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 journalArticlepeer-review

66 Citations (Scopus)


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
Publication statusPublished - 1 Jun 2011


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


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