Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression

When the underlying asset price process follows a Lévy process, the market becomes incomplete, in which the option pricing can be a complicated problem. This paper proposes a method of asymptotic option pricing when the underlying asset price process follows a pure-jump Lévy process. We express the option price as the expected value of the discounted payoff and expand it at the Black-Scholes price assuming that the price process converges weakly to the Black-Scholes model. The price can be approximated by a formula with 4 parameters, which can easily be estimated using option prices observed in the market. The proposed price explains the market option data better than the Black-Scholes price in real data application with KOSPI 200.