Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model

Lukasz Szpruch, Xuerong Mao, Desmond J. Higham, Jiazhu Pan

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We are interested in the strong convergence of Euler-Maruyama type approximations to the solution of a class of stochastic differential equations models
with highly nonlinear coefficients, arising in mathematical finance. Results in this
area can be used to justify Monte Carlo simulations for calibration and valuation.
The equations that we study include the Ait-Sahalia type model of the spot interest
rate, which has a polynomial drift term that blows up at the origin and a diffusion
term with superlinear growth. After establishing existence and uniqueness for the solution, we show that an appropriate implicit numerical method preserves positivity
and boundedness of moments, and converges strongly to the true solution.
Original languageEnglish
Pages (from-to)405-425
Number of pages21
JournalBIT Numerical Mathematics
Volume51
DOIs
Publication statusPublished - 1 Jun 2011

Keywords

  • interest rate
  • model calibration
  • monte carlo method
  • moment bound

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  • Activities

    • 1 Consultancy

    Stochastic Modelling in Finance

    Xuerong Mao (Advisor)

    1 Oct 201031 Mar 2014

    Activity: Consultancy typesConsultancy

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