Revealing the Implied Risk-neutral MGF from Options: the Wavelet Method

Options are believed to contain unique information on the risk-neutral moment generating function (MGF) or the risk-neutral probability density function (PDF) of the underlying asset. This paper applies the wavelet method to approximate the implied risk-neutral MGF from option prices. Monte Carlo simulations are carried out to show how the risk-neutral MGF can be obtained using the wavelet method. With the Black–Scholes model as the benchmark, we offer a novel method to reveal the implied MGF, and to price in-sample options and forecast out-of-sample option prices with the estimated MGF.