发帖
雷达卡
a b s t r a c t
In this paper, we introduce a new numerical scheme, based on the ADI (alternating
directionimplicit)method,topriceAmericanputoptionswithastochasticvolatilitymodel.
Upon applying a front-fixing transformation to transform the unknown free boundary
into a known and fixed boundary in the transformed space, a predictor–corrector finite
difference scheme is then developed to solve for the optimal exercise price and the option
values simultaneously. Based on the local von Neumann stability analysis, a stability
requirement is theoretically obtained first and then tested numerically. It is shown that the
instability introduced by the predictor can be damped, to some extent, by the ADI method
that is used in the corrector. The results of various numerical experiments show that this
new approach is fast and accurate, and can be easily extended to other types of financial
derivatives with an American-style exercise.
Another key contribution of this paper is the proposition of a set of appropriate
boundaryconditions,particularlyinthevolatilitydirection,uponrealizingthatappropriate
boundary conditions in the volatility direction for stochastic volatility models appear to
be controversial in the literature. A sound justification is also provided for the proposed
boundary conditions mathematically as well as financially.
京公网安备 11010802022788号
