Convergence of Monte Carlo Simulations involving the Mean-Reverting Square Root Process

By Desmond J. Higham, X. Mao. 2005

146 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d6f26b9304cbbeda842b8fb5cb09978a7cb4dc3f

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Citations in the corpus

Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model (2011, methodology): “In particular, although recent work, such as [2, 4, 5, 13 , 19], has dealt with numerical simulations of SDEs with diffusion coefficient of the form σx( t) ρ”
A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations (2008, background): “Therefore, for any t ∈ [0, T ], by the Hölder inequality and the Doob martingale inequality (cf. Mao [9]), we have E ( sup 0≤t1≤t |R(t1 ∧ θk)− r(t1 ∧ θk)|2 ) ≤ 2λ2tE ∫ t∧θk 0 |R(s)− r̄(s)|2ds + 8σ2E ∫ t∧θk 0 |Rγ(s)− r̄γ(s)|2ds. (4.16) Note that the function h(x) = xγ for any x > 0 and γ ≥ 1 is loca”
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients (2009, unknown): “An explicit bound for the strong L 1 -error is established in Higham & Mao (2005) for the mean-reverting square-root process (a.k.a. CIR process) which has linearly bounded coeﬃcients.”
A comparison of biased simulation schemes for stochastic volatility models (2010, background): “Higham and Mao ( 2005 ) considered an Euler discretization of the Heston model with a novel fix, for which they prove strong convergence.”
A CLOSED‐FORM EXACT SOLUTION FOR PRICING VARIANCE SWAPS WITH STOCHASTIC VOLATILITY (2010, background): “Higham and Mao (2005) proved that the Euler-Maruyama discretization is an attractive approach, providing qualitatively correct approximations.”