Hard-To-Borrow Stock And Option Pricing

Standard option pricing assumes you can costlessly short the underlying stock to hedge or arbitrage, but for "hard-to-borrow" names — heavily shorted stocks with few shares available to lend — that assumption breaks down. Borrowing the stock to short it can cost an annualized fee of several percent, or the shares may simply be unavailable at any price, which makes the textbook no-arbitrage relationships between calls, puts, and the stock only approximately true.

Put-call parity says a call minus a put at the same strike should equal the stock price minus the present value of the strike (adjusted for dividends). When shorting is expensive, that link weakens: since few traders can cheaply short the stock itself, they turn to synthetic shorts built from options instead — buying a put and selling a call — pushing put prices up and call prices down relative to parity. The gap between actual option-implied prices and textbook parity is, in effect, a market-priced estimate of the stock's borrow cost, and it tends to widen exactly for the stocks where the underlying is hardest to locate.

An option-implied borrow rate can be backed out directly: if parity would predict a call-minus-put spread of $X$ but the market spread is $Y$ lower, that gap annualizes into an implied fee close to what the stock loan desk is actually charging. Options market makers on hard-to-borrow names build this fee into their quotes, and traders who watch the options-implied borrow rate can sometimes spot short-squeeze risk building before it shows up in the stock loan market itself.