Valuation of boundary-linked assets by stochastic boundary value problems solved with a wavelet-collocation algorithm
AbstractThis article studies the valuation of boundary-linked assets and their derivatives in continuous-time markets. Valuing boundary-linked assets requires the solution of a stochastic differential equation with boundary conditions, which, often, is not Markovian. We propose a waveletcollocation algorithm for solving a Milstein approximation to the stochastic boundary problem. Its convergence properties are studied. Furthermore, we value boundary-linked derivatives using Malliavin calculus and Monte Carlo methods. We apply these ideas to value European call options of boundary-linked assets.
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Bibliographic InfoPaper provided by Universidad Carlos III de Madrid in its series Open Access publications from Universidad Carlos III de Madrid with number info:hdl:10016/7312.
Length: 162 p.
Date of creation: Jul 2006
Date of revision:
Publication status: Published in Computers and Mathematics with Applications (2006-07) v.v. 52, p.137-160
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Web page: http://www.uc3m.es
Stochastic boundary value problems; Financial derivatives; Wavelets; Collocation methods;
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