December 2013
Intermediate to advanced
484 pages
14h 54m
English
Content preview from Nonlinear Option Pricing
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32 Monte Carlo
are recent and not often mentioned in the literature, we will review these
properties of the Euler bias in greater detail in Section 2.2. Then Section 2.3
will be devoted to the reduction of bias.
REMARK 2.1 When the SDE has dimension one, meaning that its solu-
tion X and the driving Brownian motion are scalars, we can exactly simulate
X
T
; see [60] and Chapter 13, Section 13.6.4, for an alternative but related
method. However, finite difference schemes are more efficient than the Monte
Carlo method in this one-dimensional case.
2.2 Euler discretization error
To make the statements precise, we must introduce some notation. Let d, r ≥
1 be
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