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Title: Pricing finite horizon fund protection with early withdrawal option
Keywords: American dynamic fund protection options; Finite maturity; Change of numeraire; Space-time transformation; Optimal stopping; Decomposition formula
Issue Date: 13-Sep-2005
Citation: ANG SOOK CHEN (2005-09-13). Pricing finite horizon fund protection with early withdrawal option. ScholarBank@NUS Repository.
Abstract: We present an efficient method to compute the prices and early exercise boundaries of American dynamic fund protection options with finite maturity. A crucial step involves a change of numeraire which reduces the number of states in the valuation problem. This change of numeraire simplifies our valuation procedure by allowing a space-time transformation to be performed to reduce the valuation to a single canonical optimal stopping problem for standard Brownian motion, indexed by two parameters. Further, we prove that, after the space-time transformation, the boundaries are piecewise linear functions for fixed canonical time. This in turn allows us to completely specify the boundaries by considering their behaviour at z*=0, where z* is the transformed maximum asset price. Extensive computations using the Bernoulli walk show that the boundary values at z*=0 are well approximated by piecewise linear functions with a few pieces, which in turn provides us with a fast approximate method to obtain the American dynamic fund protection option values using a decomposition formula.
Appears in Collections:Master's Theses (Open)

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