American Options

Hilber, Norbert; Reichmann, Oleg; Schwab, Christoph; Winter, Christoph

doi:10.1007/978-3-642-35401-4_5

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American Option: Linear Complementary Problem2

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2016

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“…Then, for any w ∈ W A , multiplying (17a) by w − U 0 (which does not change the inequality sign), taking integral over the domain Ω and subtracting the integral of (17b) from it, we obtain the variational formulation of ( 17) as [39,Chapter 12]…”

Section: American Option: Linear Complementary Problemmentioning

confidence: 99%

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Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements

Kozpınar,

Uzunca,

Karasözen

2016

Preprint

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We apply interior penalty discontinuous Galerkin finite element method (dGFEM) for pricing of European and American options for Heston PDE. The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with non-smooth initial and boundary conditions are illustrated in several numerical examples for European call, as well as butterfly spread, digital call and American put options. The convection dominated Heston PDE for vanishing volatility is efficiently solved utilizing the adaptive dGFEM algorithm. The linear complementary problem for the American option is solved using the norm preconditioned projected successive over relaxation (PSOR) method. Numerical experiments illustrate that dGFEM is an accurate and efficient method for pricing options.

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Section: American Option: Linear Complementary Problemmentioning

confidence: 99%

“…The PSOR method converges for symmetric positive definite matrices B [40]. The PSOR works also for non-symmetric but diagonally dominant matrices [39]. But the matrix B resulting from SIPG discretization is not diagonally dominant.…”

Section: American Option: Linear Complementary Problemmentioning

confidence: 99%