Hard-to-Borrow Stocks, Synthetic Shorts, and Option Carry
Summary
The document explains how stock borrow scarcity can affect put-call parity and the prices of options. Buying a put and selling a call at the same strike and expiry creates a synthetic short forward, which can provide short exposure without borrowing shares directly. The response says the associated financing cost appears as more negative carry in the option pricing inputs, lowering the synthetic forward's value relative to a readily borrowable stock.
It also describes the reverse-and-conversion trade: a participant who owns shares can sell them and take the opposite synthetic position, effectively lending stock through the options market and capturing the financing benefit. The discussion is conceptual and gives no numerical example, pricing derivation, or empirical evidence. Actual option prices also depend on market supply and demand and other pricing inputs, so the account should be read as an explanation of the carry mechanism rather than a complete pricing model.
Key ideas
- A long put combined with a short call at the same strike and expiry replicates a short forward.
- Hard-to-borrow conditions can appear in option prices through higher negative carry.
- Put-call parity links the synthetic forward price to the financing economics of the underlying.
- Reverse-and-conversion trades can let stock holders capture borrow-related carry through options.
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Full text
# How does a stock becoming hard to borrow affect puts and calls?
# How does a stock becoming hard to borrow affect puts and calls?
Here is my understanding from what I’ve gathered, but I want to confirm if this is correct (and/or if there’s something I’m missing).
If a stock becomes hard to borrow, one can create a synthetic short forward position by selling calls and buying puts at the same strike and expiry. This allows a trader to replicate the exposure of a short position without paying the borrow cost. This means that call prices go down due to selling pressure, and put prices go up. This implies the forward price due to PCP goes down due to the hard to borrow nature of the stock.
I haven’t been able to find many resources that say this explicitly, so I’m looking to verify my current understanding.
## Answer by AlRacoon (score 6, accepted)
https://quant.stackexchange.com/a/77950
As you described, buying a put and selling a call in the hard to borrow stock, you have created a synthetic short future.
Like other equity finance positions, the "difficulty to borrow the stock" will manifest itself in a higher negative carry that must be paid to the "stock lender" to lend the stock. The difficulty in borrowing the stock is manifested in the price of the options through the interest rate input in the options pricing formula.
There are players in the reversal and conversion market ("rev-con"), where participants that own the stock will lend it, by selling the stock and buying the "cheap" synthetic future (sell put, buy call at the same strike and expiry). This is the "cheap" synthetic future that you as the borrower are selling through your long put-short call. The lender effectively earns the carry by being able to buy the stock back cheaper in the future, thereby earning the higher interest rate or carry of hard to borrow stocks.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.