TITLE:
Non-Negativity Preserving Numerical Algorithms for Problems in Mathematical Finance
AUTHORS:
Yuan Yuan
KEYWORDS:
Stochastic Differential Equations, Numerical Methods, Splitting-Step Algorithm, Non-Negativity, Convergence, Simulation
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.3,
March
30,
2018
ABSTRACT:
We give a study result to analyze a rather different, semi-analytical numerical
algorithms based on splitting-step methods with their applications to mathematical
finance. As certain subsistent numerical schemes may fail due to producing
negative values for financial variables which require non-negativity preserving.
These algorithms which we are analyzing preserve not only the
non-negativity, but also the character of boundaries (natural, reflecting, absorbing,
etc.). The derivatives of the CIR process and the Heston model are
being extensively studied. Beyond plain vanilla European options, we creatively
apply our splitting-step methods to a path-dependent option valuation.
We compare our algorithms to a class of numerical schemes based on Euler
discretization which are prevalent currently. The comparisons are given with
respect to both accuracy and computational time for the European call option
under the CIR model whereas with respect to convergence rate for the
path-dependent option under the CIR model and the European call option
under the Heston model.