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

Abstract

We present a novel idea of a wavelet-based approximation technique using a multi-resolution analysis to investigate the sensitivities of various path-independent binary options under the Black–Scholes environment. The final value problem is transformed into a dimensionless initial value problem; also, to avoid the large truncation error, the infinite domain is truncated into a finite domain. A noteworthy observation is that the proposed Haar wavelet scheme is effective and easy to implement to analyze the different physical and numerical aspects of the options' Greeks. It explicitly provides the numerical approximation of all the derivatives of the solution function. Also, the non-smooth payoff functions are approximated well with the Haar wavelet approximation technique of estimating the spiked functions, so there is no need to deal with the discontinuity separately. We prove the consistency and stability of the proposed method and show that the proposed method is the first- and second-order accurate in the temporal and spatial directions, respectively. A variety of test examples conclusively demonstrates the computational proficiency and the theoretical results of the proposed scheme. Different attributes of the Greeks of distinct binary options are analyzed graphically. The motivational work of the study of various Greeks of different binary options significantly impacts the hedging strategies used by different financial institutes.