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High order splitting schemes with complex timesteps and their application in mathematical finance

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  • Philipp Doersek
  • Eskil Hansen

Abstract

High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory, the CIR2 model, is considered. The numerical results are robust for drift-dominated problems, and confirm our theoretical results.

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  • Philipp Doersek & Eskil Hansen, 2012. "High order splitting schemes with complex timesteps and their application in mathematical finance," Papers 1210.5392, arXiv.org.
    • Handle: RePEc:arx:papers:1210.5392
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    References listed on IDEAS

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    1. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
    2. Panagiota Daskalopoulos & Paul M. N. Feehan, 2011. "Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance," Papers 1109.1075, arXiv.org.
    3. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    4. Philipp Doersek & Josef Teichmann, 2010. "A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial) Differential Equations," Papers 1011.2651, arXiv.org.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
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