Statistical options: Crash resistant financial contracts based on robust estimation

We propose a class of European-type options, which is named here as statistical options, utilizing robust location estimators from the statistics literature. The main motivating objective is to protect the buyer of a call option against a sudden drop in the security price or a put option against a sharp upward move. The vast literature on the asymptotics for the location estimator can be called upon to accurately approximate the prices of these options, when the price formulae are not obtainable in closed form. The statistician's eternal quest for robust estimators which are highly efficient under normality finds here another reason. A notion of limit loss option emerges as a special case, possessing practical appeal. The pricing of the options is carried out under the popular Black-Scholes model. A theory based on the jump diffusion processes ascertains that these robust options manage to nullify the effect of jump arrivals (or that of just the negative ones) in a limiting sense. Finally, a notion of ratio hedging is proposed for the statistical options.