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  • Liu, Shican  (5)
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  • 1
    Online Resource
    Online Resource
    Using Particle Swarm Optimization Algorithm to Calibrate the Term Structure Model
    Hindawi Limited ; 2021
    In:  Mathematical Problems in Engineering Vol. 2021 ( 2021-1-4), p. 1-11
    Details
    In: Mathematical Problems in Engineering, Hindawi Limited, Vol. 2021 ( 2021-1-4), p. 1-11
    Abstract: One of the advantages of stochastic differential equations (SDE) is that they can follow a variety of different trends so that they can establish complex dynamic systems in the economic and financial fields. Although some estimation methods have been proposed to identify the unknown parameters in virtue of the results in the SDE model to speed up the process, these solutions only focus on using explicit approach to solve SDEs, and therefore they are not reliable to deal with data source merged being large and varied. Thus, this study makes progress in creating a new implicit way to fill in the gaps of accurately calibrating the unknown parameters in the SDE model. Essentially, the primary goal of the article is to generate rigid SDE simulation. Meanwhile, the particle swarm optimization method serves a purpose to search and simultaneously obtain the optimal estimation of the model unknown parameters in the complicated experiment of parameter space in an effective way. Finally, in an interest rate term structure model, it is verified that the method effectively deals with parameter estimation in the SDE model.
    Type of Medium: Online Resource
    ISSN: 1563-5147 , 1024-123X
    URL: Article
    DOI: 10.1155/2021/8893940
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2021
    detail.hit.zdb_id: 2014442-8
    SSG: 11
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    Online Resource
  • 2
    Online Resource
    Online Resource
    The Correction of Multiscale Stochastic Volatility to American Put Option: An Asymptotic Approximation and Finite Difference Approach
    Hindawi Limited ; 2021
    In:  Journal of Function Spaces Vol. 2021 ( 2021-9-17), p. 1-14
    Details
    In: Journal of Function Spaces, Hindawi Limited, Vol. 2021 ( 2021-9-17), p. 1-14
    Abstract: It has been found that the surface of implied volatility has appeared in financial market embrace volatility “Smile” and volatility “Smirk” through the long-term observation. Compared to the conventional Black-Scholes option pricing models, it has been proved to provide more accurate results by stochastic volatility model in terms of the implied volatility, while the classic stochastic volatility model fails to capture the term structure phenomenon of volatility “Smirk.” More attempts have been made to correct for American put option price with incorporating a fast-scale stochastic volatility and a slow-scale stochastic volatility in this paper. Given that the combination in the process of multiscale volatility may lead to a high-dimensional differential equation, an asymptotic approximation method is employed to reduce the dimension in this paper. The numerical results of finite difference show that the multiscale volatility model can offer accurate explanations of the behavior of American put option price.
    Type of Medium: Online Resource
    ISSN: 2314-8888 , 2314-8896
    URL: Article
    DOI: 10.1155/2021/1217665
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2021
    detail.hit.zdb_id: 2861541-4
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    Online Resource
  • 3
    Online Resource
    Online Resource
    Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes
    Hindawi Limited ; 2019
    In:  Journal of Function Spaces Vol. 2019 ( 2019-02-03), p. 1-12
    Details
    In: Journal of Function Spaces, Hindawi Limited, Vol. 2019 ( 2019-02-03), p. 1-12
    Abstract: In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.
    Type of Medium: Online Resource
    ISSN: 2314-8896 , 2314-8888
    URL: Article
    DOI: 10.1155/2019/9754679
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2019
    detail.hit.zdb_id: 2861541-4
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    Online Resource
  • 4
    Online Resource
    Online Resource
    Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate
    Hindawi Limited ; 2020
    In:  Journal of Function Spaces Vol. 2020 ( 2020-11-19), p. 1-10
    Details
    In: Journal of Function Spaces, Hindawi Limited, Vol. 2020 ( 2020-11-19), p. 1-10
    Abstract: In order to tackle the problem of how investors in financial markets allocate wealth to stochastic interest rate governed by a nested stochastic differential equations (SDEs), this paper employs the Nash equilibrium theory of the subgame perfect equilibrium strategy and propose an extended Hamilton-Jacobi-Bellman (HJB) equation to analyses the optimal control over the financial system involving stochastic interest rate and state-dependent risk aversion (SDRA) mean-variance utility. By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. Finally, the numerical examples provided are used to analyze how stochastic (short-term) interest rates and risk aversion affect the optimal control strategies to illustrate the validity of our results.
    Type of Medium: Online Resource
    ISSN: 2314-8888 , 2314-8896
    URL: Article
    DOI: 10.1155/2020/3153297
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2020
    detail.hit.zdb_id: 2861541-4
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    Online Resource
  • 5
    Online Resource
    Online Resource
    The Study of Utility Valuation of Single-Name Credit Derivatives with the Fast-Scale Stochastic Volatility Correction
    MDPI AG ; 2018
    In:  Sustainability Vol. 10, No. 4 ( 2018-03-30), p. 1027-
    Details
    In: Sustainability, MDPI AG, Vol. 10, No. 4 ( 2018-03-30), p. 1027-
    Type of Medium: Online Resource
    ISSN: 2071-1050
    URL: Article
    DOI: 10.3390/su10041027
    Language: English
    Publisher: MDPI AG
    Publication Date: 2018
    detail.hit.zdb_id: 2518383-7
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