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Adaptive Methods For Variational Inequalities: Theory And Applications In Option Pricing,Used
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Variational inequalities (VIs) arise from a wide range of application areas, like mechanics, control theory, engineering, and finance. One of the emerging applications of variational inequalities in finance is valuation of Americanstyle options. An option is a derivative contract where the future payoffs to the buyer and seller of the contract are determined by the price of another security, such as a common stock or a basket of stocks. American option pricing can be formulated as an obstacle problem, a particular example of VIs. To solve time dependent variational inequalities numerically, we employ the explicit or implicit Euler method for timediscretization and the finite element method (FEM) for spacediscretization with adaptive timespace mesh refinement techniques. Adaptive mesh refinement is an important tool to deal with multiscale phenomena and to reduce the size of the linear systems that arise from the discretization.
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