Trading in derivatives when the underlying is scarce

Regulatory restrictions and market frictions can constrain the aggregate quantity of long and short positions in a security. When these constraints bind, we refer to the security as scarce, and its price becomes distorted relative to its value in a frictionless market. We show that an otherwise redundant derivative can reduce the price distortion of the underlying security by relaxing its scarcity. We also show that it is especially important to analyze the underlying and derivative markets jointly when evaluating the impact of regulation, such as short-sales bans and position limits in derivatives, that restricts trade.