Raahauge, Peter (Department of Finance, Copenhagen Business School)
Abstract
Kinks and jumps in the payoff function of option contracts prevent an effective implementation of higher-order numerical approximation methods. Moreover, the derivatives (the greeks) are not easily determined around such singularities, even with standard lower-order methods. This paper suggests a transformation to turn the original ill-conditioned pricing problem into a well-behaved numerical problem. For a standard test case, both vanilla- and binary call price functions are approximated with (tensor) B-splines of up to 10’th order. Polynomial convergence rates of orders up to approximately 10 are obtained for prices as well as for first and second order derivatives(delta and gamma). Unlike similar studies, numerical approximation errors are measured both as weighted averages and in the supnorm over a state space including time-to-maturities down to a split second.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Copenhagen Business School, Department of Finance in its series Working Papers with number
2004-5.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.: