6533b873fe1ef96bd12d4f1f
RESEARCH PRODUCT
High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation
Bertram DüringMichel FourniéAnsgar Jüngelsubject
DiscretizationMathematical analysisFinite differenceFinite difference coefficientBlack–Scholes modelStability (probability)Parabolic partial differential equationNonlinear systemOption pricing transaction costs parabolic equations compact finite difference discretizationsValuation of optionsScheme (mathematics)Applied mathematicsddc:004General Economics Econometrics and FinanceFinanceMathematicsdescription
A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-01-01 | SSRN Electronic Journal |