Revealing the Implied Risk-neutral MGF with the Wavelet Method

Options are believed to contain unique information about the risk- neutral moment generating function (MGF hereafter) or the risk-neutral probability density function (PDF hereafter). This paper applies the wavelet method to approximate the risk-neutral MGF of the under- lying asset from option prices. Monte Carlo simulation experiments are performed to elaborate how the risk-neutral MGF can be obtained using the wavelet method. The Black-Scholes model is chosen as the benchmark model. We offer a novel method for obtaining the implied risk-neutral MGF for pricing out-of-sample options and other complex or illiquid derivative claims on the underlying asset using information obtained from simulated data.