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Title of article :
Highly nonlinear model in finance and convergence of Monte Carlo simulations
Author/Authors :
Cheng، نويسنده , , Shuenn-Ren Cheng، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2009
Pages :
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Abstract :
In this paper we consider the highly nonlinear model in finance proposed by Ait-Sahalia [Y. Ait-Sahalia, Testing continuous-time models of the spot interest rate, Rev. Finan. Stud. 9 (2) (1996) 385–426]. Both the drift and diffusion coefficients in this model do not obey the classical linear growth condition. To overcome the difficulties due to the highly nonlinear coefficients, we develop several new techniques to study the analytical properties of the model including the positivity and boundedness. In particular, we show that the Euler–Maruyama approximate solutions converge to the true solution in probability. The convergence result justifies clearly that the Monte Carlo simulations based on the Euler–Maruyama scheme can be used to compute the expected payoff of financial products e.g. options.
Keywords :
stochastic differential equation , convergence in probability , Euler–Maruyama method , Monte Carlo simulation
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications
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Link To Document :