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The Difference between European Option Prices in the Black-Scholes and NIG Models Computed with the DFT
The Difference between European Option Prices in the Black-Scholes and NIG Models Computed with the DFT
This Demonstration shows the difference between the price of a European call option on stock (no dividend is paid and the interest rate is 0) in the Black–Scholes model and the model (due to Barndorff–Nielson) based on a centered exponential Normal Inverse Gaussian (NIG) Lévy process, as a function of the strike price. There are three model parameters that control the NIG process: steepness, asymmetry, and scale (the fourth parameter, location, is set to 0). The other control parameter is the time to expiry of the option.
Given the values of the NIG parameters one can compute instantaneous volatility, which together with the time to expiry and the initial stock price (set to 60) enables us to compute the price of the call option in the Black–Scholes model. The corresponding call option price for the NIG model is computed by means of the Esscher transfer and the fast Fourier transform.