Bid-ask spread, strike prices and risk-neutral densities

In empirically deriving risk-neutral densities (RNDs) from option prices, one of the key assumptions that the strike prices should be continuous over the entire spectrum of nonnegative real numbers, is not met due to market trading mechanism. This study looks at how this failure affects the empirical RND. It also tests the possible impact that bid-ask spread has on the empirical RNDs. With Heston (1993) option pricing model of stochastic volatility as a mapping tool between option prices and risk-neutral price distributions and realistic assumptions of option specifications, simulation results show that RNDs are less stable and reliable when there are a limited number of different strike prices, even less so when bid-ask spread is incorporated into option prices.