Haar‐wavelet based approximation for pricing American options under linear complementarity formulations

Abstract

In this manuscript, we present a novel and highly accurate wavelet‐based approximation technique to explore the sensitivities and value of American options diagnosed by linear complementarity problems. For a detailed analysis of such financially relevant problems, we transform the actual final value problem into a dimensionless initial value problem. To avoid the unacceptable large truncation error, the unbounded domain is trimmed into a bounded domain. A remarkable observation is that to investigate the various physical and numerical aspects of the options' sensitivities; the proposed scheme is efficient as it explicitly provides the numerical approximation of all the derivatives of the solution function. The multiresolution technique of the wavelets and the convergence of the proposed wavelet scheme are comprehensively analyzed. The wavelet analysis is accompanied by illustrative examples to demonstrate the proficiency and robustness of the present method coupled with graphical representations. It has been shown that the present method is efficient to solve free boundary problems. It is worthy to note that the highly accurate and promising computational results are enough to confirm the performance of the proposed method. The simulated results of options' Greeks analyzed and discussed have vast applications in different financial institutes and trading markets.

A wavelet‐based novel approximation to investigate the sensitivities of various path‐independent binary options

“…Their characteristics can distinguish the standard options (European and American): a European option can only be exercised at the expiry date. In contrast, an American option 1 can be exercised at any time up to and including the expiry date. On the other hand, the exotic options differ from the vanilla options in several ways 2 .…”