Metode Numerik Untuk Menentukan Harga Opsi Dengan Model Volatilitas Leland

arsyad L


Option price under transaction cost with leland volatility model is the solution of a non linear diferential equations. To solve this equation used numerical methods based on an upwind finite difference for spatial discretization as well as the use of explicit and implicit methods for discretizing time-stepping. upwind finite difference method with explicit time-stepping scheme proved to be unstable so as not konvegen. While the use of implicit time-stepping scheme is proved monotonous, consistent and stable so that converge to the viscosity solution.


option value, leland volatility model, upwind finite difference methode, convergence, nonlinear partial difeferencial equation

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Ankudinova J. and M. Ehrhardt. 2008. The numerical solution of nonlinear Black-Scholes equations. Computers and Mathematics with Applications.

Bodie Z. Kane A. Marcus AJ. 2002. Investments. Ed ke-3. New Jersey: Prentice Hall.

Barles G. 1997. Convergence of numerical schemes for degenerate parabolic equation arising in finance, in: L.C.G. Rogers, D. Talay (Eds.), Numerical Methods in Finance. Cambridge University Press. Cambridge.

Black F &Scholes M. 1973. The Pricing of Option and Corporate Liabilities. J. Polit. Econ.

Hull J. White A. 2006. Option. Future. and Other Derivatives. 8th edition. New Jersey: Prentice – Hall.

Hull J. White A. 1987. The pricing of option on asset with stochastic volatilities.J. Finance. 42:281-300.

Leland H. E. 1985. Option pricing and replication with transaction costs. Journal of finance.

Lesmana DC& WangS. 2013. An upwind finite difference for a nonlinear Black-Scholes equation governing European option valuation under transaction costs. Journal of applied mathematics and computation.

Niwiga DB. 2005. Numerical method for valuation of financial derivatives. [Thesis]. South Africa : University of Werstern Cape.

Strikwerda JC.1989. Finite difference schemes and partial differential Equation (1 st ed.). chapman & Hall.


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