Abstract
Our primary goal was to find analytic expressions for delta of option prices, where the underlying asset’s price is modeled with an exponential normal inverse Gaussian (NIG) process. We used the density method, starting with a Black-Scholes style price, we moved the derivative into the expectation used in the pricing by Leibniz’ rule. In a Brownian model setting we considered delta and gamma for options, as well as for spread options. We found expressions for delta in a NIG modeled setting. We also found an exponential integrability condition for NIG processes, and a Martingale condition for discounted NIG price processes. We ended with numerical implementations of the price and delta for both NIG and Brownian models, using realistic parameter values, and compared these. We reached a conclusion that except for options with very short strike times, the differences in price and delta between the two models are small.