Option Prices and Costly Short-Selling

Abstract

We provide an analysis of option prices with costly short-selling. Short-sellers incur a shorting fee to borrow stock shares from investors who do not necessarily lend all their long positions (partial lending). We incorporate costly short-selling and options market-making into the classic Black-Scholes framework and obtain unique option bid and ask prices in closed-form. Option prices represent market-makers' expected cost of hedging, and are in terms of and preserve the well-known properties of the Black-Scholes prices. Consistently with empirical evidence, we show that bid-ask spreads of typical options and apparent put-call parity violations are increasing in the shorting fee. We also find that option bid-ask spreads are decreasing in the partial lending, and the effects of costly short-selling on option bid-ask spreads are more pronounced for relatively illiquid options with lower trading activity. We then apply our model to the recent 2008 short-selling ban period and obtain implications consistent with the documented behavior of option prices of banned stocks. Finally, our quantitative analysis reveals that the effects of costly short-selling on option prices are economically significant for expensive-to-short stocks and also sheds light on the behavior of option prices and apparent mispricings of the Palm stock in 2000.