Pricing Exotic Options Under NIG Model

Option is an important financial derivatives which is appropriate for hedging risks and locking the cost,while option pricing is particularly important.In this paper we first find the risk-neutral measure Q by utilizing the Esscher transform under the assumption that the underlying asset price follows exponential NIG process.Then the pricing of power option and forward-start option are studied by using the risk-neutral pricing method.The main results are as follows:Firstly,we derive the pricing formulas for the power option in terms of the Fourier integral of the characteristic function by Fourier transform and its inverse.The values of power option across the whole spectrum of the exercise price are calculated by FFT algorithm after truncating and discretizing Fourier integral.We also test the proposed model for Shanghai 50 ETF options and find that the NIG prices are closer to the market prices than BSM ones.Secondly,by using the method of measure transform we convert the expected payoff at maturity of forward-start option into the expectation of the indicator function.And then we obtain the pricing formula of forward-start option by utilizing the relationship between probability distribution function and characteristic function.Moreover we perform numerical analysis.