An explicit and positivity preserving numerical scheme for the mean reverting CEV model. (English) Zbl 1323.60087
Summary: In this paper, we propose an explicit and positivity preserving scheme for the mean reverting constant elasticity of variance model which converges in the mean square sense with convergence order \(a(a-1/2)\).
MSC:
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
Keywords:
mean reverting CEV model; stochastic differential equation; explicit numerical scheme; positivity preservation; order of convergenceReferences:
| [1] | Alfonsi, A.: Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process. Stat. Probab. Lett. 83(2), 602-607 (2013) · Zbl 1273.65007 · doi:10.1016/j.spl.2012.10.034 |
| [2] | Andersen, L.: Simple and efficient simulation of the Heston stochastic volatility model. J. Comput. Financ. 11(3), 1-42 (2008) |
| [3] | Berkaoui, A., Bossy, M., Diop, A.: Euler scheme for SDEs with non-Lipchitz diffusion coefficient: strong convergence. ESAIM 12, 1-11 (2008) · Zbl 1183.65004 · doi:10.1051/ps:2007030 |
| [4] | Gyongy, I., Rasonyi, M.: A note on Euler approximations for SDEs with Holder continuous diffusion coefficients. Stoch. Process. Appl. 121, 2189-2200 (2011) · Zbl 1226.60095 · doi:10.1016/j.spa.2011.06.008 |
| [5] | Halidias, N.: Semi-discrete approximations for stochastic differential equations and applications, Int. J. Comput. Math. 89, 780-794 (2012) · Zbl 1255.65020 |
| [6] | Halidias, N.: Construction of positivity preserving numerical schemes for a class of multidimensional stochastic differential equations. Discret. Contin. Dyn. Syst. 20, 153-160 (2015) · Zbl 1325.65017 |
| [7] | Halidias, N.: A novel approach to construct numerical methods for stochastic differential equations. Numer. Algorithms 66(1), 79-87 (2014) · Zbl 1298.65013 · doi:10.1007/s11075-013-9724-9 |
| [8] | Karatzas, I., Shreve, S.: Brownian Motion and Stochastic Calculus. Springer, New York (1991) · Zbl 0734.60060 |
| [9] | Hurd, T.R., Kuznetsov, A.: Explicit formulas for Laplace transforms of stochastic integrals. Markov Process. Relat. Fields 14, 277-290 (2008) · Zbl 1149.60021 |
| [10] | Mitrinovic, D.S., Pecaric, J.E., Fink, A.M.: Inequalities Involving Functions and Their Integrals and Derivatives. Kluwer, Dordrecht (1991) · Zbl 0744.26011 · doi:10.1007/978-94-011-3562-7 |
| [11] | Yamada, T., Watanabe, S.: On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11, 155-167 (1971) · Zbl 0236.60037 |
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