Wu, F. and Mao, X. and Chen, K. and , Chinese Scholarship Council (Funder) (2008) A highly sensitive meanreverting process in finance and the EulerMaruyama approximations. Journal of Mathematical Analysis and Applications, 348 (1). pp. 540554. ISSN 0022247X

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Abstract
Empirical studies show that the most successful continuoustime 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 MonteCarlo 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 meanreverting 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, EulerMaruyama method, MonteCarlo simulation, Mathematics, Analysis, Applied Mathematics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  15 Dec 2009 16:30 
Last modified:  21 May 2015 11:06 
URI:  http://strathprints.strath.ac.uk/id/eprint/13888 
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