Pricing Embedded Options Using Fast Fourier Transform to Compare Variance Gamma and Black-Scholes-Merton Model Efficiency

Embedded options are virtually new instruments identical to options in many aspects except their non-tradable nature. Testing the efficiency of the Variance Gamma and Black-Scholes-Merton model on these instruments would provide a vision of transitioning from the classical model with its deficiency to more intricate models. Considering the complicated nature of the Variance Gamma stochastic process to price options, the Fast Fourier Transform (FFT) method is used in conjunction with the Nelder-Mead Simplex method to calibrate models. This research uses the Fast Fourier Transform (FFT) to price four embedded options with the ticker symbols Hefars912, Heghadir912, Heksho208, and Hetrol911 under the two models. The result approves that the Variance Gamma process is more efficient than the Black-Scholes-Merton model in pricing embedded options. Consequently, the variance gamma process would generate fewer errors in pricing those options that can be used in a practical sense.