Abstract
In this paper, we introduce a special kind of finite volume method called Multi-Point Flux Approximation method (MPFA) to price European and American options in two dimensional domain. We focus on the L-MPFA method for space discretization of the diffusion term of Black–Scholes operator. The degeneracy of the Black-Scholes operator is tackled using the fitted finite volume method. This combination of fitted finite volume method and L-MPFA method coupled to upwind methods gives us a novel scheme, called the fitted L-MPFA method. Numerical experiments show the accuracy of the novel fitted L-MPFA method comparing to well known schemes for pricing options.
Highlights
IntroductionAn option is a contract which gives to the holder the right but not the obligation to buy (call) or to sell (put) an asset at a specific price (strike) at a certain date in the future (expiry date)
In finance, an option is a contract which gives to the holder the right but not the obligation to buy or to sell an asset at a specific price at a certain date in the future
The integrals over the eastern and northern edges of the control C11, which are not in the degeneracy region, are approximated using the L-Multi-Point Flux Approximation method (L-MPFA) method coupled to the upwind methods (1st and 2nd order)
Summary
An option is a contract which gives to the holder the right but not the obligation to buy (call) or to sell (put) an asset at a specific price (strike) at a certain date in the future (expiry date). European options are options that can be exercised only at expiry date while American options can be exercised anytime before the expiry date. Many studies focused on the pricing problem of American options were conducted and the linear complementary problem approach was quite popular for pricing American options (see Kovalov et al 2007; Zhang et al 2009; Wang et al 2006; Topper 2005). This approach brings us to solve linear complementary problem stated as follows (see Topper 2005):
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