3 research outputs found
Collocation method based on modified âcubicâ B-spline âfor option pricing âmodels
Collocationââ âmethod âbased âon âmodifiedâ cubic B-spline functions âhas âbeen âdevelopedâ âfor âthe âvaluation âââof Europeanâ, âAmerican and Barrier options of single âasset. âThe ânew âapproach âcontains ââdiscretizing âofâ tââemporal âderivativeâ âusing âfinite âdifference âapproximations âand âapproximatingâ the option price with the âmodifiedâ B-spline functionsâ. âStability of this method has been discussed and shown that it is unconditionally stableâ. âThe âefficiency âof âtheâ âproposed âmethod âis âtested âby âdifferent âexamplesâââ.
Parameter estimation approach to the free boundary for the pricing of an American call option
In this paper, we consider a free boundary problem which arises in the pricing of an American call option. The free boundary represents the optimal exercise price as a function of time before a maturity date. We are developing a parameter estimation technique to obtain both the optimal exercise curve of an American call option and its price. For the numerical solution of a forward problem, a time marching finite element method is adopted. Numerical experiment shows the convergence property of the approximation scheme. (C) 2006 Elsevier Ltd. All rights reserved.X111sciescopu