Recovery of asset information from options prices

ABSTRACT

Past data on an asset is of limited value to market agents seeking information about an asset’s future behaviour. Options, on the other hand, are forward-looking instruments: their payoff is based on the distribution of the underlying asset’s future price at the time of maturity of the option. Current prices of traded options therefore contain information about the market’s view on future asset prices and allow us to find implied risk-neutral probability distributions for such assets. David Shimko developed a method which gives an analytic expression for implied risk-neutral probability density functions, and a procedure for generating lognormal tails for the distribution (Shimko, 1993).

Researchers have noted that the distributions generated by his formula are not quite satisfactory in terms of area under the density function, skewness and kurtosis. In this paper, we prove that the ‘Shimko formula’ (Shimko, 1993, p. 36) contains errors, and we derive the correct formula. This new expression for the density function now gives an area below the curve equal to one, and improved values for the kurtosis and skewness of distributions. We also provide a new way of generating non-lognormal tails for the density function.

Shimko, D. C. (1993). Bounds of probability. Risk (Concord, NH), 6(4), 33–37.