Stephen Figlewski, Bin Gao
ABSTRACT
Exact closed-form valuation equations for traded derivative securities
are rare. Numerical approximation, most commonly with Binomial and Trinomial
lattice models, gives exact valuation in the limit, but convergence is
non-monotonic and often slow, due to 'distribution error' and 'truncation
error.' This paper explains how truncation error arises and describes the
Adaptive Mesh Model (AMM), a new approach that sharply reduces it by grafting
one or more small sections of fine high-resolution lattice onto a tree
with coarser time and price steps. Three different AMM structures are presented,
one for pricing ordinary options, one for barrier options, and one for
computing delta and gamma efficiently. The AMM approach can be adapted
to a wide variety of contingent claims, yielding significant improvement
in efficiency with very little increase in computational effort. For some
common problems, including calculating delta, accuracy increases by several
orders of magnitude relative to the standard models with no measurable
increase in execution time at all.
Subject: Investments, Derivatives, Hedging (Theoretical)
Figlewski: (212)-998-0712 sfiglews@stern.nyu.edu
Gao: (919) 962-7182 gaob.bsacd1@mhs.unc.edu
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