Highly Efficient Option Valuation Under the Double Jump Framework with Stochastic Volatility and Jump Intensity Based on Shannon Wavelet Inverse Fourier Technique

In this paper, we explore the highly efficient valuation of financial options under a double exponential jump framework, with stochastic volatility and jump intensity. In particular, we investigate both the accuracy and efficiency of pricing options using the novel Shannon wavelet inverse Fourier technique (SWIFT). Resulting prices are compared to the benchmark Fast Fourier Transform (FFT) and, its more recent alternative, the Fourier Cosine (COS) expansion prices. We demonstrate that not only is the SWIFT method more efficient, it is also accurate with exponential error convergence for both call and put valuations. Finally, further evidence of model robustness and stability is presented through a price sensitivity analysis, where we investigate the significant impact of changing model parameters to the resulting option values.