A fractional Black-Scholes model with stochastic volatility and European option pricing

He, Xin‐Jiang; Lin, Sha

doi:10.1016/j.eswa.2021.114983

Cited by 29 publications

(8 citation statements)

References 30 publications

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“…It is worthy of note that our model can be extended to the jump model with stochastic volatility. For the introduction of this model, readers can refer to He and Lin [24,25], He and Chen [26,27]. Stochastic volatility model can describe the phenomenon of volatility clustering of default intensity, but the derivation of basket CDS price is quite difficult.…”

Section: Introductionmentioning

confidence: 99%

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Chen

Xing

2022

Discrete Dynamics in Nature and Society

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In this paper, we study the basket CDS pricing with two defaultable counterparties based on the reduced-form model. The default jump intensities of the reference firms and counterparties are all assumed to follow the mean-reverting constant elasticity of variance (CEV) processes. Taking the Vasicek process which is a special case of CEV process as an example, the approximate analytic solutions of the joint survival probability density, the probability densities of the first default and the first two defaults can be solved by using PDE method. In addition, we also extend the Vasciek process to the Vasciek process with cojumps and obtain the approximate closed-form solutions of the relevant default probability densities. Then with the expressions of the probability densities, we can get the formula of the basket CDS price with two defaultable counterparties. In the numerical analysis, we do sensitivity analysis and compare the basket CDS prices under our model with that with only one defaultable counterparty. The numerical results show that our model can be applied into practice.

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Section: Introductionmentioning

confidence: 99%

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Chen

Xing

2022

Discrete Dynamics in Nature and Society

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“…However, the assumptions of the classical Black‐Scholes model are so idealistic that many characteristic properties of markets cannot be captured. Therefore, several modified models have been proposed, such as Lévy models, 2 stochastic volatility models, 3–5 and fractional Black‐Scholes models 6–13 …”

Section: Introductionmentioning

confidence: 99%

A high‐order and fast scheme with variable time steps for the time‐fractional Black‐Scholes equation

Song

Lyu

2022

Math Methods in App Sciences

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In this paper, a high‐order and fast numerical method is investigated for the time‐fractional Black‐Scholes equation. In order to deal with the typical weak initial singularity of the solution, we construct a finite difference scheme with variable time steps, where the fractional derivative is approximated by the nonuniform Alikhanov formula and the sum‐of‐exponentials (SOE) technique. In the spatial direction, an average approximation with fourth‐order accuracy is employed. The stability and the convergence with second order in time and fourth order in space of the proposed scheme are religiously derived by the energy method. Numerical examples are given to demonstrate the theoretical statement.

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“…A reasonable option pricing model can accurately predict the future trend of the market, which is of great significance to the steady development of the financial market. In 1973 [2], the first complete option pricing model "B-S model" created by Black and Scholes was used publicly, and since then this model has been widely used in European options pricing [3] [4]. In its basic assumptions, such as the stock price follows a log-normal distribution, the risk-free interest rate is known, the stock price volatility is constant, there is no transaction cost in the hedging portfolio, etc.…”

Section: Introductionmentioning

confidence: 99%

Fractional Stochastic Volatility Pricing of European Option Based on Self-Adaptive Differential Evolution

Hu¹,

Dong²,

Fu³

et al. 2022

JMF

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The option pricing model can predict the future trend of the financial market. In order to more accurately describe the changing process of the financial market, the Hurst index which can describe the characteristics of long-term memory is introduced into the traditional Heston model. Under the assumption that the underlying asset price follows fractional Brownian motion, the fractional stochastic volatility pricing of European option pricing model (Hurst-Heston model) is constructed, and the closed solution of the model is obtained according to the partial differential equation satisfied by the model. By analyzing the relationship between Hurst index and asset price, it is found that the movement process of asset price under the hypothesis of this model is more consistent with the real market change law, which verifies the rationality of the model. In the process of empirical analysis of SSE 50ETF put option data, Self-adaptive Differential Evolution algorithm is used to estimate parameters. The results showed that the error of Hurst-Heston model is smaller than other models, and the prediction error for consecutive trading days is similar. It showed that the pricing results of Hurst-Heston model are more accurate and stable.

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A fractional Black-Scholes model with stochastic volatility and European option pricing

Cited by 29 publications

References 30 publications

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

A high‐order and fast scheme with variable time steps for the time‐fractional Black‐Scholes equation

Fractional Stochastic Volatility Pricing of European Option Based on Self-Adaptive Differential Evolution

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