Option Prices and Costly Short-Selling

Abstract

Much empirical evidence shows that stock short-selling costs and bans have significant effects on option prices. We reconcile these findings by providing a dynamic analysis of option prices with costly short-selling and option marketmakers. In our framework, short-sellers incur a shorting fee to borrow stock shares from lenders, who only partially lend their long positions. We obtain simple, closed-form, unique option bid and ask prices that represent option marketmakers' expected hedging costs, and are weighted-averages of well-known benchmark prices (Black-Scholes, Heston). Consistent with evidence, we show that bid-ask spreads of typical options, put option implied volatilities, and apparent put-call parity violations are increasing in the shorting fee. Our analysis also uncovers several novel predictions, most notably, option bid-ask spreads are decreasing in the partial lending, the option marketmakers’ participation in the stock lending market is decreasing in the shorting fee for each call option sold, and the effects of short-selling costs on option bid-ask spreads are more pronounced for relatively illiquid options. We also apply our methodology to corporate bonds, which have option-like payoffs.

Keywords: Option prices, short-selling, shorting fee, partial lending, options marketmaking, bid-ask spreads, put-call parity violations, short-selling bans, stochastic volatility

JEL Classification: G12, G13, G23