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

34 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.
LanguageEnglish
Pages405-425
Number of pages21
JournalBIT Numerical Mathematics
Volume51
DOIs
Publication statusPublished - 1 Jun 2011

Fingerprint

Interest Rate Models
Mathematical Finance
Implicit Method
Strong Convergence
Valuation
Justify
Blow-up
Stochastic Equations
Euler
Boundedness
Existence and Uniqueness
Calibration
Monte Carlo Simulation
Numerical Methods
Differential equation
Moment
Converge
Numerical Simulation
Polynomial
Computer simulation

Keywords

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

Cite this

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Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model. / Szpruch, Lukasz; Mao, Xuerong; Higham, Desmond J.; Pan, Jiazhu.

In: BIT Numerical Mathematics, Vol. 51, 01.06.2011, p. 405-425.

Research output: Contribution to journalArticle

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