High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation

72 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Analytical and Numerical Methods for Pricing Financial Derivatives (2011, background): “[64], Avellaneda and Paras [10]), feedback and illiquid market effects due to large traders choosing given stock-trading strategies (Frey [50], Frey and Patie [51], Frey and Stremme [52], During et al.[39], Schönbucher and Wilmott [99]), imperfect replication and investor’s preferences (Barles and S”
Compact finite difference method for American option pricing (2007, methodology): “[13,14] give a compact finite difference method to solve the nonlinear Black–Scholes equation, however, their methods are hard to extend to American option pricing problems.”
Convergence of a High-order Compact Finite Difference Scheme for a Nonlinear Black-Scholes Equation (2004, methodology): “We use the following abbreviations α = λh 2 , r = k h2 , µ = λk h · (10) We define the two-level three-point scheme R3C as in [13] by DtU n i = β ( 1 2 + A1 ) ∆2Uni + β ( 1 2 + A2 ) ∆2Un+1i − λ ( 1 2 + B1 ) ∆0Uni − λ ( 1 2 + B2 ) ∆0Un+1i , (11) where DtUni = (U n+1 i − Uni )/k, and Ai, Bi are real c”