate the firm volatility numerically. It is shown that the proposed method is stable in the maximum-norm sense. Furthermore, a sharp theoretical error estimate for the current method is provided, which is also verified numerically. Numerical examples suggest that the current method is efficient and can produce results that are, overall, closer to real market prices than other existing approaches. A great advantage of the current method is that it can be extended easily to price equity warrants under other complicated models.

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The sub-fractional CEV model

Cited by 12 publications

References 22 publications

Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

Asset Pricing and Simulation Analysis Based on the New Mixture Gaussian Processes

An Imex-Based Approach for the Pricing of Equity Warrants Under Fractional Brownian Motion Models

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