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A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations

Wu, F. and Mao, X. and Chen, K. and , Chinese Scholarship Council (Funder) (2008) A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations. Journal of Mathematical Analysis and Applications, 348 (1). pp. 540-554. ISSN 0022-247X

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    Abstract

    Empirical studies show that the most successful continuous-time models of the short term rate in capturing the dynamics are those that allow the volatility of interest changes to be highly sensitive to the level of the rate. However, from the mathematics, the high sensitivity to the level implies that the coe±cients do not satisfy the linear growth condition, so we can not examine its properties by traditional techniques. This paper overcomes the mathematical difculties due to the nonlinear growth and examines its analytical properties and the convergence of numerical solutions in probability. The convergence result can be used to justify the method within Monte-Carlo simulations that compute the expected payoff of financial products. For illustration, we apply our results compute the value of a bond with interest rate given by the highly sensitive mean-reverting process as well as the value of a single barrier call option with the asset price governed by this process.

    Item type: Article
    ID code: 13888
    Keywords: structure of interest rate, stochastic differential equation, convergence in probability, Euler-Maruyama method, Monte-Carlo simulation, Mathematics
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science
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      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 15 Dec 2009 16:30
      Last modified: 12 Mar 2012 17:46
      URI: http://strathprints.strath.ac.uk/id/eprint/13888

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