
CMUCS97140
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS97140
Accurate Approximations for EuropeanStyle Asian Options
Prasad Chalasani*, Somesh Jha, Ashok Varikooty**
May 1997
CMUCS97140.ps
Keywords: Computational finance, option pricing, asian options,
dynamic programming
In the binomial tree model, we provide efficient algorithms for
computing an accurate lower bound for the value of a Europeanstyle
Asian option with either a fixed or a floating strike. These
algorithms are inspired by the continuoustime analysis of Rogers and
Shi. Specifically we consider lower bounds on the option value that
are given by the expectation of the conditional expectation of the
payoff conditioned on some random variable Z.
For a specific Z, Rogers and Shi estimate this conditional
expectation numerically in continuous time, and show experimentally
that their lower bound is very accurate. We consider a modified random
variable Z that gives a strictly better lower bound. In addition, we
show that this lower bound can be computed exactly in the
nstep binomial tree model in time proportional to n^{7}.
We show that computing the approximation is equivalent to counting paths of
various types, and that this can be done efficiently by a dynamic
programming technique. We present other choices of Z that yield
accurate and efficientlycomputable lower bounds. We also show
algorithms to compute a bound on the error of these approximations, so
that we can compute an upper bound on the option value as well.
15 pages
*Los ALamos National Laboratory, chal@lanl.gov
http://www.c3.lanl.gov/~chal
**CS First Boston, avarikoo@fir.fbc.com
