| Abstract: |
| We present ways in which barrier and lookback options can
be regarded, in some sense, as \emph{ path-independent options}. Exploiting
this, we derive closed form formulae for the coefficients of $1/\sqrt{n}$ and
$1/n$ in the expansion of the error of our \emph{path-independent pricing}
when the underlying is approximated by the Cox, Ross, and Rubinstein
model. This yields a convergence of order $n^{-3/2}$ to the price of barrier
and lookback options in the Black-Scholes model. Our results are supported and
illustrated by numerical examples. |
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