an:01591306
Zbl 1072.91578
Forsyth, P. A.; Vetzal, K. R.
Implicit solution of uncertain volatility/transaction cost option pricing models with discretely observed barriers
EN
Appl. Numer. Math. 36, No. 4, 427-445 (2001).
00073201
2001
j
91G60 65M06 91G20
option pricing; nonlinear PDE; implicit method
Summary: Option pricing models with uncertain volatility/transaction costs give rise to a nonlinear PDE. Previous work has focused on explicit methods. However, pricing discretely observed barrier options requires a very small grid spacing near the barrier, and as a result, the maximum stable timestep for an explicit method is impractically small. A fully implicit method is developed for nonlinear option pricing models, and applied to arithmetic step options, where the option loses a fraction of its value for every day over the barrier.